EJERCICIO_DINAMICA_ND_ok.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/E1N1K0/APPZE1N1K0/blob/main/EJERCICIO_DINAMICA_ND_ok.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**TAREA SMGdl**\n",
        "\n",
        "---\n",
        "\n"
      ],
      "metadata": {
        "id": "zd03nuusWgV0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**DATOS INICIALES**"
      ],
      "metadata": {
        "id": "PhZeZaIzWlQC"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "6el54sv14mJ-"
      },
      "outputs": [],
      "source": [
        "# IMPORTAR LIBRERIAS\n",
        "from sympy import *\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# DEFINICION DE SIMBOLOS\n",
        "init_printing()\n",
        "\n",
        "EI = symbols(\"EI\")              #EI: Rigidez a la flexión.\n",
        "L = symbols(\"L\")                #L: Longitud.\n",
        "rho = symbols(\"rho\")            #rho: Densidad.\n",
        "omega = symbols(\"omega\")        #omega: Frecuencia natural.\n",
        "lambd = symbols(\"lambda\")       #omega^2.\n",
        "u1,u2,u3 = symbols(\"u1,u2,u3\")  #u1, u2, u3: Desplazamientos.\n",
        "psi = symbols(\"psi\")            #psi: Función de forma.\n",
        "t = symbols(\"t\")                #t: Tiempo."
      ],
      "metadata": {
        "id": "iI0f_UY-WNSF"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# CIFRAS PERSONALIZADAS\n",
        "\"\"\"Para determinar los ejercicios a desarrollar\"\"\"\n",
        "C1 = 1\n",
        "C2 = 0.89\n",
        "C3 = 0.9\n",
        "C4 = 1.1\n",
        "\n",
        "estructuras = [f\"Se evaluará la estructura numero {num}.\" for num in [\n",
        "                1 if C1 % 2 == 0 else 2,\n",
        "                3 if C2 % 2 == 0 else 4,\n",
        "                5 if C3 % 2 == 0 else 6\n",
        "                                        ]]\n",
        "\n",
        "for estructura in estructuras:\n",
        "    print(estructura)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "y-9FOcVfXX47",
        "outputId": "1e4838bd-ae6d-4763-d64f-e9dc1d752c11"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Se evaluará la estructura numero 2.\n",
            "Se evaluará la estructura numero 4.\n",
            "Se evaluará la estructura numero 6.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**SOLUCION DEL EJERCICIO**"
      ],
      "metadata": {
        "id": "0NtrzK2ZXml8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**DATOS DE ENTRADA PARA RESOLVER EL EJERCICIO**"
      ],
      "metadata": {
        "id": "YFCNeCM_YzFG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Definir la matriz de masa sin condensar y rigidez sin condensar,\n",
        "#para el ejercicio que se desea resolver.\n",
        "\n",
        "Ej = \"1\"   #<==== Definir el ejercicio a desarrollar.\n",
        "\n",
        "if Ej == \"1\":\n",
        "    M=Matrix([[rho*L/2,0,0],[0,0,0],[0,0,0]])\n",
        "    K=Matrix([[12*EI/L**3, -6*EI/L**2, -6*EI/L**2],[-6*EI/L**2, 4*EI/L**1,2*EI/L**1],[-6*EI/L**2,2*EI/L**1, 12*EI/L**1]])\n",
        "\n",
        "elif Ej == \"2\":\n",
        "    M=Matrix([[rho*L/2,0,0],[0,0,0],[0,0,0]])\n",
        "    K=Matrix([[12*EI/L**3, -6*EI/L**2, 0],[-6*EI/L**2, 12*EI/L**1,4*EI/L**1],[0,4*EI/L**1, 8*EI/L**1]])\n",
        "\n",
        "elif Ej == \"3\":\n",
        "    M=Matrix([[rho*L/2,0,0,0],[0,rho*L,0,0],[0,0,0,0],[0,0,0,0]])\n",
        "    K=Matrix([[12*EI/(L**3), -12*EI/(L**3), -6*EI/(L**2), 0], [-12*EI/(L**3), 36*EI/(L**3), -6*EI/(L**2), -12*EI/(L**2)], [-6*EI/(L**2), -6*EI/(L**2), 12*EI/(L**1), 4*EI/(L**1)], [0, -12*EI/(L**2), 4*EI/(L**1), 8*EI/(L**1)]])\n",
        "\n",
        "elif Ej == \"4\":\n",
        "    M=Matrix([[rho*L/2,0,0,0],[0,rho*L/2,0,0],[0,0,0,0],[0,0,0,0]])\n",
        "    K=Matrix([[24*EI/(L**3), 0, -12*EI/(L**2), 0], [0, 12*EI/(L**3), 6*EI/(L**2), 6*EI/(L**2)], [-12*EI/(L**2), 6*EI/(L**2), 12*EI/(L**1), 2*EI/(L**1)], [0, 6*EI/(L**2), 2*EI/(L**1), 4*EI/(L**1)]])\n",
        "\n",
        "elif Ej == \"5\":\n",
        "    M=Matrix([[3*rho*L,0,0],[0,2*rho*L,0],[0,0,0],[0,0,0]])\n",
        "    K=Matrix([[96*EI/L**3, -24*EI/L**3, 18*EI/L**2],[-24*EI/L**3, 24*EI/L**3, 0],[18*EI/L**2,0, 12*EI/L**1]])\n",
        "\n",
        "elif Ej == \"6\":\n",
        "    M=Matrix([[5*rho*L/2,0,0],[0,rho*L/2,0],[0,0,0],[0,0,0]])\n",
        "    K=Matrix([[48*EI/L**3, -12*EI/L**3, 6*EI/L**2],[-12*EI/L**3, 12*EI/L**3, 0],[6*EI/L**2,0, 4*EI/L**1]])\n",
        "\n",
        "elif Ej == \"3x3\":\n",
        "    M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
        "    K = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
        "\n",
        "elif Ej == \"4x4\":\n",
        "    M = Matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]])\n",
        "    K = Matrix([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]])\n",
        "\n",
        "elif Ej == \"libro\":\n",
        "    M=Matrix([[rho*L/4,0,0,0],[0,rho*L/2,0,0],[0,0,0,0],[0,0,0,0]])\n",
        "    K = 4*EI/L**3*Matrix([[24, -24, -6*L, -6*L],[-24, 48, 6*L, 0],[-6*L, 6*L, 2*L**2, L**2],[-6*L, 0, L**2, 4*L**2]])\n",
        "\n",
        "else:\n",
        "    M = None\n",
        "    K = None"
      ],
      "metadata": {
        "id": "bbV0WInNXwNB"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 79
        },
        "id": "w9sf3BuZ4mKG",
        "outputId": "4bd7dfa8-1477-4c10-b2fa-efdaa5d4166c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡L⋅ρ      ⎤\n",
              "⎢───  0  0⎥\n",
              "⎢ 2       ⎥\n",
              "⎢         ⎥\n",
              "⎢ 0   0  0⎥\n",
              "⎢         ⎥\n",
              "⎣ 0   0  0⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{L \\rho}{2} & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "#Matriz de masas sin condensar\n",
        "M"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 80
        },
        "id": "EdT5Gl7-4mKD",
        "outputId": "cffc89c1-e286-4a6f-cc05-2b148719980b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡12⋅EI   -6⋅EI   -6⋅EI ⎤\n",
              "⎢─────   ──────  ──────⎥\n",
              "⎢   3       2       2  ⎥\n",
              "⎢  L       L       L   ⎥\n",
              "⎢                      ⎥\n",
              "⎢-6⋅EI    4⋅EI    2⋅EI ⎥\n",
              "⎢──────   ────    ──── ⎥\n",
              "⎢   2      L       L   ⎥\n",
              "⎢  L                   ⎥\n",
              "⎢                      ⎥\n",
              "⎢-6⋅EI    2⋅EI   12⋅EI ⎥\n",
              "⎢──────   ────   ───── ⎥\n",
              "⎢   2      L       L   ⎥\n",
              "⎣  L                   ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{12 EI}{L^{3}} & - \\frac{6 EI}{L^{2}} & - \\frac{6 EI}{L^{2}}\\\\- \\frac{6 EI}{L^{2}} & \\frac{4 EI}{L} & \\frac{2 EI}{L}\\\\- \\frac{6 EI}{L^{2}} & \\frac{2 EI}{L} & \\frac{12 EI}{L}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 6
        }
      ],
      "source": [
        "#Matriz de Rigidez sin condensar\n",
        "K"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**DESARROLLO:**"
      ],
      "metadata": {
        "id": "LCwsW0c_Y-aa"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Para automatizar el proceso, definir aceleraciones, u¨:\n",
