{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Universidade Federal do Rio Grande do Sul (UFRGS)   \n",
    "Programa de Pós-Graduação em Engenharia Civil (PPGEC)   \n",
    "\n",
    "# PEC00025: Introduction to Vibration Theory\n",
    "\n",
    "\n",
    "## Test P2 (2023/1): Discrete and continuous mdof systems\n",
    "\n",
    "---\n",
    "\n",
    "**NAME:** <br/>\n",
    "**CARD:** \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing Python modules required for this notebook\n",
    "# (this cell must be executed with \"shift+enter\" before any other Python cell)\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pickle as pk\n",
    "import scipy.linalg as sc\n",
    "\n",
    "from MRPy import *\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vibration_modes(K, M):\n",
    "\n",
    "# Uses scipy to solve the standard eigenvalue problem\n",
    "    w2, Phi = sc.eig(K, M)\n",
    "\n",
    "# Ensure ascending order of eigenvalues\n",
    "    iw  = w2.argsort()\n",
    "    w2  = w2[iw]\n",
    "    Phi = Phi[:,iw]\n",
    "\n",
    "# Eigenvalues to vibration frequencies\n",
    "    wk  = np.sqrt(np.real(w2)) \n",
    "    fk  = wk/2/np.pi\n",
    "\n",
    "    return fk, wk, Phi\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 1\n",
    "\n",
    "O sistema estrutural abaixo, com 2 g.d.l., representa um pórtico plano dotado de um amortecedor de massa sintonizada. Calcule os coeficientes de rigidez $k_1$ e $k_2$, e as respectivas formas modais, correspondentes às frequências naturais dadas. \n",
    "\n",
    "<img src=\"resources/tests/PEC00025A_231_P2_Q1.png\" alt=\"Question 1\" width=\"540px\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solução\n",
    "\n",
    "As matrizes de massa e de rigidez são:\n",
    "\n",
    "$$ \\mathbf{K} =  \\left[ \\begin{array}{cc}\n",
    "                  k_1 + k_2 &  -k_2  \\\\\n",
    "                      - k_2 &   k_2\n",
    "                 \\end{array} \\right] $$\n",
    "                 \n",
    "$$ \\mathbf{M} =  \\left[ \\begin{array}{cc}\n",
    "                        M_1 &    0   \\\\\n",
    "                         0  &   M_2\n",
    "                 \\end{array} \\right] $$\n",
    "\n",
    "Lembrando agora o problema de autovalores e autovetores:\n",
    "\n",
    "$$ \\mathbf{K} \\, \\vec{\\varphi}_i = \\omega_i^2 \\, \\mathbf{M} \\, \\vec{\\varphi}_i  $$ \n",
    "\n",
    "Considerando que as formas modais são normalizadas pela sua coordenada em $M_1$:\n",
    "\n",
    "$$\\left[ \\begin{array}{cc}\n",
    "   k_1 + k_2 &  -k_2  \\\\\n",
    "       - k_2 &   k_2\n",
    "  \\end{array} \\right] \\cdot\n",
    "  \\left[ \\begin{array}{c}\n",
    "       1      \\\\\n",
    "   \\varphi_i\n",
    "  \\end{array} \\right] = \\omega_i^2\n",
    "  \\left[ \\begin{array}{cc}\n",
    "   M_1 &    0   \\\\\n",
    "    0  &   M_2\n",
    "  \\end{array} \\right] \\cdot\n",
    "  \\left[ \\begin{array}{c}\n",
    "       1      \\\\\n",
    "   \\varphi_i\n",
    "  \\end{array} \\right] $$\n",
    "\n",
    "Isso resulta em um par de equações:\n",
    "\n",
    "$$\\begin{align*}\n",
    "(k_1 + k_2) - k_2 \\varphi_i &= \\omega_i^2 M_1 \\\\\n",
    "      -k_2  + k_2 \\varphi_i &= \\omega_i^2 M_2 \\varphi_i \n",
    "\\end{align*}$$\n",
    "\n",
    "para $i = 1$ e $i = 2$. Portanto, tem-se um sistema com 4 equações para 4 incógnitas\n",
    "($k_1$, $k_2$, $\\varphi_1$, $\\varphi_2$). A dificuldade está na não-linearidade. \n",
    "\n",
    "Somando-se as duas equações:\n",
    "\n",
    "$$ k_1 = \\omega_i^2 (M_1 + M_2\\varphi_i) $$\n",
    "\n",
    "Isolando-se $k_2$ na primeira equação:\n",
    "\n",
