{
 "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 (2022/1): Discrete and continuous mdof systems\n",
    "\n",
    "---\n",
    "\n",
    "**NAME:** <br/>\n",
    "**CARD:** \n",
    "\n",
    "\n",
    "#### Instruções\n",
    "\n",
    "1. Entregar a resolução da prova em arquivo único, com no máximo 10Mb, até às 24h de hoje, 25 de maio de 2022.\n",
    "2. Recomenda-se verificar atentamente se todas as folhas da resolução foram incluídas no arquivo gerado, pois não serão aceitas entregas posteriores.\n",
    "3. Na primeira folha do arquivo deve constar claramente o NOME e o cartão de MATRÍCULA.\n",
    "4. A consulta ao material de estudo e o uso do computador para cálculos são LIVRES.\n",
    "5. A prova deve ser realizada INDIVIDUALMENTE, sem recorrer ao auxílio de colegas ou outras pessoas! Caso se verifique o descumprimento desta regra, todos os envolvidos na fraude terão a nota da prova zerada.\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 MRPy\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",
    "Um cabo com comportamento elástico linear é disposto horizontalmente.\n",
    "O cabo tem comprimento total $L = 6{\\rm m}$, rigidez axial $EA = 4000{\\rm kN}$ \n",
    "e duas massas $m = 20{\\rm kg}$ fixadas nos terços. \n",
    "O cabo tem uma protensão inicial $T_0 = 20{\\rm kN}$. \n",
    "O amortecimento do sistema é $\\zeta = 0.01$ (razão do crítico).\n",
    "A rigidez à flexão bem como a massa do cabo são desprezáveis.\n",
    "A aceleração da gravidade no local é $g = 9.81{\\rm m/s^2}$.\n",
    "Os dois graus de liberdade considerados são os deslocamentos verticais das\n",
    "duas massas, $u_1(t)$ e $u_2(t)$.\n",
    "\n",
    "<img src=\"resources/tests/PEC00025A_221_P2_Q1.jpg\" alt=\"Question 1\" width=\"680px\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solução\n",
    "\n",
    "Admitindo-se uma condição de pequenos deslocamentos, calcule os modos de vibração e as respectivas frequências naturais de vibração livre do sistema. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "L   = 6.0\n",
    "m   = 20.\n",
    "T0  = 20000. \n",
    "\n",
    "k   = 6*T0/L\n",
    "\n",
    "K1  = np.array([[k,  -k/2],[-k/2,  k]])\n",
    "M1  = np.array([[m,   0  ],[ 0,    m]])\n",
    "\n",
    "fk1, wk1, Phi1 = vibration_modes(K1, M1)\n",
    "\n",
    "f1  = plt.figure(1, figsize=(10,5))\n",
    "x   = np.arange(0, 8, 2)\n",
    "\n",
    "for k in range(2):\n",
    "    qk = np.zeros(4)\n",
    "    qk[1:-1] = Phi1[:,k]\n",
    "    qk /= np.max(np.abs(qk))   # adjust scale for unity amplitude\n",
    "    \n",
    "    plt.subplot(2,1,k+1)\n",
    "    plt.plot(x, qk)\n",
    "    \n",
    "    plt.xlim( 0.0, 6.0);\n",
    "    plt.ylim(-1.5, 1.5);  plt.ylabel(str(k+1));\n",
    "    plt.text(3.5, 0.6, 'fk = {0:4.2f}Hz'.format(fk1[k]), fontsize=14);\n",
    "    plt.grid(True)\n",
    "\n",
    "plt.xlabel('x');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 2\n",
    "\n",
    "No grau de liberdade $u_1(t)$ do problema anterior é aplicada uma carga transiente, \n",
    "$F_1(t)$, dada pela função abaixo, com amplitude $F_0 = 500{\\rm N}$ e duração \n",
    "$T_{\\rm d} = 0.1{\\rm s}$. A variável $\\tau$ representa o tempo adimensionalizado \n",
    "por $T_{\\rm d}$.\n",
    "\n",
    "<img src=\"resources/tests/PEC00025A_221_P2_Q2.jpg\" alt=\"Question 2\" width=\"480px\"/>  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Desconsiderando a parcela estática da resposta (devida ao peso próprio), e considerando todos os modos de vibração, apresente o deslocamento $u_1(t)$ como uma função do tempo.\n",