        "#segun criterio: Si no tiene masa la aceleracion es 0.\n",
        "a = b = 1 if np.count_nonzero(M) == 1 else 2\n",
        "print(f'Se reducirá a una matriz de {a,b}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "z6-79euQZE5q",
        "outputId": "a999f182-939a-49ea-812b-0e6b8432d817"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Se reducirá a una matriz de (1, 1)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "6jKpsWq14mKH",
        "outputId": "bfa9d338-394a-4fb5-f09d-02ce78f6534e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡12⋅EI⎤\n",
              "⎢─────⎥\n",
              "⎢   3 ⎥\n",
              "⎣  L  ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{12 EI}{L^{3}}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "#Submatriz de rigidez asociada a los gdl de desplazamiento\n",
        "#Acceder a la submatriz en la esquina superior izquierda\n",
        "Ktt= K[:a, :b]\n",
        "Ktt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 59
        },
        "id": "55E_cNzJ4mKI",
        "outputId": "e7bfd6f9-191f-4eaf-bb2d-fbd4160cec6f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡-6⋅EI ⎤\n",
              "⎢──────⎥\n",
              "⎢   2  ⎥\n",
              "⎢  L   ⎥\n",
              "⎢      ⎥\n",
              "⎢-6⋅EI ⎥\n",
              "⎢──────⎥\n",
              "⎢   2  ⎥\n",
              "⎣  L   ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}- \\frac{6 EI}{L^{2}}\\\\- \\frac{6 EI}{L^{2}}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "#Submatriz de rigidez asociada a los gdl de de desplazamiento y giro\n",
        "#Acceder a la submatriz en la esquina inferior izquierda\n",
        "Kot = K[a:, :b]\n",
        "Kot"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 59
        },
        "id": "ayRrUwHK4mKI",
        "outputId": "d0fed8a6-ab76-4f9d-e248-e7d404cd9b78"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡4⋅EI  2⋅EI ⎤\n",
              "⎢────  ──── ⎥\n",
              "⎢ L     L   ⎥\n",
              "⎢           ⎥\n",
              "⎢2⋅EI  12⋅EI⎥\n",
              "⎢────  ─────⎥\n",
              "⎣ L      L  ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{4 EI}{L} & \\frac{2 EI}{L}\\\\\\frac{2 EI}{L} & \\frac{12 EI}{L}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 10
        }
      ],
      "source": [
        "#Submatriz de rigidez asociada a los gdl de giro\n",
        "# Acceder a la submatriz en la esquina inferior derecha\n",
        "Koo = K[(a):, (b):]\n",
        "Koo"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "t92sC78R4mKJ",
        "outputId": "5d17cb04-21f5-440c-969f-92e0b2bc0125"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡24⋅EI⎤\n",
              "⎢─────⎥\n",
              "⎢    3⎥\n",
              "⎣11⋅L ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{24 EI}{11 L^{3}}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "#Matriz de rigidez condensada\n",
        "Kcond = Ktt - Kot.transpose()*Koo.inv()*Kot\n",
        "Kcond"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "id": "WhbAJlaq4mKK",
        "outputId": "2e2bb24d-0fa9-4c41-d620-ba9fc20fa1cd"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡L⋅ρ⎤\n",
              "⎢───⎥\n",
              "⎣ 2 ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{L \\rho}{2}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "#Matriz de Masa condensada, Mcond=Mtt\n",
        "#Submatriz de masa asociada a los gdl de traslación\n",
        "#Acceder a la submatriz en la esquina superior izquierda\n",
        "Mcond = M[:a, :b]\n",
        "Mcond"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "id": "90pUVAKl4mKL",
        "outputId": "008ef1ee-fb74-45cc-9e22-a2e6a85bc2a2"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡15⋅u₁⎤\n",
              "⎢─────⎥\n",
              "⎢ 11⋅L⎥\n",
              "⎢     ⎥\n",
              "⎢3⋅u₁ ⎥\n",
              "⎢──── ⎥\n",
              "⎣11⋅L ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{15 u_{1}}{11 L}\\\\\\frac{3 u_{1}}{11 L}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "#Obtención de giros, en función de los desplazamientos\n",
        "#Definir un vector que contiene los desplazamientos\n",
        "#Segun el tamaño de la martiz M (a).\n",
        "if a == 1:  #Solo u1.\n",
        "    u = Matrix([[u1]])\n",
        "\n",
        "else:  #u1 y u2.\n",
        "    u = Matrix([[u1],[u2]])\n",
        "\n",
        "u3 = -Koo.inv()*Kot*u\n",
        "u3"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "_EjuZsnw4mKM",
        "outputId": "8e246135-ff0c-4f0e-b415-547b166543c8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "24⋅EI   L⋅λ⋅ρ\n",
              "───── - ─────\n",
              "    3     2  \n",
              "11⋅L         "
            ],
            "text/latex": "$\\displaystyle \\frac{24 EI}{11 L^{3}} - \\frac{L \\lambda \\rho}{2}$"
          },
          "metadata": {},
          "execution_count": 14
        }
      ],
      "source": [
        "#Polinomio característico de det[(Kcond-w^2*M)]=0\n",
        "Pol = det(Kcond-lambd*Mcond)\n",
        "simplify(Pol)  #Con N() se muestra el resultado con decimales."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "id": "IbG1XsKb4mKM",
        "outputId": "6fd75a6a-ebc1-4385-9291-761faba2f10f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡ 48⋅EI ⎤\n",
              "⎢───────⎥\n",
              "⎢    4  ⎥\n",
              "⎣11⋅L ⋅ρ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[ \\frac{48 EI}{11 L^{4} \\rho}\\right]$"
          },
          "metadata": {},
          "execution_count": 15
        }
      ],
      "source": [
        "#Resolución del polinomio característico de det[(Kcond-w^2*M)]=0\n",
        "#La solución son las frecuencias al cuadrado w^2 (lambd)\n",
        "freqs=solve(Pol,lambd)\n",
        "freqs"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 55
        },
        "id": "0QZFKhP04mKM",
        "outputId": "09601012-1211-49c1-bf86-efe229e95a1d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              " 48⋅EI \n",
              "───────\n",
              "    4  \n",
              "11⋅L ⋅ρ"
            ],
            "text/latex": "$\\displaystyle \\frac{48 EI}{11 L^{4} \\rho}$"
          },
          "metadata": {},
          "execution_count": 16
        }
      ],
      "source": [
        "#Primera frecuencia al cuadrado\n",
        "freq1=simplify(freqs[0])\n",
        "freq1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "Mpxhj1ED4mKN",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "55a73e20-b98f-4b0f-cd27-475ca74f114e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ],
            "text/latex": "$\\displaystyle \\text{False}$"
          },
          "metadata": {},
          "execution_count": 17
        }
      ],
      "source": [
        "#Segunda frecuencia al cuadrado\n",
        "if a != 1: #cuando se cumpla que a sea diferente de 1, se imprimirán los resultados\n",
        "    freq2=simplify(freqs[1])\n",
        "    freq2\n",
        "else:\n",
        "    freq2 = false\n",
        "simplify(freq2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 47
        },
        "id": "2H5m8T4F4mKN",
        "outputId": "2d979400-d383-45fd-8399-7981a105106e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡ 48⋅EI ⎤\n",