    "$$ k_2 = \\frac{\\omega_i^2 M_1 - k_1}{1 - \\varphi_i} $$\n",
    "\n",
    "Inicialmente vamos atribuir um valor inicial às rigidezes para se obter as formas modais e então tentar iterar.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Frequência no primeiro modo:           0.89 Hz\n",
      "Frequência no segundo modo:            1.12 Hz\n",
      "\n",
      "Rigidez das colunas inferiores (k1): 394784 N/m\n",
      "Rigidez do TMD (k2):                  19739 N/m\n",
      "\n",
      "Coordenada do primeiro modo em M2:     5.00\n",
      "Coordenada do segundo modo em M2:     -4.00\n"
     ]
    }
   ],
   "source": [
    "M1   =  10000.\n",
    "M2   =  500.\n",
    "\n",
    "w1_2 = (2*np.pi*1.00)**2\n",
    "w2_2 = (2*np.pi*1.00)**2\n",
    "\n",
    "k1   =  w1_2*M1\n",
    "k2   =  w2_2*M2\n",
    "\n",
    "KG  = np.array([[ k1+k2,  -k2 ],[-k2,  k2]])\n",
    "MG  = np.array([[   M1,    0  ],[ 0,   M2]])\n",
    "\n",
    "fk, wk, Phi = vibration_modes(KG, MG)\n",
    "\n",
    "ph1 = Phi[:,0]/Phi[0,0]    # normalizando pela coordenada da massa M1\n",
    "ph2 = Phi[:,1]/Phi[0,1]\n",
    "\n",
    "print('Frequência no primeiro modo:         {0:6.2f} Hz'.format(fk[0])) \n",
    "print('Frequência no segundo modo:          {0:6.2f} Hz\\n'.format(fk[1])) \n",
    "\n",
    "print('Rigidez das colunas inferiores (k1): {0:6.0f} N/m'.format(k1)) \n",
    "print('Rigidez do TMD (k2):                 {0:6.0f} N/m\\n'.format(k2)) \n",
    "\n",
    "print('Coordenada do primeiro modo em M2:   {0:6.2f}'.format(ph1[1])) \n",
    "print('Coordenada do segundo modo em M2:    {0:6.2f}'.format(ph2[1])) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Após algumas tentativas, percebe-se que a única maneira de se obter as frequências dadas é \n",
    "reduzindo a massa $M_2$ para 100kg (1% da massa $M_1$), ou aumentando-se a massa $M_1$ para 50 ton (mesma relação).\n",
    "As rigidezes são calculadas usando-se a média das duas frequências alvo, que é 1Hz.\n",
    "\n",
    "Portanto, adota-se as frequências 0.89 e 1.12Hz obtidas acima, correspondentes às rigidezes propostas. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 2\n",
    "\n",
    "Para a estrutura do problema anterior, calcule as máximas amplitudes de deslocamento de cada massa para uma carga dinâmica harmônica aplicada na massa $M_1$.\n",
    "\n",
    "$$F(t) = F_0 \\sin(2\\pi f_0 t)$$\n",
    "\n",
    "onde $F_0 = 1$kN e $f_0 = 1$Hz. \n",
    "\n",
    "#### Método 1: solução numérica por Duhamel\n",
    "\n",
    "Inicialmente construímos o vetor de cargas NODAIS, sendo uma força harmônica na massa $M_1$ e zero na massa $M_2$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simulação das forças NODAIS\n",
    "\n",
    "Td  = 128\n",
    "N   = 2**16\n",
    "F0  = 1000.\n",
    "f0  = 1.00\n",
    "\n",
    "t   = np.linspace(0, Td, N)\n",
    "F1  = F0*np.sin(2*np.pi*f0*t)\n",
    "F2  = np.zeros_like(F1)\n",
    "\n",
    "FG  = MRPy(np.vstack((F1, F2)), Td=Td)\n",
    "FG.plot_time(fig=1, figsize=(12,6), axis_t=[0, FG.Td, -2000, 2000]);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cálculo dos parâmetros modais, usando a matriz $\\Phi$ original (fornecida pelo algoritmo de\n",
    "autovalores do Python, com a escala que tiver). Abaixo também são calculadas as forças modais.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "zk = np.array([0.01, 0.01])\n",
    "Mk = np.diag(np.dot(Phi.T, np.dot(MG, Phi)))\n",
    "Kk = Mk*(wk**2)\n",
    "Fk = MRPy(np.dot(Phi.T, FG), fs=FG.fs)\n",
    "\n",