    "Indique a amplitude e o instante no tempo em que o máximo deslocamento é atingido.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solução\n",
    "\n",
    "#### Método 1: por superposição modal simulando o carregamento"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Simulação das forças NODAIS\n",
    "\n",
    "N   = 8192\n",
    "Td  = 0.1\n",
    "F0  = 500.\n",
    "t   = np.linspace(0, 20*Td, N)\n",
    "τ   = t/Td\n",
    "fs  = N/t[-1]\n",
    "\n",
    "F1  = 4*F0*(τ - τ**2)\n",
    "F1[t > Td] = 0.\n",
    "F1  = MRPy(np.vstack((F1, np.zeros_like(F1))), fs=fs)\n",
    "\n",
    "f2  = F1.plot_time(fig=2, figsize=(10,4), axis_t=[0, F1.Td, -200, 800]);\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Cálculo das forças MODAIS\n",
    "\n",
    "zk1 = np.array([0.01, 0.01])\n",
    "Mk1 = np.diag(np.dot(Phi1.T, np.dot(M1, Phi1)))\n",
    "Kk1 = Mk1*(wk1**2)\n",
    "Fk1 = MRPy(np.dot(Phi1.T, F1), fs=F1.fs)\n",
    "\n",
    "f3  = Fk1.plot_time(fig=3, figsize=(10,5), axis_t=[0, F1.Td, -500, 500])\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Deslocamento de pico da massa 1 é 0.0426m\n",
      "Deslocamento de pico da massa 2 é 0.0378m\n"
     ]
    },
    {
     "data": {
      "image/png": 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RtEGxFFXWYbVq87hS7rQ97yyFlXV8Y0nGpxI9gD4RoXzvykzyyi9w+EyLlyL0X8YYck9f4JW9Rbyyt4icUxe8HZIKADr1Sg/tO1nJpJR4Qh1MCeKsyzISeD/3jAuj8n//2VfM56YN6/H+89IT+CBPE2il3KWoso4d+RXcNndEp9t9ad5ICqqtfFyqg9Gc9XFpFb9ak8WRkipmjxzInFEDOVpWxS/f+phjpzXpUz2nK2j00NpDp/jJirG9OoaIMGFYHAeLzjMpJd41gfmxCw3NiEBsZM/flvPTE/jD+mwuGz3IhZEFnsKKOt46VEpjswVEsFitpA6M4TOTky+qqVGqlcVqeOr9fH7s5LVvxahw/r23mNSrYnr1uQ4Gr+4rpqq+mZ+sGPupeUVTBkRz9cSh/HVbPkXn6lg8ZrAXo1T+Sq/qPbD9+FlmjRrgcKLf7loxIYl1h8tcEJX/e3VfMZ+b2vNaPbANfkmKi6LkfL2LogosFxqaeXhDDpuyT/PF2al898pMvnvFaH5w1RgmDovjt+uydFog1aEXdp3kppnDne5mESLCPYvSeWxznpsj82//2nmSmMgwvjx/pMPvlbDQEO5ZlE7JuXq2aWuQ6oEukz0RiRaRn4rIU/b7GSKy0v2h+SZjDBuPnubKca75dRUWGsKw/n04WVHrkuP5K6vVUFbVQMqA6F4f6+pJQ1l7qNQFUQWWg0XneXhjLrfNHcHt80YS1yf8U8+PGdKPn60cx7ZjZ9geoE3hVqthV34FT23L50/vHuPlPYWcOBvcnz1nVdQ0cqamibFJ/bq136C+kYwfGscH2j/ZoTWHShkYE+HUuum3zBnBR4XnySuv8UBkKpA4U7P3d6ARmGO/Xwz82m0R+bituWdYMHqQS0fQXjt1GK9/VOKy4/mjnfkVzElzzei9gbGRVNY26zyGbWzLPcOO/Ap+tnIcA2MjO9wuJMS2ystHRecDrq/VxqOn+d3bWdQ1W7h+Rgr3Lk5nbloCe05U8us1R9nw8Sl9z3TiH9sLuKMbc1+2tXzCEN7LLtd5+No5UHSeU1UNLJuQ5PQ+9yxK47kdBTS2aFkq5zmT7KUZYx4AmgGMMfVAUM4VYoz5JNlzpdjIMIyB2sbgHbm27dhZLs1wXblOGhbHoeLASlZ6auPR0xRU1PK1BWlO/0i5e0Ear+4roarO/9dxtlgNf3w3FwF+vGIcizITiesTTmiIkDIgmutnpPDjFWOJjQzjl28dJf+M1pq0d7KiloExEcRFh3e9sQMiwpfnj+Af2wtcG5gfq25oZvWBUu6Y370EOiw0hK9eOkqX3VTd4kyy1yQifQADICJp2Gr6gs6Go6e5Ytxgt8yLd+2U5KCt3Ttf10TfqLBejWxub/HYRDZlnXbZ8fzVmkOlVNQ0cuucEd3aLyRE+OaSdJ7Ydtw9gXmIMYYHN+SwfEISl3fS9UJEmJuewI9XjGVTVjn/3HlSa/naeGVvETfM6N3CScP6R2OxGk5XN7goKv/22OY87l2c3qPvk5QB0URHhJJXriN0lXOcSfZ+DqwHUkTkeWATcJ9bo/JBtr4+lcxNc8+KFyMSYoJ2jrjVB0u5ZtJQlx4zMiwUAzS1WF16XH/y6r5imi1WbpzZsy/p+OgIJqfEszmn3MWRec7T75/gqkuGMNqJNZYBwkND+Oplo7hkaD9+tSYrIGo2e6uoso4BMZHdWtGmI7fOSeVZrd1jzaFS5qYldGuZzfa+ODuVf+0s1B8lyildJnvGmI3AZ7Etk/YiMN0Ys8W9Yfmetw6VsnKS8/0qemJ+RgLvB2jH+I4YYyg5V++SgRntzU9P4MPjwVWerV7YVUifiFCundK70c1XXTKE93PP0mzxv6R5e95ZBsbaEtbumjq8P99aksGfNh3jo8Jzrg/Oj/x7bxE3zkhxybH6RoWTMiCao6XVLjmeP6ppMhwtre51d6Dw0BCWjE1kU5b//hhzt4ZmC2VV9eSfqaGipjEoK1NadZjsicjU1huQCpQBpcBw+2NBo9li5XBxFVOH93freeanJ/BhkCV7R0qqGZ8c55ZjTx8xgL0FwbfYy98/PMHgfpEs70an787cMCOFl/f413LYVXXNbMk9w7U9XOEGIC46nJ+uHMuRkiqe3V4QlDUo1Q3NhIeGEOPCOfKumzaMV/cXu+x4/mZ9QTNfvXSUS441Pz2B7ccrgjqJaavZYmVLTjkPvpPDQxtyePr9fLbknOFQcRVrDpXxx3dz+cP6bNYcKg26Vp/OPsEP2f+NAqYDB7ENzJgI7ALmuzc