              "⎢───────⎥\n",
              "⎢    4  ⎥\n",
              "⎣11⋅L ⋅ρ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{48 EI}{11 L^{4} \\rho}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 18
        }
      ],
      "source": [
        "#Método alternativo de sacar las frecuencias de los modos, resolver det[(Kcond*M^(-1)-w^2*I)]=0\n",
        "#Esta transformación permite calcular las frecuencias como un problema de valores propios.\n",
        "#Maux es la matriz (Kcond*M^(-1)-w^2*I)\n",
        "Maux = Mcond.inv()*Kcond\n",
        "Maux"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "id": "KlS4jGly4mKN",
        "outputId": "0d9fa9b6-cb9a-45d1-cb72-e8e6bebd137a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎧ 48⋅EI    ⎫\n",
              "⎪───────: 1⎪\n",
              "⎨    4     ⎬\n",
              "⎪11⋅L ⋅ρ   ⎪\n",
              "⎩          ⎭"
            ],
            "text/latex": "$\\displaystyle \\left\\{ \\frac{48 EI}{11 L^{4} \\rho} : 1\\right\\}$"
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "#De esta manera, el cálculo de fecuencias (valores propios), es más sencillo con el comando eigenvals()\n",
        "#El resultado es un vector, donde en cada componente el primer valor es la frecuencia al cuadrado.\n",
        "#El segundo (después de los :) es el número de veces que se repite\n",
        "freqss=Maux.eigenvals()\n",
        "freqss"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "id": "ZPiT5FHs4mKN",
        "outputId": "6f7b3d9e-8a35-412b-8a97-4aed32dbe521"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡⎛ 48⋅EI           ⎞⎤\n",
              "⎢⎜───────, 1, [[1]]⎟⎥\n",
              "⎢⎜    4            ⎟⎥\n",
              "⎣⎝11⋅L ⋅ρ          ⎠⎦"
            ],
            "text/latex": "$\\displaystyle \\left[ \\left( \\frac{48 EI}{11 L^{4} \\rho}, \\  1, \\  \\left[ \\left[\\begin{matrix}1\\end{matrix}\\right]\\right]\\right)\\right]$"
          },
          "metadata": {},
          "execution_count": 20
        }
      ],
      "source": [
        "#De la mimsa manera, el cálculo de modos (valores propios), es más sencillo con el comando eigenvects()\n",
        "#El resultado es un vector, donde en cada componente el primer valor es la frecuencia al cuadrado.\n",
        "#El segundo es el número de veces que se repite\n",
        "#El tercero es el vector propio\n",
        "Modes = Maux.eigenvects()\n",
        "Modes"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "ranb_JZJ4mKO",
        "outputId": "61fdb16d-96f9-449b-e66b-a6f3e5ed4082"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[1]"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}1\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 21
        }
      ],
      "source": [
        "#Guardamos el primer vector propio (asociado a la primera frecuencia) en la variable V1\n",
        "V1 = Modes[0][2][0]\n",
        "V1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "rkCDNRYA4mKO",
        "outputId": "77e429e1-7f9a-4f3a-86d4-07870358abc2"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[1]"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}1\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 22
        }
      ],
      "source": [
        "#Como V1 no está normalizado a la primera componente, multiplicamos V1 por la inversa de la primera componente\n",
        "V1 = V1*1.0/V1[0]\n",
        "simplify(V1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "id": "ETLZ4kx44mKO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "outputId": "64cf7f0a-f949-4aeb-99de-10ae9105eecc"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡ 15 ⎤\n",
              "⎢────⎥\n",
              "⎢11⋅L⎥\n",
              "⎢    ⎥\n",
              "⎢ 3  ⎥\n",
              "⎢────⎥\n",
              "⎣11⋅L⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{15}{11 L}\\\\\\frac{3}{11 L}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 23
        }
      ],
      "source": [
        "#Para obtener las componentes del vector de modos de vibración asociadas al giro,\n",
        "#se utiliza la expresión de los giros u3, donde insertamos los valores de la primera y segunda componetes del vector\n",
        "#Modo 1\n",
        "#Segun el tamaño de la martiz M (a).\n",
        "if a == 1:  #Solo u1.\n",
        "    s=u3.subs([(u1,V1[0])])\n",
        "else:  #u1 y u2.\n",
        "    s=u3.subs([(u1,V1[0]),(u2,V1[1])])\n",
        "simplify(s)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "u_nhi5AJ4mKP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "6529ff23-45e9-4566-e5b2-5385cef7ed5c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ],
            "text/latex": "$\\displaystyle \\text{False}$"
          },
          "metadata": {},
          "execution_count": 24
        }
      ],
      "source": [
        "#Guardamos el segundo vector propio (asociado a la segunda frecuencia) en la variable V2 (sera falso si la matriz es de 1x1)\n",
        "if a != 1:  #Solo u1.\n",
        "    V2 = Modes[1][2][0]\n",
        "else:\n",
        "    V2 = false\n",
        "V2"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "id": "lr3QJkdg4mKP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "da970402-5cf6-451a-b582-c61bafa58196"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ],
            "text/latex": "$\\displaystyle \\text{False}$"
          },
          "metadata": {},
          "execution_count": 25
        }
      ],
      "source": [
        "#Como V2 no está normalizado a la primera componente, multiplicamos V2 por la inversa de la primera componente\n",
        "if a != 1:\n",
        "    V2 = V2*1.0/V2[0]\n",
        "else:\n",
        "    V2 = false\n",
        "simplify(V2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "id": "hfqGDJwF4mKP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "824b3c59-19dd-495c-8b5d-161929e2b8d2"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ],
            "text/latex": "$\\displaystyle \\text{False}$"
          },
          "metadata": {},
          "execution_count": 26
        }
      ],
      "source": [
        "#Para obtener las componentes del vector de modos de vibración asociadas al giro,\n",
        "#se utiliza la expresión de los giros u3, donde insertamos los valores de la primera y segunda componetes del vector\n",
        "#modo 2\n",
        "if a != 1:\n",
        "    mvg = simplify(u3.subs([(u1,V2[0]),(u2,V2[1])]))\n",
        "else:\n",
        "    mvg = false\n",
        "\n",
        "mvg"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "id": "914roPt84mKP"
      },
      "outputs": [],
      "source": [
        "#Masa modal del modo 1\n",
        "M1 = V1.transpose()*Mcond*V1\n",
        "M1 = M1[0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "faEuYM2R4mKP",
        "outputId": "74eeb1cd-b8b1-4d63-fda0-462e1eac4d7b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "L⋅ρ\n",
              "───\n",
              " 2 "
            ],
            "text/latex": "$\\displaystyle \\frac{L \\rho}{2}$"
          },
          "metadata": {},
          "execution_count": 28
        }
      ],
      "source": [
        "simplify(M1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "id": "WmADF2Bs4mKQ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "1ba40b75-6c46-40c5-9a54-d0a3572e676b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ],