    "Fk.plot_time(fig=2, figsize=(12,6), axis_t=[0, FG.Td, -500, 500]);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cálculo dos deslocamentos por superposição MODAL e retorno aos valores NODAIS:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Deslocamento modal de pico do primeiro modo: 28.7mm\n",
      "Deslocamento modal de pico do segundo modo:  23.1mm\n",
      "\n",
      "Deslocamento de pico da massa M1:             1.1mm\n",
      "Deslocamento de pico da massa M2:            50.5mm\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ak  = MRPy(np.dot(np.diag(1/Mk), Fk), fs=Fk.fs)   # divide force by modal mass\n",
    "uk  = ak.sdof_Duhamel(fk, zk)                     # modal space solution\n",
    "uG  = 1000*MRPy(np.dot(Phi, uk), fs=uk.fs)        # back to nodal solution\n",
    "uG  = uG.extract(segm=(2/3, 1), by='fraction')    # avoid transiente start\n",
    "\n",
    "uG.plot_time(4, figsize=(12,6), axis_t=[0, uG.Td, -60, 60]);\n",
    "\n",
    "f       = uG.f_axis()\n",
    "Su, fs  = uG.periodogram()\n",
    "\n",
    "plt.figure(5, figsize=(12,4))\n",
    "plt.semilogy(f, Su[0], 'b', f, Su[1], 'g')\n",
    "plt.axis([0, 5, 1e-4, 1e5])\n",
    "plt.legend(('Massa M1', 'Massa M1'))\n",
    "plt.grid(True)\n",
    "\n",
    "\n",
    "ukp = uk.extract(segm=(3/4, 1), by='fraction').max(axis=1)\n",
    "up  = uG.max(axis=1)\n",
    "\n",
    "print('Deslocamento modal de pico do primeiro modo: {0:4.1f}mm'.format(1000*ukp[0]))\n",
    "print('Deslocamento modal de pico do segundo modo:  {0:4.1f}mm\\n'.format(1000*ukp[1]))\n",
    "\n",
    "print('Deslocamento de pico da massa M1:            {0:4.1f}mm'.format(up[0]))\n",
    "print('Deslocamento de pico da massa M2:            {0:4.1f}mm'.format(up[1]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observa-se que a frequência da carga está situada bem entre as duas frequências naturais, de modo que se evita um\n",
    "forte pico de ressonância.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Método 2: pela função de admitância\n",
    "\n",
    "As propriedades modais já foram calculadas no método anterior. \n",
    "Agora calcula-se a amplitude das forças modais:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Amplitude da força modal no primeiro modo: 196.1 N\n",
      "Amplitude da força modal no segundo modo:  242.5 N\n"
     ]
    }
   ],
   "source": [
    "FG  = np.array([[F0, 0]]).T     # amplitudes das forças nodais (vetor coluna)\n",
    "Fk  = np.dot(Phi.T, FG)\n",
    "\n",
    "Fk1 = Fk[0,0]\n",
    "Fk2 = Fk[1,0]\n",
    "\n",
    "print('Amplitude da força modal no primeiro modo: {0:4.1f} N'.format(Fk1))\n",
    "print('Amplitude da força modal no segundo modo:  {0:4.1f} N'.format(Fk2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A amplitude dos deslocamentos modais é calculada usando-se a função de ganho, $A(\\beta, \\zeta)$, \n",
    "na frequência da excitação $f_0$ (1Hz):\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Amplificação dinâmica no primeiro modo:  3.98\n",
      "Deslocamento modal no primeiro modo:    28.59 mm\n",
      "\n",
      "Amplificação dinâmica no segundo modo:   4.98\n",
      "Deslocamento modal no segundo modo:     23.12mm\n"
     ]
    }
   ],
   "source": [
    "Aw  =  lambda f: np.sqrt(1/( (1 - (f/fn)**2)**2 + (2*zt*(f/fn))**2 ))\n",
    "\n",
    "fn  =  fk[0]\n",
    "zt  =  zk[0]\n",
    "A1  =  Aw(f0)\n",
    "u1  =  1000*A1*Fk1/Kk[0]\n",
    "\n",
    "fn  =  fk[1]\n",
    "zt  =  zk[1]\n",
    "A2  =  Aw(f0)\n",
    "u2  =  1000*A2*Fk2/Kk[1]\n",
    "\n",
    "print('Amplificação dinâmica no primeiro modo: {0:5.2f}'.format(A1))\n",
    "print('Deslocamento modal no primeiro modo:    {0:5.2f} mm\\n'.format(u1))\n",
    "\n",
    "print('Amplificação dinâmica no segundo modo:  {0:5.2f}'.format(A2))\n",