03/GffcV8fnrvakicISIMHxDNibO1jEyIcfv5fMGGo6e4d3G6W44dGiKEhoTQ1GINiomCjTE8sTWf8cn9XDrYJXNIX948UEJdk/8MIPrbB/ncddmoXvevFRFumTOCg0Xn+X9rjvKtJRnER/e86c3fvPlRz5eE7EhYaAiTU+LZW1DJ9BEDXHpsX7fvZCVDYoT+vWi+bUtEWDkpibcOlbJqsmv/n/xFi8XKzvxKduZXECIwNz2B71wxusM+4MYYDhZX8Yf12cxPT2DRmEQPR+wdna2Nu8gYswg4CUw1xkw3xkwDpgBBM0NmfZOFgopaxgzp3txSPRVMAzXqmyyEiPRoHVxnzUsbGBS1pVar4ZGNucwcOcCliV6rG2cM5xU/qd37uLSKIXF9Op1iprsmpcTz7ctH8+imPPYHSbOuMYZiN3WxWDEhibVBNpl8s8XKWwfLmDfUtSuJTB3en8PFVbT4YVeLnrJYDTuOV/DQhhz++O4xAL59eQbfvTKT2aMGdjrYT0SYnBLPT1eOo7HFyiMbc4Oils+Z6o4xxpjDrXeMMUeAyW6LyMf8Y3sBX5yV6rHzxUSGESpCdUPgdwx/+0gZyyZ0PZFob0wfMYC9JwO7Kbepxcof1mezbEIS01Ld09Vg+MBoTlU30uzjzUXGGP6zr5gbXNTHrK24PrZm3aOl1fxly/GAn+ds94lKZrip5i0kRJgzamDATt7tyPM7T3LzrOFumc1h+cQk3j5yyuXH9SVWq2FPQSUPb8jh4Y05NLZY+OaSDL5/VSbzMxIIC+1+683S8UP47NRkfrP2KPVNgf15dqZ0skTkaRFZKCIL7CtpZLk7MF9QWFFHiOCWX7ad+fz0Yby6L/D7tOScvuD2GtPQECFUJGB/uZ2taeTXa4/yxdmp3V7ZoLs+OzWZ7SW+3ZT7YV4F89MTXDqNT1siwhdnp7J8whB+ty6b3ScC94fE5pwzbm3iumLcYDZmnQ6KvpAl5+upbbKQ4eSo8O6aOrw/B4rOB1xZGmM4VHyeRzbm8uCGHKrqmrlncTo/uGoMCzMTCe9Bgtde6sAY7lmUzu/ezgroH3DOlNTtwMfAt4BvA0ftjwU0YwzP7ijgtrkjPH7u5Pg+nKpu8MsRkM4qrKhjWH/PJNHzAnTgy4Gi8/xly3F+uHSMR36QjB7cl7Ja47NfKMYY3ssuZ7EH+uCkDozh51ePo6yqnt+ty6K8LrA+q2drGomPDndb0gy2xHlhZiJbgmCt179/cIIv93D1EWddNnoQ2wJkSbqyqnqe2pbP79dnU1RZz90L07hv6RguHzfYLd1+EvtFcdeCNB58JydgB7s4M/VKgzHmEWPMtfbbI8aYgJ8V861DZSzKTCQq3H39yTqzYkIS6wK4T8tbh0q5ZqJr59bryPQRA9gTQKNymy1Wnth6nKOl1fxkxViXjpTsyriBIXyYV+Gx83XH1twzLMh07VKGnRERVk1O5jtXjOZAuYWHN+ZytiYw5pt/fX8Jn3XxwAxHLstIYFvuGZ/9AeEK7x49zbz0BJfMU9iZ1rL0V8YY9p2s5Hfrsnj78CmunZrMj5aNZcXEJI98DyfH9+EzU5J5+oN8t5/LG7pM9kTkhIjkt795IjhvOVXVQF55DfMz3DOBsjMmDovncHFVQF4ErVbDhYaWHi+91F22UbmB0ZT7wbGz/GZtFleMG8wX3NT/pzPjE0J5/5hvfqFsP17BZV74zEaFh3LliHDumDeSl3YX8tjmPKrq/bfPrdVqOFvbSGK/KLefS0S46pIhvPNxYK52U9fUws78Co+M+GwdeOCPA4j2F57jhewmzlxo5L6lY/jy/JEkuHCAlbMuGRrHgJjIgOxL6kwz7nRghv12KfAo8C93BuVNjS0WHtucx90L0rwdCrNHDWRnfuDUSLXafryCeekDPXpOf2/KPVpazf976yj1zRZ+fvU40gbFeiWOEBGGxvehqLLOK+fvyPEzNYxKiPF48ttWXHQ49y7O4Lppw/jb+/k8/X6+X3b63nrsDAvcMKK7I7NHDWT3iUosAdh89swHJ7jjUvc237a1bPwQ1vvRQI2KmkZ+93YWRZV13DQmgqXjk9zadcAZn5uazNZjZwKmlr6VM824FW1uJcaYPwKL3R+a5xlj+OO7x7hrwSi3V7k7Y/GYRN7LDrxfvB8eP+u2Zec6MsNPm3JLz9fz+7ezOVh8nv9ZPsZtazN3x7VTk3nDx6YHWn2glGsme6ZbQFcS+0Xx3SszueqSITz63jGe33XSr2qVdxyvYE6aZ3+MXTslmdcCbKLl3NMX6NcnnKS4Ph47Z1hoCCn9+1BwttZj5+ypjUdP87cPTnDPonRWTU4mxMvXtVYiwr2L0vnrVv9eF7w9Z5pxp7a5TReRrwEuGVIkIktFJEdE8kTkfgfPi4g8an/+UNuVO7rat7ta5ylbNn6IxwYOdCUkRMgc0o/DxVXeDsVlquqbiY0M8/ivN39ryr3Q0Mz/vXeM1QdL+cbidG6aObxHUwu4Q7+ocOqbLT4zgKi+yYIBoiM813fRGSkDovnh0jHMHDGAB9Zn+0V/qpLz9STFRXn8B8WEYXHknamhodn/akIdMcbwwq5CvtDDdal743M+vkKJ1Wp4fEseLRYr9y0dQ78oz3Tn6Y6+UeHMS09g/ZHA6TfvzLfHQ21uvwOmAtf39sQiEgo8BiwDxgE3ici4dpstAzLstzuBv3RjX6dV1TXz67VZLB2fxMRh8T09jFt8ZvJQ3jzgW7UovbHmUClXe2hgRntz0xLY7uNr5Vqshpd2F/KXLce5fnoKX1uQ5tEBGM5aPCaRzdm+sSbnWwdLuXqie9et7o2MwX35ycpxVDc089CGHJ9u2n3jo5JeLTHXGzfPTOX5XYVeObervbSniM9MSfbKD7ToiDCiwkOp8MFmyMYWC79Zl8WizESWuWg5R3dZmJnIweIqztc1eTsUl3DmnXhH62oaxpgrjDF3Aq549TOBPGNMvjGmCXgJWNVum1XAc8ZmJxAvIklO7tul6oZm/rnzJH/ddpxvLclg3FDPrJLRHWGhIYxPjuNg0Xlvh9JrxhhOVtQxfKB3ak5njvTtptycUxf45VsfMz45jvuWjvFIB/mempban30+0hE870yN2+Yvc6WVE4fyxdmp/HZdFiXn670dzkWaLVZqGlu8thzc8IHRVNc3+/2Xa2FFHZW1TUxOifdaDNdPT+GVvb5Vu9fQbOG3a7P48vyRbp8T1FXuvHQUz3xwwtthuIQzVQb/wVab1/6xab08dzLQdv2lYmCWE9skO7nvRc43Gh7emAvGYLCNols+Icnn16G9etJQfrsui0levHi4wkdF55nixdcQGiKEiNBssbpkMk5XMcbwz50nabEYfn71JV7voOwMEWFQbCTl1Q1eTUoPFp1n4rA4r52/uwb3i+LHK8byyLu5rJwwlAk+FPvGo6e5ctxgr8Zw65xUnt1+km9dnuHVOHrKajX87YN8/mfFWK/GMahvJLWNLdQ3WXyi/3lji4XfrsvinkXpDPbhH7Ht9Y+JICm+D0dKqhif7Duf1Z6Qjqb2EJExwCXAA8AP2jzVD/iBMeaSXp1Y5DrgKmPMV+z3bwFmGmO+