            "text/latex": "$\\displaystyle \\text{False}$"
          },
          "metadata": {},
          "execution_count": 29
        }
      ],
      "source": [
        "#Masa modal del modo 2\n",
        "if a != 1:\n",
        "    M2 = V2.transpose()*Mcond*V2\n",
        "    M2 = M2[0]\n",
        "else:\n",
        "    M2 = false\n",
        "simplify(M2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "id": "AvD4LupF4mKQ"
      },
      "outputs": [],
      "source": [
        "#Rigidez modal asociada al modo 1\n",
        "K1 = V1.transpose()*Kcond*V1\n",
        "K1 = K1[0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "N5hBn64R4mKQ",
        "outputId": "c8e6968e-1a23-4868-f285-e4726d76af8b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "24⋅EI\n",
              "─────\n",
              "    3\n",
              "11⋅L "
            ],
            "text/latex": "$\\displaystyle \\frac{24 EI}{11 L^{3}}$"
          },
          "metadata": {},
          "execution_count": 31
        }
      ],
      "source": [
        "simplify(K1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "id": "EtmMOVLG4mKQ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "344ae161-4e49-4b90-b99b-10612c72c997"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ],
            "text/latex": "$\\displaystyle \\text{False}$"
          },
          "metadata": {},
          "execution_count": 32
        }
      ],
      "source": [
        "#Rigidez modal asociada al modo 2\n",
        "if a != 1:\n",
        "    K2 = V2.transpose()*Kcond*V2\n",
        "    K2 = K2[0]\n",
        "else:\n",
        "    K2 = false\n",
        "simplify(K2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "id": "6qAYDwVV4mKR"
      },
      "outputs": [],
      "source": [
        "#Comprobación de que los modos son ortogonales con respecto a la matriz de rigidez\n",
        "if a == 1:  #Solo u1.\n",
        "    pass\n",
        "else:\n",
        "    simplify(V1.transpose()*Kcond*V2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "id": "K12adHBu4mKR"
      },
      "outputs": [],
      "source": [
        "#Comprobación de que los modos son ortogonales con respecto a la matriz de masas\n",
        "if a != 1:\n",
        "    simplify(V1.transpose()*Mcond*V2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "MxUK3OMH4mKR"
      },
      "outputs": [],
      "source": [
        "#Problema de vibraciones libres, condiciones iniciales\n",
        "if a == 1:  #Solo u1.\n",
        "    Uo = Matrix([[1]]) #Desplazamientos iniciales\n",
        "    Vo = Matrix([[0]]) #Velocidades iniciales\n",
        "else:\n",
        "    Uo = Matrix([[1],[0]]) #Desplazamientos iniciales\n",
        "    Vo = Matrix([[0],[0]]) #Velocidades iniciales"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "ZXqaof4q4mKS",
        "outputId": "662ddf74-1f54-4cfe-830b-8e76584d6f8a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[1]"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}1\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 36
        }
      ],
      "source": [
        "#Condicion inicial de desplazamiento asociada al modo 1\n",
        "q1o = V1.transpose()*Mcond*Uo/M1\n",
        "simplify(q1o)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
      "metadata": {
        "id": "8p8cY6Z84mKS",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "021d12a7-86da-47d0-aceb-a6dca67088db"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ],
            "text/latex": "$\\displaystyle \\text{False}$"
          },
          "metadata": {},
          "execution_count": 37
        }
      ],
      "source": [
        "#Condicion inicial de desplazamiento asociada al modo 2\n",
        "if a != 1:\n",
        "    q2o=V2.transpose()*Mcond*Uo/M2\n",
        "else:\n",
        "    q2o=false\n",
        "simplify(q2o)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "_s6cjp2e4mKS",
        "outputId": "5d264a6e-c4e4-4f16-c5ab-12f2b41b17d4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0]"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}0\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 38
        }
      ],
      "source": [
        "#Condicion inicial de velocidad asociada al modo 1\n",
        "qv1o=V1.transpose()*Mcond*Vo/M1\n",
        "simplify(qv1o)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "id": "R6--R9uc4mKS",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "e0a12584-5d64-4a60-ee72-5ecd8ed440b4"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ],
            "text/latex": "$\\displaystyle \\text{False}$"
          },
          "metadata": {},
          "execution_count": 39
        }
      ],
      "source": [
        "#Condicion inicial de velocidad asociada al modo 2\n",
        "if a != 1:\n",
        "    qv2o=V2.transpose()*Mcond*Vo/M2\n",
        "else:\n",
        "    qv2o=false\n",
        "simplify(qv2o)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 82
        },
        "id": "4noHmeHP4mKS",
        "outputId": "8f7be60a-e70c-4413-cc39-a0d8c50c3570"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡                                                                             \n",
              "⎢                                                                             \n",
              "⎢⎛     ⎛             ______    ________⎞                  ⎛             ______\n",
              "⎢⎜     ⎜            ╱  EI     ╱      2 ⎟                  ⎜            ╱  EI  \n",
              "⎢⎜     ⎜4⋅√33⋅t⋅   ╱  ──── ⋅╲╱  1 - ψ  ⎟                  ⎜4⋅√33⋅t⋅   ╱  ──── \n",
              "⎢⎜     ⎜          ╱    4               ⎟      ________    ⎜          ╱    4   \n",
              "⎢⎜     ⎜        ╲╱    L ⋅ρ             ⎟     ╱      2     ⎜        ╲╱    L ⋅ρ \n",
              "⎢⎜ψ⋅sin⎜───────────────────────────────⎟ + ╲╱  1 - ψ  ⋅cos⎜───────────────────\n",
              "⎢⎝     ⎝               11              ⎠                  ⎝               11  \n",
              "⎢─────────────────────────────────────────────────────────────────────────────\n",
              "⎢                                                       ________              \n",
              "⎢                                                      ╱      2               \n",
              "⎣                                                    ╲╱  1 - ψ                \n",
              "\n",
              "                                ______ ⎤\n",
              "                               ╱  EI   ⎥\n",
              "    ________⎞⎞  -4⋅√33⋅ψ⋅t⋅   ╱  ────  ⎥\n",
              "   ╱      2 ⎟⎟               ╱    4    ⎥\n",
              "⋅╲╱  1 - ψ  ⎟⎟             ╲╱    L ⋅ρ  ⎥\n",
              "            ⎟⎟  ───────────────────────⎥\n",
              "            ⎟⎟             11          ⎥\n",
              "────────────⎟⎟⋅ℯ                       ⎥\n",
              "            ⎠⎠                         ⎥\n",
              "───────────────────────────────────────⎥\n",
              "                                       ⎥\n",
              "                                       ⎥\n",