    "print('Deslocamento modal no segundo modo:     {0:5.2f}mm'.format(u2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observa-se que os deslocamentos MODAIS coincidem com os valores obtidos por simulação.\n",
    "Finalmente os deslocamentos MODAIS são superpostos (ignorando-se a fase) para se calcular os deslocamentos NODAIS.\n",
    "Como a informação de fase é perdida, é feita uma combinação quadrática das amplitudes, que traz alguma imprecisão.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Deslocamento de pico da massa M1:  7.9mm\n",
      "Deslocamento de pico da massa M2: 35.9mm\n"
     ]
    }
   ],
   "source": [
    "uG = np.sqrt((Phi[:,0]*u1)**2 + (Phi[:,1]*u2)**2)        # Combinação quadrática de amplitudes\n",
    "\n",
    "print('Deslocamento de pico da massa M1: {0:4.1f}mm'.format(uG[0]))\n",
    "print('Deslocamento de pico da massa M2: {0:4.1f}mm'.format(uG[1]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observa-se que os resultados diferem dos obtidos por simulação, onde a fase é levada em conta.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 3\n",
    "\n",
    "Para a viga com as restrições de apoio dadas, proponha uma forma aproximada para o primeiro modo de vibração, $\\varphi(x)$, e calcule a respectiva frequência natural em função do comprimento, $L$, da massa por unidade de comprimento, $\\mu$, e da rigidez à flexão, $EI$.\n",
    "\n",
    "<img src=\"resources/tests/PEC00025A_231_P2_Q3.png\" alt=\"Question 3\" width=\"480px\"/>  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solução:\n",
    "\n",
    "Vamos usar como modo de vibração a função de interpolação para uma rotação do nó B. Logo:\n",
    "\n",
    "$$ \\phi(\\xi) = \\xi^3 - \\xi^2 $$\n",
    "\n",
    "onde $\\xi = x/L$. A escala da função acima não é importante. A curvatura é a segunda derivada dessa função:\n",
    "\n",
    "$$ \\phi^{\\prime \\prime}(\\xi) = \\left( 6\\xi - 2 \\right)/L^2 $$\n",
    "\n",
    "Logo a energia cinética de referência é:\n",
    "\n",
    "$$ 2T_{\\rm ref} = \\int_0^1{\\mu \\phi^2(\\xi) \\; Ld\\xi} = \\frac{\\mu L}{105}$$\n",
    "\n",
    "e a energia potencial elástica é:\n",
    "\n",
    "$$ 2V = \\int_0^1{EI \\left[ \\phi^{\\prime \\prime}(\\xi)\\right] ^2 \\; Ld\\xi} = \\frac{4EI}{L^3} $$\n",
    "\n",
    "Portanto, pelo quociente de Rayleigh temos:\n",
    "\n",
    "$$ f_{\\rm n} = \\frac{1}{2\\pi} \\sqrt{\\frac{V}{T_{\\rm ref}}} = \n",
    "               \\frac{1}{2\\pi} \\sqrt{\\frac{420EI}{\\mu L^4}} = \n",
    "               \\frac{1}{2\\pi} \\left( \\frac{4.5270}{L} \\right)^2 \\sqrt{\\frac{EI}{\\mu}}$$\n",
    "\n",
    "Na tabela abaixo o resultado exato é encontrado como sendo 3.93 ao invés de 4.53 com a função aproximada.\n",
    "Lembrando que o quociente de Rayleigh sempre dá uma frequência _acima_ do valor correto.\n",
    "\n",
    "<img src=\"images/beams.png\" alt=\"Beam solutions\" width=\"540px\"/>\n",
    "\n",
    "O gráfico abaixo é só para conferir a forma modal aproximada escolhida.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "phi = lambda xi: L*(xi*xi*xi - xi*xi)\n",
    "\n",
    "L   = 1.\n",
    "x   = np.linspace(0, L, 1024)\n",
    "phx = phi(x)\n",
    "\n",
    "plt.figure(6, figsize=(12,4))\n",
    "plt.plot(x, phx)\n",
    "plt.axis([0, 1, -0.2, 0.1])\n",
    "plt.grid(True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternativamente podemos usar a linha elástica que resulta da aplicação de uma carga distribuída sobre\n",
    "uma viga com as condições de contorno dadas:\n",
    "\n",
    "$$ \\phi(\\xi) = 2\\xi^4 - 5\\xi^3 + 3\\xi^2$$\n",
    "\n",
    "onde $\\xi = x/L$. A escala da função acima é irrelevante. A curvatura é a segunda derivada dessa função:\n",