              "                                       ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{\\left(\\psi \\sin{\\left(\\frac{4 \\sqrt{33} t \\sqrt{\\frac{EI}{L^{4} \\rho}} \\sqrt{1 - \\psi^{2}}}{11} \\right)} + \\sqrt{1 - \\psi^{2}} \\cos{\\left(\\frac{4 \\sqrt{33} t \\sqrt{\\frac{EI}{L^{4} \\rho}} \\sqrt{1 - \\psi^{2}}}{11} \\right)}\\right) e^{- \\frac{4 \\sqrt{33} \\psi t \\sqrt{\\frac{EI}{L^{4} \\rho}}}{11}}}{\\sqrt{1 - \\psi^{2}}}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 40
        }
      ],
      "source": [
        "#Frecuencia del modo 1, es la raiz cuadrada de w1^2, también se calcula la frecuencia amortiguada\n",
        "omega1  = sqrt(freq1)\n",
        "omega1d = omega1*sqrt(1-psi**2)\n",
        "\n",
        "#Respuesta del primer modo\n",
        "q1 = exp(-psi*omega1*t)*(q1o*cos(omega1d*t)+(psi*q1o*omega1+qv1o)/omega1d*sin(omega1d*t))\n",
        "simplify(q1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "id": "ezhhVVYa4mKX"
      },
      "outputs": [],
      "source": [
        "#Frecuencia del modo 2, es la raiz cuadrada de w1^2, también se calcula la frecuencia amortiguada\n",
        "if a == 1:  #Solo u1.\n",
        "    pass\n",
        "else:\n",
        "    omega2=sqrt(freq2)\n",
        "    omega2d = omega2*sqrt(1-psi**2)\n",
        "    #Respuesta del segundo modo\n",
        "    q2=exp(-psi*omega2*t)*(q2o*cos(omega2d*t)+(psi*q2o*omega2+qv2o)/omega2d*sin(omega2d*t))\n",
        "    simplify(q2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "id": "q3Wlc5ui4mKY",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 82
        },
        "outputId": "dc208e46-a44a-4f88-d165-4f658b766448"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡                                                                             \n",
              "⎢                                                                             \n",
              "⎢⎛     ⎛             ______    ________⎞                  ⎛             ______\n",
              "⎢⎜     ⎜            ╱  EI     ╱      2 ⎟                  ⎜            ╱  EI  \n",
              "⎢⎜     ⎜4⋅√33⋅t⋅   ╱  ──── ⋅╲╱  1 - ψ  ⎟                  ⎜4⋅√33⋅t⋅   ╱  ──── \n",
              "⎢⎜     ⎜          ╱    4               ⎟      ________    ⎜          ╱    4   \n",
              "⎢⎜     ⎜        ╲╱    L ⋅ρ             ⎟     ╱      2     ⎜        ╲╱    L ⋅ρ \n",
              "⎢⎜ψ⋅sin⎜───────────────────────────────⎟ + ╲╱  1 - ψ  ⋅cos⎜───────────────────\n",
              "⎢⎝     ⎝               11              ⎠                  ⎝               11  \n",
              "⎢─────────────────────────────────────────────────────────────────────────────\n",
              "⎢                                                       ________              \n",
              "⎢                                                      ╱      2               \n",
              "⎣                                                    ╲╱  1 - ψ                \n",
              "\n",
              "                                ______ ⎤\n",
              "                               ╱  EI   ⎥\n",
              "    ________⎞⎞  -4⋅√33⋅ψ⋅t⋅   ╱  ────  ⎥\n",
              "   ╱      2 ⎟⎟               ╱    4    ⎥\n",
              "⋅╲╱  1 - ψ  ⎟⎟             ╲╱    L ⋅ρ  ⎥\n",
              "            ⎟⎟  ───────────────────────⎥\n",
              "            ⎟⎟             11          ⎥\n",
              "────────────⎟⎟⋅ℯ                       ⎥\n",
              "            ⎠⎠                         ⎥\n",
              "───────────────────────────────────────⎥\n",
              "                                       ⎥\n",
              "                                       ⎥\n",
              "                                       ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{\\left(\\psi \\sin{\\left(\\frac{4 \\sqrt{33} t \\sqrt{\\frac{EI}{L^{4} \\rho}} \\sqrt{1 - \\psi^{2}}}{11} \\right)} + \\sqrt{1 - \\psi^{2}} \\cos{\\left(\\frac{4 \\sqrt{33} t \\sqrt{\\frac{EI}{L^{4} \\rho}} \\sqrt{1 - \\psi^{2}}}{11} \\right)}\\right) e^{- \\frac{4 \\sqrt{33} \\psi t \\sqrt{\\frac{EI}{L^{4} \\rho}}}{11}}}{\\sqrt{1 - \\psi^{2}}}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 42
        }
      ],
      "source": [
        "#Respuesta total, suma de las respuestas de los modos (ver principio de descomposicón modal)\n",
        "if a == 1:  #Solo u1.\n",
        "    u = V1*q1\n",
        "else:\n",
        "    u = V1*q1 + V2*q2\n",
        "simplify(u)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67
        },
        "id": "4UVArGIV4mKY",
        "outputId": "6731f817-3e58-4c73-c6fc-a54ef74d19ff"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡                                                                             \n",
              "⎣(0.100503781525921⋅sin(0.361813613493316⋅√33⋅t) + cos(0.361813613493316⋅√33⋅t\n",
              "\n",
              "    -0.0363636363636364⋅√33⋅t⎤\n",
              "))⋅ℯ                         ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\left(0.100503781525921 \\sin{\\left(0.361813613493316 \\sqrt{33} t \\right)} + \\cos{\\left(0.361813613493316 \\sqrt{33} t \\right)}\\right) e^{- 0.0363636363636364 \\sqrt{33} t}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 43
        }
      ],
      "source": [
        "#Metemos los valores de parámetros en la fórmula\n",
        "N(simplify(u.subs({EI:1,psi:0.1,L:1,rho:1})))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67
        },
        "id": "NqLSdPNF4mKY",
        "outputId": "01566daf-e488-4eee-db67-54b0835fe9f7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡                                                                             \n",
              "⎣(0.100503781525921⋅sin(0.361813613493316⋅√33⋅t) + cos(0.361813613493316⋅√33⋅t\n",
              "\n",
              "    -0.0363636363636364⋅√33⋅t⎤\n",
              "))⋅ℯ                         ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\left(0.100503781525921 \\sin{\\left(0.361813613493316 \\sqrt{33} t \\right)} + \\cos{\\left(0.361813613493316 \\sqrt{33} t \\right)}\\right) e^{- 0.0363636363636364 \\sqrt{33} t}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 44
        }
      ],
      "source": [
        "#Evaluamos numéricamente la fórmula\n",
        "N(u.subs({EI:1,psi:0.1,L:1,rho:1}))"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**GRAFICA DE LA SOLUCION**"
      ],
      "metadata": {
        "id": "oKrR9HJLNTYS"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {
        "id": "1_6FUou54mKY"
      },
      "outputs": [],
      "source": [
        "#Importar librerias para generar la gráfica de la solución\n",
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "bZKYI8Qy4mKZ"
      },
      "outputs": [],
      "source": [
        "#Grafica de la solución del primer gdl\n",
        "#de t=0 a t=50s, cada 0.1s\n",
        "t_vec  = np.arange(0, 50, 0.1)\n",
        "if a == 1:  #Solo u1.\n",
        "    u_vec1 = np.array([N(u[0].subs({EI:1,psi:0.1,L:1,rho:1,t:tt})) for tt in t_vec])\n",
        "    u_vec2 = false\n",
        "else:\n",
        "    u_vec1 = np.array([N(u[0].subs({EI:1,psi:0.1,L:1,rho:1,t:tt})) for tt in t_vec])\n",
        "    u_vec2 = np.array([N(u[1].subs({EI:1,psi:0.1,L:1,rho:1,t:tt})) for tt in t_vec])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "id": "joF7zkwi4mKZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "28b78fb5-d07b-4064-be34-117eb9b3028b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
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              "       0.000912396234201789, 0.000956234882943536, 0.000957561146016506,\n",
              "       0.000918058067365815, 0.000841078428021216, 0.000731433655058758,\n",
              "       0.000595129255594120, 0.000439060229699492, 0.000270681069816317,\n",
              "       9.76654386876863e-5, -7.24295601886121e-5, -0.000232480411395580,\n",
              "       -0.000376082781125708, -0.000497794800466012,\n",
              "       -0.000593329410146581, -0.000659689660586887,\n",
              "       -0.000695243540016330, -0.000699737618708149,\n",
              "       -0.000674251431843649, -0.000621096968338401,\n",
              "       -0.000543669791769597, -0.000446260112119795,\n",
              "       -0.000333833492050523, -0.000211791768210649, -8.57251776393685e-5,\n",
              "       3.88333958598939e-5, 0.000156641677386355, 0.000262959337497180,\n",
              "       0.000353729307357763, 0.000425722580100411, 0.000476641826497949,\n",
              "       0.000505181098000869, 0.000511040871664955, 0.000494899623640875,\n",
              "       0.000458344920451045, 0.000403768618788507, 0.000334232105067641,\n",
              "       0.000253308539036641, 0.000164909760014383, 7.31058540411589e-5,\n",
              "       -1.80546345261935e-5, -0.000104716217555801, -0.000183372738899334,\n",
              "       -0.000251002380339488, -0.000305176519190956,\n",
              "       -0.000344138872093612, -0.000366852770707830,\n",
              "       -0.000373015860184863, -0.000363042927511833,\n",
              "       -0.000338018894998206, -0.000299625201326075,\n",
              "       -0.000250043793948152, -0.000191843737147222,\n",
              "       -0.000127855975568232, -6.10420707227652e-5, 5.63725343030693e-6,\n",
              "       6.93481503955090e-5, 0.000127499131034901, 0.000177841498150150,\n",
              "       0.000218551074648818, 0.000248288510556555, 0.000266236477378525,\n",
              "       0.000272113111713839, 0.000266162107495707, 0.000249120834241753,\n",
              "       0.000222168738040322, 0.000186859029262853, 0.000145037249763447,\n",
              "       9.87507240189299e-5, 5.01531229907176e-5, 1.40840456784773e-6,\n",
              "       -4.54017534710792e-5, -8.83632291743907e-5, -0.000125804107929245,\n",
              "       -0.000156355965662803, -0.000178999721162030,\n",
              "       -0.000193094736418628, -0.000198390611298292,\n",
              "       -0.000195021878403694, -0.000183486523724503,\n",
              "       -0.000164609909528152, -0.000139496233044776,\n",
              "       -0.000109470097952571, -7.60110912429232e-5, -4.06844375327001e-5,\n",
              "       -5.07084421936961e-6, 2.93014420633395e-5, 6.10195649845828e-5,\n",
              "       8.88414995339656e-5, 0.000111741950131110, 0.000128947141860242,\n",
              "       0.000139957477812359, 0.000144557594229109, 0.000142813900934015,\n",
              "       0.000135060223861177, 0.000121872647892013, 0.000104035073148880,\n",
              "       8.24973314210392e-5, 5.83279506423388e-5, 3.26637978044348e-5,\n",
              "       6.65887234975037e-6, -1.85655347044370e-5, -4.19672494589118e-5,\n",
              "       -6.26243558953270e-5, -7.97695323969981e-5, -9.28164003181537e-5,\n",
              "       -0.000101377089471717, -0.000105270631943859,\n",
              "       -0.000104522202094057, -9.93536096583608e-5, -9.01658086855516e-5,\n",
              "       -7.75144938100903e-5, -6.20801058784924e-5, -4.46337529137153e-5,\n",
              "       -2.60006647142909e-5, -7.02283819085902e-6, 1.14775028022249e-5,\n",
              "       2.87321105064535e-5, 4.40572183591793e-5, 5.68792004914701e-5,\n",
              "       6.67544912576191e-5, 7.33831514462915e-5, 7.66157634587122e-5,\n",
              "       7.64536348068330e-5, 7.30425750758358e-5, 6.66607743022704e-5,\n",
              "       5.77015402912382e-5, 4.66518403174895e-5, 3.40677326282722e-5,\n",
              "       2.05478611918405e-5, 6.70622159190898e-6, -6.85461242022481e-6,\n",
              "       -1.95686804923633e-5, -3.09292373715254e-5, -4.05079082790619e-5,\n",
              "       -4.79697232990034e-5, -5.30835592043589e-5, -5.57277320034832e-5,\n",
              "       -5.58907004860097e-5, -5.36670508576414e-5, -4.92491265350478e-5,\n",
              "       -4.29148377138052e-5, -3.50123261207775e-5, -2.59422666391067e-5,\n",
              "       -1.61386561361011e-5, -6.04896944880910e-6, 3.88544657604083e-6,\n",
              "       1.32479158632535e-5, 2.16631666219266e-5, 2.88116170712724e-5,\n",
              "       3.44407052200585e-5, 3.83729012038061e-5, 4.05101967395803e-5,\n",
              "       4.08350246765348e-5, 3.94077155588311e-5, 3.63607412044288e-5,\n",
              "       3.18901218895936e-5, 2.62444790996365e-5, 1.97122963425729e-5,\n",
              "       1.26080038108330e-5, 5.25752756264691e-6, -2.01605951828211e-6,\n",
              "       -8.90617813547941e-6, -1.51351225213691e-5, -2.04647043184741e-5,\n",
              "       -2.47047781961208e-5, -2.77193728380314e-5, -2.94302642130672e-5,\n",
              "       -2.98179436278370e-5], dtype=object)"
            ]
          },
          "metadata": {},
          "execution_count": 47
        }
      ],
      "source": [
        "u_vec1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "id": "515Xmoid4mKZ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "outputId": "31f4e0f1-2da4-463e-f7f4-5207fd249312"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "if a == 1:  #Solo u1.\n",
        "    plt.plot(t_vec, u_vec1);\n",
        "    plt.show()\n",
        "else:\n",
        "    plt.plot(t_vec, u_vec1);\n",
        "    plt.plot(t_vec, u_vec2);\n",
        "    plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {
        "id": "Xgp3K0xK4mKZ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 161
        },
        "outputId": "b8c33334-d006-4f1c-f19b-bad0fe471bc2"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡                      ⎛     ⎛             ______    ________⎞                \n",
              "⎢                      ⎜     ⎜            ╱  EI     ╱      2 ⎟                \n",
              "⎢                      ⎜     ⎜4⋅√33⋅t⋅   ╱  ──── ⋅╲╱  1 - ψ  ⎟      ⎛         \n",
              "⎢                      ⎜     ⎜          ╱    4               ⎟      ⎜         \n",
              "⎢                      ⎜     ⎜        ╲╱    L ⋅ρ             ⎟      ⎜4⋅√33⋅t⋅ \n",
              "⎢               ______ ⎜ψ⋅sin⎜───────────────────────────────⎟      ⎜         \n",
              "⎢              ╱  EI   ⎜     ⎝               11              ⎠      ⎜        ╲\n",
              "⎢  4⋅√33⋅ψ⋅   ╱  ──── ⋅⎜────────────────────────────────────── + cos⎜─────────\n",
              "⎢            ╱    4    ⎜                ________                    ⎝         \n",