    "\n",
    "$$ \\phi^{\\prime \\prime}(\\xi) = \\left( 24\\xi^2 - 30\\xi + 6 \\right)/L^2 $$\n",
    "\n",
    "Logo a energia cinética de referência é:\n",
    "\n",
    "$$ 2T_{\\rm ref} = \\int_0^1{\\mu \\phi^2(\\xi) \\; Ld\\xi} = \\frac{19\\mu L}{630}$$\n",
    "\n",
    "e a energia potencial elástica é:\n",
    "\n",
    "$$ 2V = \\int_0^1{EI \\left[ \\phi^{\\prime \\prime}(\\xi)\\right] ^2 \\; Ld\\xi} = \\frac{36EI}{5L^3} $$\n",
    "\n",
    "Portanto, pelo quociente de Rayleigh temos:\n",
    "\n",
    "$$ f_{\\rm n} = \\frac{1}{2\\pi} \\sqrt{\\frac{V}{T_{\\rm ref}}} = \n",
    "               \\frac{1}{2\\pi} \\sqrt{\\frac{22680EI}{95\\mu L^4}} = \n",
    "               \\frac{1}{2\\pi} \\left( \\frac{3.9308}{L} \\right)^2 \\sqrt{\\frac{EI}{\\mu}}$$\n",
    "\n",
    "Observa-se que essa função de interpolação proposta é (quase) exatamente o valor apresentado na tabela. \n",
    "\n",
    "Abaixo está um gráfico para visualização da forma modal proposta.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "phi = lambda xi: -2*xi*xi*xi + 5*xi*xi*xi - 3*xi*xi\n",
    "\n",
    "L   = 1.\n",
    "x   = np.linspace(0, L, 1024)\n",
    "phx = phi(x)\n",
    "\n",
    "plt.figure(6, figsize=(12,4))\n",
    "plt.plot(x, phx)\n",
    "plt.axis([0, 1, -0.6, 0.2])\n",
    "plt.grid(True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 4\n",
    "\n",
    "Para a viga do problema anterior, com os valores dados abaixo, calcule a máxima amplitude de deslocamento para o peso próprio sendo aplicado de forma súbita a partir do tempo $t = 0$, ou seja, como uma função passo unitário, $h(t)$.\n",
    "\n",
    "<img src=\"resources/tests/PEC00025A_231_P2_Q4.png\" alt=\"Question 4\" width=\"540px\"/>  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solução\n",
    "\n",
    "Inicialmente define-se os dados numéricos do problema.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "L  = 6.           # comprimento das barras (m)\n",
    "EI = 48000000.    # rigidez à flexão (Nm2)\n",
    "μ  = 250.         # massa por unidade de comprimento (kg/m)\n",
    "g  = 9.81         # gravidade (m/s2)\n",
    "q  = μ*g          # carga por unidade de comprimento (N/m)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Usando-se a função de interpolação proposta são calculados os valores modais. Primeiro a massa modal:\n",
    "\n",
    "$$ M_k = \\int_0^1{\\mu \\phi^2(\\xi) \\; Ld\\xi} = \\frac{19\\mu L}{630} \\approx 45.2{\\rm kg}$$\n",
    "\n",
    "e em seguida a frequência modal:\n",
    "\n",
    "$$ w_k = \\left( \\frac{3.931}{L} \\right)^2 \\sqrt{\\frac{EI}{\\mu}} \\approx 188.1{\\rm rad/s} \\approx 29.93{\\rm Hz}$$\n",
    "\n",
    "com as quais calculamos a rigidez modal:\n",
    "\n",
    "$$ K_k = \\omega_k^2 M_k \\approx 1600{\\rm kN/m} $$\n",
    "\n",
    "A amplitude da força modal (passo unitário) é calculada a partir da forma modal:\n",
    "\n",
    "$$ F_k = \\int_0^1{\\mu g \\phi(\\xi) \\; Ld\\xi} = \\frac{3}{20} \\mu g L \\approx 2.21{\\rm kN} $$\n",
    "\n",
    "A amplificação dinâmica para uma carga passo unitário é $A = 2$, que deve ser aplicada sobre\n",
    "o deslocamento modal estático:\n",
    "\n",
    "$$ u_{k, {\\rm dyn}} = A u_{k, {\\rm est}} = A \\frac{F_k}{K_k} = 2 \\cdot \\frac{2.21}{1600} = 2.76{\\rm mm}$$\n",
    "\n",
    "A máxima amplitude da forma modal é calculada como sendo $\\phi_{\\rm max} \\approx 0.26$. \n",
    "Portanto a máxima amplitude de deslocamento é dada por:\n",
    "\n",
    "$$ u_{\\max} = \\phi_{\\rm max} u_{k, {\\rm dyn}} \\approx 0.72{\\rm mm} $$.\n"
   ]
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