              "⎢          ╲╱    L ⋅ρ  ⎜               ╱      2                               \n",
              "⎢                      ⎝             ╲╱  1 - ψ                                \n",
              "⎢- ───────────────────────────────────────────────────────────────────────────\n",
              "⎣                                                               11            \n",
              "\n",
              "                       ⎞                  ______                              \n",
              "                       ⎟                 ╱  EI                                \n",
              "    ______    ________⎞⎟  -4⋅√33⋅ψ⋅t⋅   ╱  ────                               \n",
              "   ╱  EI     ╱      2 ⎟⎟               ╱    4       ⎛                       ⎛ \n",
              "  ╱  ──── ⋅╲╱  1 - ψ  ⎟⎟             ╲╱    L ⋅ρ     ⎜                       ⎜ \n",
              " ╱    4               ⎟⎟  ───────────────────────   ⎜                       ⎜4\n",
              "╱    L ⋅ρ             ⎟⎟             11             ⎜             ______    ⎜ \n",
              "──────────────────────⎟⎟⋅ℯ                          ⎜            ╱  EI      ⎜ \n",
              "      11              ⎠⎟                            ⎜4⋅√33⋅ψ⋅   ╱  ──── ⋅cos⎜─\n",
              "                       ⎟                            ⎜          ╱    4       ⎝ \n",
              "                       ⎠                            ⎜        ╲╱    L ⋅ρ       \n",
              "───────────────────────────────────────────────── + ⎜─────────────────────────\n",
              "                                                    ⎝                         \n",
              "\n",
              "                                                                              \n",
              "                                                                              \n",
              "                                                                              \n",
              "            ______    ________⎞                                    ⎛          \n",
              "           ╱  EI     ╱      2 ⎟                                    ⎜          \n",
              "⋅√33⋅t⋅   ╱  ──── ⋅╲╱  1 - ψ  ⎟                                    ⎜4⋅√33⋅t⋅  \n",
              "         ╱    4               ⎟              ______    ________    ⎜          \n",
              "       ╲╱    L ⋅ρ             ⎟             ╱  EI     ╱      2     ⎜        ╲╱\n",
              "──────────────────────────────⎟   4⋅√33⋅   ╱  ──── ⋅╲╱  1 - ψ  ⋅sin⎜──────────\n",
              "              11              ⎠           ╱    4                   ⎝          \n",
              "                                        ╲╱    L ⋅ρ                            \n",
              "─────────────────────────────── - ────────────────────────────────────────────\n",
              "  11                                                              11          \n",
              "\n",
              "                                                ⎤\n",
              "                                                ⎥\n",
              "                                                ⎥\n",
              "   ______    ________⎞⎞                         ⎥\n",
              "  ╱  EI     ╱      2 ⎟⎟                  ______ ⎥\n",
              " ╱  ──── ⋅╲╱  1 - ψ  ⎟⎟                 ╱  EI   ⎥\n",
              "╱    4               ⎟⎟  -4⋅√33⋅ψ⋅t⋅   ╱  ────  ⎥\n",
              "    L ⋅ρ             ⎟⎟               ╱    4    ⎥\n",
              "─────────────────────⎟⎟             ╲╱    L ⋅ρ  ⎥\n",
              "     11              ⎠⎟  ───────────────────────⎥\n",
              "                      ⎟             11          ⎥\n",
              "──────────────────────⎟⋅ℯ                       ⎥\n",
              "                      ⎠                         ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}- \\frac{4 \\sqrt{33} \\psi \\sqrt{\\frac{EI}{L^{4} \\rho}} \\left(\\frac{\\psi \\sin{\\left(\\frac{4 \\sqrt{33} t \\sqrt{\\frac{EI}{L^{4} \\rho}} \\sqrt{1 - \\psi^{2}}}{11} \\right)}}{\\sqrt{1 - \\psi^{2}}} + \\cos{\\left(\\frac{4 \\sqrt{33} t \\sqrt{\\frac{EI}{L^{4} \\rho}} \\sqrt{1 - \\psi^{2}}}{11} \\right)}\\right) e^{- \\frac{4 \\sqrt{33} \\psi t \\sqrt{\\frac{EI}{L^{4} \\rho}}}{11}}}{11} + \\left(\\frac{4 \\sqrt{33} \\psi \\sqrt{\\frac{EI}{L^{4} \\rho}} \\cos{\\left(\\frac{4 \\sqrt{33} t \\sqrt{\\frac{EI}{L^{4} \\rho}} \\sqrt{1 - \\psi^{2}}}{11} \\right)}}{11} - \\frac{4 \\sqrt{33} \\sqrt{\\frac{EI}{L^{4} \\rho}} \\sqrt{1 - \\psi^{2}} \\sin{\\left(\\frac{4 \\sqrt{33} t \\sqrt{\\frac{EI}{L^{4} \\rho}} \\sqrt{1 - \\psi^{2}}}{11} \\right)}}{11}\\right) e^{- \\frac{4 \\sqrt{33} \\psi t \\sqrt{\\frac{EI}{L^{4} \\rho}}}{11}}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 49
        }
      ],
      "source": [
        "#Respuesta en velocidad (derivada del desplazamiento con respecto al tiempo)\n",
        "v = diff(u,t)\n",
        "v"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Grafica de la solución del primer gdl\n",
        "#de t=0 a t=50s, cada 0.1s\n",
        "t_vec  = np.arange(0, 5, 0.01)\n",
        "if a == 1:  #Solo u1.\n",
        "    v_vec1 = np.array([N(v[0].subs({EI:1,psi:0.1,L:1,rho:1,t:tt})) for tt in t_vec])\n",
        "    v_vec2 = false\n",
        "else:\n",
        "    v_vec1 = np.array([N(v[0].subs({EI:1,psi:0.1,L:1,rho:1,t:tt})) for tt in t_vec])\n",
        "    v_vec2 = np.array([N(v[1].subs({EI:1,psi:0.1,L:1,rho:1,t:tt})) for tt in t_vec])"
      ],
      "metadata": {
        "id": "0Y-AoAsZrckY"
      },
      "execution_count": 50,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "if a == 1:  #Solo u1.\n",
        "    plt.plot(t_vec, v_vec1);\n",
        "    plt.show()\n",
        "else:\n",
        "    plt.plot(t_vec, v_vec1);\n",
        "    plt.plot(t_vec, v_vec2);\n",
        "    plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "bXMT-8qGrqtE",
        "outputId": "2c2cba60-df2c-4a02-eac5-63ce8b9c8e97"
      },
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {
        "id": "eGqx0p8o4mKa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "outputId": "f61a0a93-ed79-4d24-a32c-35f051ff8cd7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[cos(ω⋅t)]"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\cos{\\left(\\omega t \\right)}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 52
        }
      ],
      "source": [
        "#Respuesta bajo una carga armónica aplicada en el gdl 1\n",
        "if a == 1:  #Solo u1.\n",
        "    p=Matrix([[cos(omega*t)]])\n",
        "else:\n",
        "    p=Matrix([[cos(omega*t)],[0]])\n",
        "p"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {
        "id": "xLtgrsSG4mKb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 39
        },
        "outputId": "4db37312-3fe0-46a3-e2fc-cde3e1093bdb"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "cos(ω⋅t)"
            ],
            "text/latex": "$\\displaystyle \\cos{\\left(\\omega t \\right)}$"
          },
          "metadata": {},
          "execution_count": 53
        }
      ],
      "source": [
        "#Carga asociada al primer modo\n",
        "p1=V1.transpose()*p\n",
        "p1=p1[0]\n",
        "simplify(p1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {
        "id": "Hs7msLHQ4mKb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "4b638807-cc88-4ca9-81e8-dcb88a36ddee"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ],
            "text/latex": "$\\displaystyle \\text{False}$"
          },
          "metadata": {},
          "execution_count": 54
        }
      ],
      "source": [
        "#Carga asociada al segundo modo\n",
        "if a != 1:\n",
        "    p2=V2.transpose()*p\n",
        "    p2=p2[0]\n",
        "else:\n",
        "    p2 = false\n",
        "simplify(p2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {
        "id": "deyLoix74mKb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 84
        },
        "outputId": "00334916-d840-48dd-e33e-efaeab8df81b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      ⎛                              ______                              ⎞\n",
              "    3 ⎜                             ╱  EI   ⎛            4  2  ⎞         ⎟\n",
              "22⋅L ⋅⎜-8⋅√33⋅EI⋅ω⋅ψ⋅cos(ω⋅t) +    ╱  ──── ⋅⎝48⋅EI - 11⋅L ⋅ω ⋅ρ⎠⋅sin(ω⋅t)⎟\n",
              "      ⎜                           ╱    4                                 ⎟\n",
              "      ⎝                         ╲╱    L ⋅ρ                               ⎠\n",
              "──────────────────────────────────────────────────────────────────────────\n",
              "              ______ ⎛                                         2⎞         \n",
              "             ╱  EI   ⎜         4  2  2     ⎛            4  2  ⎞ ⎟         \n",
              "            ╱  ──── ⋅⎝2112⋅EI⋅L ⋅ω ⋅ψ ⋅ρ + ⎝48⋅EI - 11⋅L ⋅ω ⋅ρ⎠ ⎠         \n",
              "           ╱    4                                                         \n",
              "         ╲╱    L ⋅ρ                                                       "
            ],
            "text/latex": "$\\displaystyle \\frac{22 L^{3} \\left(- 8 \\sqrt{33} EI \\omega \\psi \\cos{\\left(\\omega t \\right)} + \\sqrt{\\frac{EI}{L^{4} \\rho}} \\left(48 EI - 11 L^{4} \\omega^{2} \\rho\\right) \\sin{\\left(\\omega t \\right)}\\right)}{\\sqrt{\\frac{EI}{L^{4} \\rho}} \\left(2112 EI L^{4} \\omega^{2} \\psi^{2} \\rho + \\left(48 EI - 11 L^{4} \\omega^{2} \\rho\\right)^{2}\\right)}$"
          },
          "metadata": {},
          "execution_count": 55
        }
      ],
      "source": [
        "#Respuesta del primer modo\n",
        "omega1=sqrt(freq1)\n",
        "omega1d = omega1*sqrt(1-psi**2)\n",
        "beta1=omega/omega1\n",
        "p1a=p1/cos(omega*t)\n",
        "q1=p1a/K1*((1-beta1**2)/((1-beta1**2)**2+(2*psi*beta1)**2)*sin(omega*t)-2*psi*beta1/((1-beta1**2)**2+(2*psi*beta1)**2)*cos(omega*t))\n",
        "q1=simplify(q1)\n",
        "q1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 56,
      "metadata": {
        "id": "2ZvGPFO74mKc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 37
        },
        "outputId": "e94dad87-cf00-4fbb-c9f5-60d73a06c51d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ],
            "text/latex": "$\\displaystyle \\text{False}$"
          },
          "metadata": {},
          "execution_count": 56
        }
      ],
      "source": [
        "if a != 1:\n",
        "    omega2=sqrt(freq2)\n",
        "    omega2d = omega2*sqrt(1-psi**2)\n",
        "    beta2=omega/omega2\n",
        "    p2a=p2/cos(omega*t)\n",
        "    q2=p2a/K2*((1-beta2**2)/((1-beta2**2)**2+(2*psi*beta2)**2)*sin(omega*t)-2*psi*beta2/((1-beta2**2)**2+(2*psi*beta2)**2)*cos(omega*t))\n",
        "else:\n",
        "    q2 = false\n",
        "simplify(q2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {
        "id": "9DKQ6UcL4mKc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 61
        },
        "outputId": "1da16035-39dd-4b6d-8454-964c695b7301"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "⎡      ⎛                              ______                              ⎞⎤\n",
              "⎢    3 ⎜                             ╱  EI   ⎛            4  2  ⎞         ⎟⎥\n",
              "⎢22⋅L ⋅⎜-8⋅√33⋅EI⋅ω⋅ψ⋅cos(ω⋅t) +    ╱  ──── ⋅⎝48⋅EI - 11⋅L ⋅ω ⋅ρ⎠⋅sin(ω⋅t)⎟⎥\n",
              "⎢      ⎜                           ╱    4                                 ⎟⎥\n",
              "⎢      ⎝                         ╲╱    L ⋅ρ                               ⎠⎥\n",
              "⎢──────────────────────────────────────────────────────────────────────────⎥\n",
              "⎢              ______ ⎛                                         2⎞         ⎥\n",
              "⎢             ╱  EI   ⎜         4  2  2     ⎛            4  2  ⎞ ⎟         ⎥\n",
              "⎢            ╱  ──── ⋅⎝2112⋅EI⋅L ⋅ω ⋅ψ ⋅ρ + ⎝48⋅EI - 11⋅L ⋅ω ⋅ρ⎠ ⎠         ⎥\n",
              "⎢           ╱    4                                                         ⎥\n",
              "⎣         ╲╱    L ⋅ρ                                                       ⎦"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}\\frac{22 L^{3} \\left(- 8 \\sqrt{33} EI \\omega \\psi \\cos{\\left(\\omega t \\right)} + \\sqrt{\\frac{EI}{L^{4} \\rho}} \\left(48 EI - 11 L^{4} \\omega^{2} \\rho\\right) \\sin{\\left(\\omega t \\right)}\\right)}{\\sqrt{\\frac{EI}{L^{4} \\rho}} \\left(2112 EI L^{4} \\omega^{2} \\psi^{2} \\rho + \\left(48 EI - 11 L^{4} \\omega^{2} \\rho\\right)^{2}\\right)}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 57
        }
      ],
      "source": [
        "if a != 1:\n",
        "    u = V1*q1+V2*q2\n",
        "else:\n",
        "    u = V1*q1\n",
        "simplify(u)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "metadata": {
        "id": "xI_uA2dU4mKc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "outputId": "f33a645f-fa50-4869-f84f-289cc5e3d6bc"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[-0.0208727146794419⋅sin(10⋅t) - 0.000911822183113062⋅cos(10⋅t)]"
            ],
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}- 0.0208727146794419 \\sin{\\left(10 t \\right)} - 0.000911822183113062 \\cos{\\left(10 t \\right)}\\end{matrix}\\right]$"
          },
          "metadata": {},
          "execution_count": 58
        }
      ],
      "source": [
        "N(u.subs({EI:1,psi:0.1,L:1,rho:1,omega:10}))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 59,
      "metadata": {
        "id": "QPS64L_24mKc"
      },
      "outputs": [],
      "source": [
        "t_vec = np.arange(0, 3, 0.01)\n",
        "if a == 1:  #Solo u1.\n",
        "    u_vec1 = np.array([N(u[0].subs({EI:1,psi:0.1,L:1,rho:1,omega:10,t:tt})) for tt in t_vec])\n",
        "else:\n",
        "    u_vec1 = np.array([N(u[0].subs({EI:1,psi:0.1,L:1,rho:1,omega:10,t:tt})) for tt in t_vec])\n",
        "    u_vec2 = np.array([N(u[1].subs({EI:1,psi:0.1,L:1,rho:1,omega:10,t:tt})) for tt in t_vec])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 60,
      "metadata": {
        "id": "Hl6fZ_E74mKd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "outputId": "1e7dba10-91d4-4bd8-bf2b-20f4037cdede"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "if a == 1:  #Solo u1.\n",
        "    plt.plot(t_vec, u_vec1);\n",
        "    plt.show()\n",
        "else:\n",
        "    plt.plot(t_vec, u_vec1);\n",
        "    plt.plot(t_vec, u_vec2);\n",
        "    plt.show()"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.10"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}