0WabtcDvjDEf2O9vAu4DRnW1b5tj3ImtCZhBgwZNe+WVV3oTttd8VN5CmMCEQa5v0qupqSE21v2jO/+d08S1GeGEeTGZyaqw0GI1XZajp8qkyWJ47Vgz04eEkh7v/YtyV9qWy/lGKztKLSwb6b0+N//JbeIz6d59T0H33y/GGN483sz4BN/5f38pu4kbMsNd2l+vJ5+jjQXNjEsIJTnWd36QOWtjQTOjB4SQ2q/j/1NPXVtO1Vo5WmFh8XDv9omzGsPLOU1cmRrOwD4d/596qly6y2oML2Q1cfPYCK8Mjlu0aNE+Y8z0Xh/IGOPwhq1Z9O9Ahf3f1tujwNyO9nP2BswB3mlz/0fAj9pt81fgpjb3c4AkZ/Z1dBs9erTxV1ar1fxi9RHT2Gxx+bE3b97s8mO2V1HTaB7bfMzt5+lKi8VqHlif1eV2niiT6vom85PXD5uy8/VuP5ertC+X3647aqxWq1diOVfbaP7vPe+/p4zp2fvFarWaR9/NNftPVro+oG7KK79gXth10uXH7Um5NLVYzM/fPOK191VP7cqvcKoMPXFtafWbtUdNi8W75find3PN0dKqLrfzZLl0196CCvPa/iKvnBvYa3qZbxljOu6zZ4x50xhzO7DSGHN7m9s3jTHbe51lwh4gQ0RGikgEcCOwut02q4Fb7aNyZwNVxpgyJ/cNKCLCzbOG8/yuk94OpUde21/MZ6cM83YYn2rK9aaqumb+sD6b714xmiFx/tOs0d701AHsKfBO373XvTiYwBVEhHsXp7Ph6Gnyz9R4NZbVB0q5ZpJvTF0THhrCiolJrD5Y6u1QnFZ+oYF3s05z44wUb4fyKVeOG8yGj703796bB0qYlBLvN330OjItdQA5p2qoafTttcE702GyJyL32f/8gn36k0/dentiY0wLcC/wDpAFvGKM+VhEvmaf3gVgHZAP5AFPAV/vbN/exuTr0hP70thi9foXQ3c1W6ycudDoM0nNnFED2XHce0t+NTRbeHBDDj+4cgz9Y7zTGd5VFmUOYkuO50flWq2GU1UNDI333Bxm7iAifO+K0Ty34yRnLnhn9GR9kwWrMT416nvGiAHknr7gtTLpjtrGFv68KY9vX57h9Tkw25s+YgB7T57zykpMeeUXKDlfz4LRnpug252+PG8Ef/fjwRqddYrIsv+7F9jn4NZrxph1xpjRxpg0Y8xv7I89YYx5wv63McbcY39+gjFmb2f7BoM75o/kH9sLaPGROc6cse5wGSt8aGqMmSMHsPuEd0blWq2GB9/J4euL0jy2XJw7hYWGEBUe6vFfvB8eP8u8dO8tZ+hKYaEh/OCqTP783jGv1DivPljiM7V6bd29MJ3Ht+T59JKRTS1W/vedHL51eYbPzfPYyjahvGdr3+ubLDy34yR3XjrKo+d1p8R+UURHhnHCgxNWu/K931kz7lv2f591dHNZBKpbwkNDuG3uCB7f4h+zextjOFxc5VPzF7bOfeWNL9anP8jns1OHeXRWfXdbMTGJtYc82+T2wbGzzA+QZA8gJjKM2+eN5PHNnv1cG2M4dto3p66JjQxj5cShvLi7qOuNvaCh2TbC9A4vrePqrCvGDebdLM+uxPTn945xz6J0n5kI3lW+OHs4/9rpua5UrjxXZ824b4nI6o5uLotAdVvaoFgmDovjP/t8ax4lR7YdO8ulPliNPydtIDvzPduUu7/wHH2jwn1yPsfeSBsUS/4Zz/3aLauqJ7FfFCF+MEVNd4xMiGHc0H6sPeS5Wfv3F55jWmp/j52vu6al9qfFavW5+THP1jTym7VZfG1BGikDfGPFpY6EhggjE2LIK7/gkfO98VEJs0cN9KspVpwVGRbKnFEDPdJ1paaxhVPVDS47Xmdp94N8evWM9jflRQszEwF8enUNYwybs8u5LMP3amBmjRzg0WSvrqmFtw6W+lwHbldJGxTrsS+T1/aX8Fk/HpjRmSvGDSb/TA2FFXUeOd+Go6e5wstz63XlltmpvJdd7rEy6cqu/Aqe2HKcHy4b4zP9kLty7ZRkXvfAetZ55TWUVtVzmQ/+wHeVJWMT2ZZ71u1Lb/5r50m+ODvVZcfrrBl3a+sN2AGcAyqBHfbHlJd9fpptdOszH5zAavW9fi0bjp7myksG+1ynZbA15YaKeGwtzr9sOc7dC9J8sixcYfnEJNYecv+ov2aLldrGFr8f2NKZuxak8fQH+W7vZlB+oYH+0RE+39QmInzn8tH8ffsJryZ8pefr+cP6bE5VN/DjFWOJ9aEBLV2JCg+lb1Q45S6sKWqvvsnCP3cUBFQ/PUdEhC/MGs4LbpwZo7K2iaYWq0u7+3T5KReRFcBxbPPr/R+QJyLLXBaB6pVVk5OZMWIA/2/NUY92HO1Ki8XK7hOVzE3zvVq9VldeMoR3PDAtwebscsYl9fPp5c96KzYyjCaLxe0JykY/qInqrYiwEL40dwRPbst363le2VPEDdP9o6Y5IiyEHy0byz93FnC4uMpj522xWHn/2Bl+/3Y26w6X8fWFaayanOyXP9pumJ7Cv93Y9efP7x3j7oWB10/PkfTEWM7XN7tttPg/d5zkFhfW6oFza+M+BCwyxiw0xiwAFgGPuDQK1SsThsXxo+Vj2JpTzu/fzubDvLM0tnh3sfXndxVyvY9/kVwytB9HS6vdeo7K2iZ2nqjw+UW/XWFRZiJbcs649RwHis57dc1RTxk1KJbEvpFu62pwoaGZZovxqxrSiLAQ/mf5WHYXVPLcDtfPSFDT2EJWWTXvfHyKx7fk8eA7OTy66RghInz/ytF85dJR9I3y3xH0/WMiaGqxUt3Q7PJjv3mghFmjBvpNs7Yr3D5vJP/Y7vqpWAor6oiOCHX5Z9OZeuhyY0xem/v5gOcn1lKdigwL5UvzRtJisbIjv4IntuTTYrUiQL8+4YwYGMOIhGiG9Y8mKty9yzOVnK+nprGFzCG+N8KvLRFhSFwUJefrSXbDfG3GGB7fnMc3/XSdz+6altqf36/PdlvNW175BdIGxfhlrUpPfH7aMH6zNosxQ/oSH+3aC/+/9xZz3XTvT3LeXSLCHfNHklVWzW/XZTNhWD+WT0giMqzra5rFajhV3UBhRR1FlXWUVtXTtvdLTEQowwdEkzIgmvnpCT4176Cr3Dx7OM9+WMA3lrjumpRXXkPxuXpWTQ7MfrQdiesTTuqAGA4Vn3fpbBPP7Sjg+1dluux4rZx5N38sIuuAVwADXAfsEZHPAhhjXnN5VKrHwkJDuDRjEJdm/LeDbFVdMycrazladoF3Pj5NY4sVjCE0JISpqfE0WVzX389iNTy59Tg/Wu7dhcCddc2kofx7XzFfW5Dm8mO/caCEJWMH08+PawO6Q0QYFBtJ+YUGEvu6/hf+6oNlfG1BYPcHaktE+MaSDP707jF+unKsy5LchmYLZ2oaGdbft0eRdmZsUj9+dvU4jpRU8Zctx2mxGEJChLg+4YSHChar4Xxd86fmKQsJEZLiokgZEM3c9IEM6RcVFE2ObSX2jSIqPJSiyjqXjCKua2rhnzsK+OnKcS6Izv98btowfrXmKBOS41zy+Xz/2BmmjxjglgoZZ5K9KOA0sMB+/wwwALgaW/KnyZ6Pi4sOZ2J0/EW/PhpbLOw/eZ61+c0caM5m0ZhEpqf279Wb9q/bjvPF2alurz10lYGxkZyra8JiNYS6cCqPoso6CivqudYHlojzpGsmDWX1gVK+4uJO2jWNLQj47MS17hLXJ5yVk5J4flehy0bmvbS70G/66nVlfHIc45PjAFtNelV9MxarIURsiV+gTc/jCrfMSeWhDTn8eEXvEjRjDH969xj3LA6OfnqOhIYIV09K4rX9JXxuWu+u9Y0tFjZllfPzq92TOHd55bSvj6sCUGRYKHPSBtJYFMG8S0fzXnY5v1mbxcSUeJaPH9LtD/Are4tIHxTrkxO0duaKsYPZePQ0S8cPccnxrFbD0+/n+03tpisl9oviTE0jxhiXNre+4efr4PbG1OH9OVB4niMlVZ8kNj1V3dDM2ZomRiTEuCg63yEiLm/uDkRR4aHMGDGATVmnWTK2510uXt5TxOIxiW6pxfcn01IH8MGxCorP1fWqtvzp909w+7wRbuum4sxo3JEi8rCIvKaTKgeu8NAQrrpkCD9ZOY7UAdH874Yc/vbBCarquu7Ma4zhHx+eIDoilCsvcU3C5EnTUvuz76TrJm19bkcBN8wY7je1m642bXh/9p103fJMxhgKK+sCMkFx1pfmjuA/+4p7vSzdc9sLXDp3l/JPV14yhN0nKp26vjvyYd5ZLMYwa9RAF0fmn+5aMIqntuVj6eEUaIeLq+jXJ5zUge67xjlTdfMGUAD8GZ1UOShMSonnR8vGsmz8EJ7bUcBDG3I4VHze4Vx+WWXV/L81R5kwLJ6VE31vfU1niAjjk+M4UtL7KR2yT1VjNQTcKhndsXhMIu9muW4M1/bjFcxJC+4vlZAQ4Z5F6fzp3dwer5eZV36B6IiwoBoxqTr2tQVp/GnTsW7P0Zp7+gJ7Ciq5eZb+aGgVFR7KDTOG89T73Z8uqbqhmf/sK+LmmcPdENl/OdMBpsEY86hbo1A+aWh8H76xJIP6Jgtbc8vZePT0p6qYLVYraYNiuX/ZGKdGw/my5ROS+N93cnrVTNbQbOHFXYX87OpLXBiZ/wkLDWFwv0iXjXLemnuG+5eOcUFk/m1Q30iWTUjibx+c6HafSKvV8K+dhfx4RfB1LVCO9Y+J4NopyTz9QT53XubcALXc0xd4dV8x9+nn8SLjhvbjZEUtaw+VsWKic1NtWa2GP248xrcvH+32/qXOJHt/EpGfAxuAT2YQNMbsd1tUyqf0iQhl6fgklo4P3LniwkNDyBzct1fD6P+y5Th3Lkhz6UAPf/W5acP4+wcFfKuX087knr7AqIQY7WhvN3V4f05VNXTrCwXgbx+c4IYZKYQHaUd65diEYXGcqm7guR0F3DpnRKfb7jtZyaascu5bOkavcR1YNiGJf3x4gi055Z8sadoRYwwPbczh+hnDPDLfpTOf/AnAV4Hf898m3AfdGZRS3vCZKcm88VFpj/bdnF1O5pC+bpmvzx/1iwrHYgy1vexj9vpHJVw7NTgHZnRk+YQkztc3sf6Ic6u/bM4pJz46nLFJwdu1QHXsinGDSR0Yw0Mbcqhvungy/sYWC0+/n8/Rsgv84KpMTfS68KV5IymqrOt03fqGZgu/X5/N0kuSGDPEM59LZ2r2rgVGGWOa3B2MUt4UGiJcNjqB9UdO0Z1eTcXn6th7spIfXKVNG21dN20YL+0p4o75I3u0f1FlHYl9I/2+i4A73DwrlZf3FPLyHttKNR2N4Psw7yy5py5wlxvmkVSBY8HoQYweHMuj7x2jT3joJz8Mck5VU9No4frpwxg1KNbLUfqPW+aMYFvuGX695ig3zEj5ZIYKi9WwNbecbbln+eplozxaOeBMsncQiEdXzVBBYGFmIr9bl8XEcOc6Ldc2tvDktnztC+VAyoBoztU2UdPY0qNF41/aU8jXF6a7IbLAcMOM4ew4XsGv12bxpbkjPjVJbmOLhX/uOEl0RBh3XhY8E1GrnkuK68MPl46hvsnCsfILAMxNGxmQK4l4wmWjBzFz5ADeOljK6oOlth9k9hHMP796nMdXAnLmf3EwkC0ie/h0n71r3BaVUl70tQVp3PdcIcuWmE77ijU0W3hgfTbfXJKhtU8duHn2cF7YddLpDuCtck5dYGh8H/2i6cKctIFMSonjpd1FVNQ2EhoSAsZgNbZ+kyODeLoa1TN9IkJduvxXMIsKD+U6H5nA3Jkr6c/dHoVSPqR/TATzk8P447u5fOeK0Q5/gVU3NPPQOzncvTCdhNhIL0TpH5Li+tDQbO3WEmrGGF7ZW8T9y7RZ3BnREWF8uYdN5Uqp4NDlAA1jzNa2N6AFuN79oSnlPan9bBNE/2pNFhU1jZ967sO8szyyMZdvXz5a5yxzwu3zRvC39084vf26w6dYmDlIR44qpZSLONVGIiKTgS9gS/JOAK+6MSalfML45DhSBkTzr50nqW+yEBIiNFusTEmJ52crPd/nwl/1jQpnamp/p5ZnOlvTyJHSKn6o83gppZTLdJjsicho4EbgJqACeBkQY8wiD8WmlNfF9QnnnkU6SKC3rrpkCA9vzGX04L6fGkjQVrPFyqObjumErUop5WKdtZNkA0uAq40x840xfwYunoRHKaWccO+idJ5+P5/S8/UXPdfUYuUPb2dzx/yRPRq5q5RSqmOdJXufA04Bm0XkKRFZAmi7lVKqRyLCQvjR8rH8a+dJ3viohKYWK8YY9hee4zdrj3Lb3BFuXQhcKaWCVYc/oY0xrwOvi0gM8BngO8BgEfkL8LoxZoNnQlRKBYqo8FDuWzqGA0XneXxLHlarYWxSP366chxhOiBDKaXcosv2EmNMLfA88LyIDACuA+7HtlauUkp12+SUeCanxHs7DKWUCgrd+iltjKk0xvzVGLPYXQEppZRSSinX0XYTpZRSSqkApsmeUkoppVQA02RPKaWUUiqAeSXZE5EBIrJRRI7Z/+3fwXZLRSRHRPJE5P42j/9CREpE5ID9ttxz0SullFJK+Q9v1ezdD2wyxmQAm+z3P0VEQoHHgGXAOOAmERnXZpNHjDGT7bd1nghaKaWUUsrfeCvZWwU8a//7WWzz+LU3E8gzxuQbY5qAl+z7KaWUUkopJ4kxxvMnFTlvjIlvc/+cMaZ/u20+Dyw1xnzFfv8WYJYx5l4R+QXwJaAa2At8zxhzroNz3QncCTBo0KBpr7zyiutfkJ+rqakhNjbW22H4FC0Tx7RcHNNycUzL5WJaJo5puTi2aNGifcaY6b09jtsWoRSRd4EhDp76sbOHcPBYa2b6F+BX9vu/Ah4CvuzoIMaYJ4EnATIzM83ChQudPH3w2LJlC1oun6Zl4piWi2NaLo5puVxMy8QxLRf3cluyZ4y5vKPnROS0iCQZY8pEJAkod7BZMZDS5v4woNR+7NNtjvUUsMY1USullFJKBRZv9dlbDdxm//s24E0H2+wBMkRkpIhEADfa98OeILa6FjjixliVUkoppfyW22r2uvB74BURuQMoxLbeLiIyFHjaGLPcGNMiIvcC7wChwDPGmI/t+z8gIpOxNeMWAHd5OH6llFJKKb/glWTPGFMBLHHweCmwvM39dcBF06oYY25xa4BKKaWUUgFCV9BQSimllApgmuwppZRSSgUwTfaUUkoppQKYJntKKaWUUgFMkz2llFJKqQCmyZ5SSimlVADTZE8ppZRSKoBpsqeUUkopFcA02VNKKaWUCmCa7CmllFJKBTBN9pRSSimlApgme0oppZRSAUyTPaWUUkqpAKbJnlJKKaVUANNkTymllFIqgGmyp5RSSikVwDTZU0oppZQKYJrsKaWUUkoFMDHGeDsGjxGRC0COt+PwQQnAWW8H4WO0TBzTcnFMy8UxLZeLaZk4puXiWKYxpm9vDxLmikj8SI4xZrq3g/A1IrJXy+XTtEwc03JxTMvFMS2Xi2mZOKbl4piI7HXFcbQZVymllFIqgGmyp5RSSikVwIIt2XvS2wH4KC2Xi2mZOKbl4piWi2NaLhfTMnFMy8Uxl5RLUA3QUEoppZQKNsFWs6eUUkopFVQCItkTkaUikiMieSJyv4PnRUQetT9/SESmOruvP3OiXG62l8chEdkuIpPaPFcgIodF5ICrRgP5CifKZaGIVNlf+wER+Zmz+/ozJ8rlB23K5IiIWERkgP25gHy/iMgzIlIuIkc6eD5Yry1dlUvQXVucKJNgva50VS5Bd10BEJEUEdksIlki8rGIfMvBNq67vhhj/PoGhALHgVFABHAQGNdum+XA24AAs4Fdzu7rrzcny2Uu0N/+97LWcrHfLwASvP06vFQuC4E1PdnXX2/dfW3A1cB7QfB+uQyYChzp4Pmgu7Y4WS7BeG3pqkyC7rriTLm02zYoriv215YETLX/3RfIdWfuEgg1ezOBPGNMvjGmCXgJWNVum1XAc8ZmJxAvIklO7uuvunxtxpjtxphz9rs7gWEejtEbevN/HtTvl3ZuAl70SGReZIzZBlR2skkwXlu6LJdgvLY48V7pSFC/V9oJiusKgDGmzBiz3/73BSALSG63mcuuL4GQ7CUDRW3uF3NxgXW0jTP7+qvuvrY7sP2CaGWADSKyT0TudEN83uJsucwRkYMi8raIXNLNff2R069NRKKBpcCrbR4O1PdLV4Lx2tJdwXJtcUawXVecFszXFREZAUwBdrV7ymXXl0BYQUMcPNZ+iHFH2zizr79y+rWJyCJsF+T5bR6eZ4wpFZFEYKOIZNt/ofk7Z8plP5BqjKkRkeXAG0CGk/v6q+68tquBD40xbX+tB+r7pSvBeG1xWpBdW7oSjNeV7gjK64qIxGJLcL9tjKlu/7SDXXp0fQmEmr1iIKXN/WFAqZPbOLOvv3LqtYnIROBpYJUxpqL1cWNMqf3fcuB1bNXGgaDLcjHGVBtjaux/rwPCRSTBmX39WHde2420a2oJ4PdLV4Lx2uKUILy2dCpIryvdEXTXFREJx5boPW+Mec3BJi67vgRCsrcHyBCRkSISge0Ns7rdNquBW+0jW2YDVcaYMif39VddvjYRGQ68BtxijMlt83iMiPRt/Ru4EnA4ksoPOVMuQ0RE7H/PxPY5qXBmXz/m1GsTkThgAfBmm8cC+f3SlWC8tnQpSK8tnQrS64pTgvG6Yn8v/A3IMsY83MFmLru++H0zrjGmRUTuBd7BNkLlGWPMxyLyNfvzTwDrsI1qyQPqgNs729cLL8PlnCyXnwEDgcft16AWY1uIejDwuv2xMOAFY8x6L7wMl3OyXD4P3C0iLUA9cKOxDYEK9vcLwLXABmNMbZvdA/b9IiIvYhtFmSAixcDPgXAI3msLOFUuQXdtcaJMgu66Ak6VCwTZdcVuHnALcFhEDtgf+x9gOLj++qIraCillFJKBbBAaMZVSimllFId0GRPKaWUUiqAabKnlFJKKRXANNlTSimllApgmuwppZRSSgUwTfaUUkoppQKYJntKKaWUUgFMkz2llFJKqQDm9ytodEd8fLxJT0/3dhg+p7a2lpiYGG+H4VO0TBzTcnFMy8UxLZeLaZk4puXi2L59+84aYwb19jhBlewNHjyYvXv3ejsMn7NlyxYWLlzo7TB8ipaJY1oujmm5OKblcjEtE8e0XBwTkZOuOI424yqllFJKBTBN9pRSSimlApgme0oppZRSAUyTPaWUUkqpAKbJnlJKKaVUANNkTymllFIqgGmyp5RSSikVwDTZU0oppZQKYJrsKaWUUkoFME32lFJKKaUCmCZ7SimllFIBTJM9pZRSSqkApsmeUkoppVQA02RPKaWUUiqAabKnlFJKKRXANNlTSimllApgmuwppZRSSgUwTfaUUkoppQKYV5M9EVkqIjkikici9zt4XkTkUfvzh0RkapvnCkTksIgcEJG9no1cKaWUUso/hHnrxCISCjwGXAEUA3tEZLUx5mibzZYBGfbbLOAv9n9bLTLGnPVQyEoppZRSfsebNXszgTxjTL4xpgl4CVjVbptVwHPGZicQLyJJng5UKaWUUspfea1mD0gGitrcL+bTtXYdbZMMlAEG2CAiBvirMeZJRycRkTuBOwEGDRrEli1bXBJ8IKmpqdFyaUfLxDEtF8e0XBzTcrmYloljWi7u5c1kTxw8ZrqxzTxjTKmIJAIbRSTbGLPtoo1tSeCTAJmZmWbhwoW9CDkwbdmyBS2XT9MycUzLxTEtF8e0XC6mZeKYlot7ebMZtxhIaXN/GFDq7DbGmNZ/y4HXsTULK6WUUkqpNryZ7O0BMkRkpIhEADcCq9ttsxq41T4qdzZQZYwpE5EYEekLICIxwJXAEU8Gr5RSSinlD7zWjGuMaRGRe4F3gFDgGWPMxyLyNfvzTwDrgOVAHlAH3G7ffTDwuoiA7TW8YIxZ7+GXoJRSSinl87zZZw9jzDpsCV3bx55o87cB7nGwXz4wye0BKqWUUkr5OV1BQymllFIqgGmyp5RSSikVwDTZU0oppZQKYF7ts6eUcq3sU9Vkl10gITaSmSMHEBGmv+eUUirY6TeBUgGg/EID/++to2SVVTNhWBwhAg9uyGFzdrm3Q1NKKeVlParZE5G3jTHLXB2MUqr7Ss7X89S2fO5bmkl0hO0jnTYolrnpCbx5oIQXdhXyhVnDvRylfzpX28SaQ6WcqWkivk84yyckMSQuytthKaVUt3SY7InI1I6eAia7JZogVVXXzMt7C6mubyEkRGi2WJmfnsC89ARvh6Z8XG1jC09sOc5PVo4lMiz0oudXTU7m7cNlvHmghFWTk70QoX8yxvDvvcWUVtVzw4wUkuL6cLamkX/vLaZvVBg3zxqOfZ5PpZTyeZ3V7O0BtuJ4fdp4t0QThD7MO8u23DPcMX8kif1sNQbGGN4+coo/vpvLNxdnEBKiXyrKsSe2HucbS9IdJnqtlk1I4omtx8kqq2ZsUj8PRuefjDE8vuU4U1LiuX7Gf1drTIiN5O6Faew+Ucljm/O4d3GGF6NUSinnddZnLwu4yxizqP0NOOuh+ALamkOlnKyo40fLx36S6AGICMsnJLF0/BAeeTcX29zSSn3a9uNnGT24L4l9u25W/Oqlo3hpdyHNFqsHIvNvz24vYMaIAcztoGZ95sgBTE3tz/O7Tno4MqWU6pnOkr1fdPL8N1wfSnDZ8PEp6pssnfalGjOkH3PSBvKffcUejEz5A6vVsPHoaVZOTHJq+9AQ4ba5I3h2e4F7A/NzH+adJToyjJkjB3S63dy0BBqbrRwpqfJQZEop1XMdJnvGmP8YY3I6eO4Nt0UUBI6UVJF/tpbrpqd0ue3ctATKLzRSVFnngciUv3jD3gevO/3GRg2KxWqMvpc6UN3QzLbcM1zvxOcS4EtzR/DvvUW0aG2pUh5V19TCC7sKeWhDDg9vzOWxzXmcOFvr7bB8mk694mHnapt4/aMS7rpslNP73DF/JM/tKHBfUMqvWKyGrLJqJqfEd3vfW2aP4F/a/OjQk1vzubMbn8uQEOGmWcN5cU+RG6NSSrW1Kes0f9p0jHnpA/nelZl894rR3DonlfePneGP7+bS0Gzxdog+SZM9DzLG8NjmPL65OKNbNTJR4aFMHzGA7XmB11WyqcVKVV2z9kvshg0fn2Lp+CE92rdPRChjhvTlQNF51wbl5/YUVJKeGMvA2Mhu7TdmSD/OVDdQ06TvX6Xc7bkdBdQ3W/jRsrGkDoz55PG+UeHcOmcE109P4Tdrs6isbfJilL5Jkz0PeuNACYvHJhIXHd7tfa8cN5hN2eUBkRQ1W6y8uLuQB9Zn89etx/nP/mIe3pjL79/OZt3hMm0W64Qxhn0nzzEttfM+ZZ1ZNSmZtw6WujAq/2a1GtYeKmPV5KE92v+WOSPYXNTs4qiUUm29uLuQYf37sHJix5/TofF9+OGyMTyyMZfqBv1MttXlpMoiEg18DxhujPmqiGQAmcaYNW6PLoAUVdZRVFnPtVOG9Wh/EWH2qIHsyK9gbpr/zr9XVFnHU+/nc/OsVG6a+enBKcYYPio6z2/XZTM3bSBLxibqXGbt7D15rsvBA10JCRFmjBjArvwKZo0a6KLI/Neaw2WsmJjU4/faoL6RWA1U1jYxICbCxdGpQGGM4XR1I+V1VhqaLUSFdzxdkvq0HccrAFg8ZnCX28ZGhvG9K0fz0Ds5/OzqSwjVqcsA52r2/g40AnPs94uBX7stogBksRqeej+fuxY43x/IkcvHJrIl54yLovK8grO1/GN7AT9eMZbMIX0vel5EmDq8Pz+7ehyhocKv1mRRfqHBC5H6rs3Z5Swek9jr41w5bjAbj552QUT+rbHFwuHi88wY0bsEelFKOC/uLnRRVIHJGEN5dQO78ivYnneWgrO1AdFS0ZXCirpPBhJsyj5N7jkLT7+fzwPrs3l+10nqm7SPWWcqahrZklPOjTOcGzgFEB8dwS1zUnli63E3RuZfnFkuLc0Yc4OI3ARgjKkXrW7pln9sL+ALs4Z3OvGtM0SEEQNjyD9Tw6hBsS6KzjPO1zV9kuiFh3b9G2NRZiIzRgzgiS3HGTe0H8snODfFSCA7X9dEbFQYYU6UX1dCQoRpqf3ZU1DZ60THn/1nXzE3dONLpCP9IoXGJgt1TS2fLFmnbErP1/Pa/mJqmywMjYtiZEIsYaHCnoJKXt5bxMCYCG6aOZyYyMAqN2MML+y2rYz09YXp9ImwXf+31J9g4ULbhNz5Z2r406ZjpCfG8tkpyTqBvgN/3ZbPvYvTu13znp7Yl6NlF9iWe4bLRg9yU3T+w5lvjSYR6QMYABFJw1bTp5xwpKSKsBBhzBDXrFywavJQ3jzgX/2trFbDnzYd4ztXjHYq0WsVGxnG96/KJDoilN+sPcq5IO90++aBUq6Z1LN+ZY5cdckQNnx8ymXH8zdNLVYKK+pIT7y4lrknPjMlmdc/KnHJsQLB6eoGXs1tYu2hMm6dO4IfLh3DLXNGMD8jgdmjBnLd9BR+uHQMyyYk8eCGHPadPOftkF3GajU88u4x0gfFcvfCtE8SvfZGDYrl/mVjGJkQwy/f+piyqnoPR+rb3vn4FHNGDaRfVPf7uQNcM2ko7x87o/33cC7Z+zmwHkgRkeeBTcB9bo0qQDQ0W/jPvmJumZ3qsmO2/vqtbWxx2THd7dX9xaycOJS4Pj37wC7MTOTexRn8dVt+0DY9GmMoPV/PsP7RLjtmSIgwcVg8HxUGzpdsd7z+UTHXTnXdesGjBsVysqIOqzXwmyY702Kx8uz2Al7ZU8SKUeF89bJRnX5ZJ8f34Wcrx3Gw6DzvBMiPj8c253HluMFO94mdltqfHy0fy/M7C9mUFZzXuPYami3sLahkUS+7rdy9MJ2/bNHm3C6TPWPMRuCzwJeAF4Hpxpgt7g0rMDy+5Th3LRjl8qr55ROSWH/EPy6KFTWNFFbWMS21f6+OE9cnnPuXjUGA372dxfm64KrlO1B0ninD411+3OUTknjbT95LrtRisZJXXuOyGvdWC0YPYusx/+1X21t7Cyr59dosZo8ayDeWZBAV5ty1T0T48vyRVNY28V62fyc7L+8pZMrw/oxPjuvWflHhoXz/qkzqmy08sfV40P9o+NfOk3zRBRUlA2IiGJfU75NBHsGqw2RPRKa23oBUoAwoBYbbH1Od2JxdzpghfUmK6+PyY2cO6Utu+QWXH9cd/rG9gK9c2ruBKW1dPm4wdy9I45kPC/jHhydobAmOzs2bc870+heuI6EhQubgvnxcGlzLfq0+WMo1k1xXq9dqbtpAdgbhl8q52iYeWJ9N0bk6fn71OIcDsJxx08zhZJVd8Nv3Y/apai40tDA/o+czJqycOJT56Qn8em2WX7XguNKZC43UNVk+NZdeb6ycmMQ7H58K6rXBO6vZe8h+ewzYBTwJPGX/+1H3h+a/ztY0sutEpVsHFQyN60Pped/u33GyopYBMRE9br7tSHx0BN+9YjSXjh7Ewxtz+ceHJ6gJ4Itii8WKxWrt9QCfjlwzeSirg2jevdYVSCYM617NizNEhMR+UZyqCo5R5MYYXt1XzN8+OMFdl6Vx7ZRhvZ4u6e4Fafx7bzF1Tf71mW5ssfDirkJunzey18canxzH3QvT+P3b2UG5vOE/dxRw29wRLjueiHDzrOE8vzN4Vw/qbG3cRcaYRcBJYKoxZroxZhowBcjzVID+xmI1/HnTMe5dnO7W86ycmMSaQ779Bf3i7qKL5tJzpbRBsfxo2ViWjB3M0+/n8+A7Oew+URlwzR878yvdOrdieGgIqQNiyPOT2uLeWne4jGVu/CH2mclDeeNA4A/UOFR8nl++dZQRCdF8/6rMHk0W70hIiPD1RWk8ttm/vmae3V7Al+ePdNm8boP6RvKTlWN5cXdhQK6e1JHT1Q1ER4a5vJIgY3BfqhtaOF0dHD/E2nNmgMYYY8zh1jvGmCPAZLdF5Of+uu04X5iVSqybpxEYGBtJZa3vLjOWf6aG5P59PDJxaMqAaL59+Wi+dXkGNY3NPLghhz9vOkbOqcBIXnbkn2W2myc//uzUZF7dH/gJitVqOFh0nqnDe9eHtDMDYyM5V9cUcD86Wh0qPs9v1h7l+JkafrJibK9Wc+lIYt8oxg+N40M/SXIKK+owBpc1O7aKDAvlB1dlUnyunr9/eMJnr/eu9OLuQrdVEnx5/kie+fCEW47t65xJ9rJE5GkRWSgiC0TkKSDL3YH5ow0fnyJ1QEyP+6t015ghfck9XeORc3XX6x+V8PmpPVstpKfCQ0NYPGYw9y0dw+3zR3K0rIrfv53NU9vy/bZZraHZQlhIiNtngY8KD2VIvyhOVtS69Tze9m7WaZaM7XoW/t6an57A+36SqDjrYNF5fr3GluT9cOkYrp0yzCVzPnZk6fghvJt12i/65T7n4mbHtkSE62ekMGV4f369Niugu6xU1DQSFiIur9VrFRsZxtgh/dhbUOmW4/syZz6ptwMfA98Cvg0ctT+m2th38hwnztayYqLnJv9dMjaRd31wmP75uiYiw0I6nFvKE2Ijw7h2yjDuXzaGa6fa1oJ98J0cSny8n2N7W3LOsDDTMxOCXjd9GP/eW+yRc3mDMYZdJyqZPcr9k0jPS0sImKa31iTvxNlafrR8rNuTvFYiwm1zRvDcdt/uZ7WnoJLJw+Pd3ooxOSWery9M43/XZ3O42D8HsHTFnbV6rVZNHsqaQ2VYArTmvSPOTL3SYIx5xBhzrf32iDHGP6tJ3CTn1AU2Z5dz52WuG3XqjL5R4T75K+8/+4r5/LTer0rgKgmxkXz1slHcvTCNNw+U8I8PT/jNB/1g8Xkmp8R75FzREWHER4cH7MSuH+SdZX56gkfWWw4JEQbERHC2xn/nn2+f5H1mSrLH1xkdkRBDfbPFZ8vRGMO6w2UsH++ZH/kDYyP5+dWXcKDoHE9uO05LAI0urW02tFgNA2Mj3XoeEeFzU4fxn31Fbj2Pr+ky2ROREyKS3/7mieD8wcGi87z+UQnfuWK0R75E2stIjOXYad/pm9ZisXK2pokhcVHeDuUiMZFhfH1hOrPTBvKrNUd9fq6+msYWYiJCPfq+umFGCi/tDsyLoCdrSQFWTU72u9VuwDZ9iLeTvLZunZPKczt8s3bP9p5K9OgyZyEhwi1zRrB4TCK/WnOUo6XVHju3O20tauYLbq7VazVhWByFlXVU1QXPyhrO1MVPB2bYb5dim3blX+4Myl+8e/Q0H+Sd5YdLM712Mbx83GA2+lBT7gd5Z7lstPtGjrrCmCH9+O6Vo3l4Yy7F53x3WoNNWae5fJz7+5e11TcqnMjwEM5c8M2alJ7aW1DJtNT+Hk2ch8RFUV7d4Ded6surG/j929kcKDzPD5eN8XqS1yo+OoJ+UWE+NwWJMcZ2vevFnHq9kZ7Yl59dfQkfFZ3jj+/mcsGPlwSraWyhwQKJ/TxXSfDleSP5WxAN1nCmGbeiza3EGPNHYLErTi4iS0UkR0TyROR+B8+LiDxqf/5Q28mcu9rXneqbLPzp3WM0tli5Z1H3F2h2pX5R4Vxo8J2m3F0nKpk90r0jR12hX1Q4P14xlr99cMLnvkRaZZ+6QOZgzwz2aeumGcN5aXehx8/rTuuPnOKqS4Z4/LxThvdnv48vR2e1Gl7cXcgLuwv5xuJ0bpw5vFtrWHvCzbNSecHH3pNbc201xd68/oeGCDfPSuXmWak8tvk4qw+W+s2Pi7Ze2l3IgmHuncGivYGxkQyKjQiYWRu64kwz7tQ2t+ki8jWg199AIhKKbcLmZcA44CYRGddus2VAhv12J/CXbuzrcharYc2hUh7emMPnpiV7dDBGZ0YlxJBX7v1RuTWNLUSHh3q0SaM3IsNC+dGysTz9fr7PVedfaGgmNjLMK18k/WMiMNhWRQgEh4urGJvUzyu1VEvGJrIpq9zj53VWVV0zv1p7lLFJ/fj25aM/WXvb1/SJCGVw30gKK3znh9kHx2x9QH3BoL6R3L9sDEP6RfHLt476VQJT32ShsraJgX08/wPjxpnDeXF3oV8myN3lTOk+1Ob2O2AqcL0Lzj0TyDPG5BtjmoCXgFXttlkFPGdsdgLxIpLk5L4uYYwh9/QF/rLlOH9Yn01SXB9+vGKcSxek760rxg32icWz1x85xdLxnq896Y2IsBC+e2UmD23M8amldDZllbNkrOuXR3PWjTNTeHGPb9Wk9NQbB0pYNXmoV84dHhpCZFioTw6kyj19gUfezeXbS0Z7bBBQb1w/I4VX9vpGf9J9J88xZbhnuwU4Y+bIAfxkxVh2n6jwm6bdV/YWcf107wzoCw8N4Ypxg/1mrfnecOZn3B3GmE8NyBCR3q8HA8lA209uMTDLiW2Sndz3Io0W2JlfgdVqsBiDxWqwGoPFyid/1zVZOHOhkfpmC9iz/ZGDYvjCzOEumyHe1eKjIzhf7/0PdV55DZ+f5tm59Vwhrk84t88byZPb8rlnkXtXPnFWzukLXktQwDapbUOzleqGZvpF+eb73hm78iuYltrfI1OFdGTFxCTWHirlhhme6XzujH0nK9mSc4afrhznE/3ynBEdEUa/PmGUVdW7Zc3x7njn41P8cOkYr8bQkbDQEG6ZM4LyCw08tvk4Y4b0ZdXkoT6XmIJtibmyqgZGJMRQ4KUY5qUn8Os1R1mYmejV6cLcTbqqvhSR/caYqe0e22dfOq3nJxa5DrjKGPMV+/1bgJnGmG+02WYt8DtjzAf2+5uA+4BRXe3b5hh3YmsCpn9i0rRfP/5PQgTbDT75WwRCRIgMhbhIITLU9z4YnXmvsJmJg0JJ6EFVeE1NDbGxsb06f2WDlX2nLVyR6r+JwYclzfSPCmHcwFCXlElP1bcYNp1sZmVahFfO3+p8o5WtRS2sSv9vHN4sl+4yxvBCdhM3jYkgxM1fdF2Vy8s5TdyQ6d3/z1bZlRbyzltYMTLc7QmAq98vtc2GDQXNXJvhvbIsqbGSd87CgpSeXes8/Rk6ds7CrrIWrhwRTmK0b/XF3FLUTEb/UJJjQ7x6bTlTZ2XPqRaWj/KNz2hbixYt2meMmd7b43RYsyciY4BLgDgR+Wybp/oBrhgyUwy0rbsdBrSfp6CjbSKc2BcAY8yTwJMAmZmZ5uufW9K7qH3UuOoG1hwq4/Pzu1/pumXLFhYuXNir8z/9fj7f/mwyg/q6d44kd1pgDL9dl8XU2Rns3/lhr8ukp974qISvju/nsZVYOnPuwxMMyxhEeqLtIuyK94qnbM4u5wtDYVGm+5vDuyqXM7FFDE2JZ7QXBty0daSkisascv73Ws8MLHPH+6Vgcx7jp6eQ4Ob52DrywPps7r8pg8iwntUCefoztBC4rcXKX7ceJyIums9MSfbYuTvT1GJlx4Ycbl4+FvD+taVi63HSJyb5VBctV+oszc8EVgLxwNVtblOBr7rg3HuADBEZKSIRwI3A6nbbrAZutY/KnQ1UGWPKnNw3qCT2i+KMlyYeNcZwpqbRrxM9sE22edeCNJ7e5t1pJHNOX2D0YN+oPbt5VirP7zrpdx2Ym1qsbDt2hoWjPTevXmdsTbllXo2h4Gwtaw6V8c0l3p1BoLdunJHCy3u803evrKqeATERPU70vCUiLIRvLMkgITaS37+dTUOz95ege+OjEq6d6huJJ8CX5o7g6fcDd/3hDpM9Y8ybxpjbgZXGmNvb3L5pjNne2xMbY1qAe4F3sK21+4ox5mMR+Zp9xC/AOiAfyAOeAr7e2b69jcnfJcRGUn7B84ubHC2rZlxSP4+f1x0SYiNJHRjDsXPeuRhWe3EUriMRYSEsykxk3WH/6sD8r50n+eLsVJ8px+iIMCxWQ1OLdwYB1TS28MyHJ/jeld6Z/N2VBsZG0thi9crgg3/vLeY6Lw0mcIX5GQncOieV36zNorzaewthNVusHCu/wJghvvO9ERUeyqrJQ3kxQCeV7zDZE5H77H9+wT7X3adurji5MWadMWa0MSbNGPMb+2NPGGOesP9tjDH32J+fYIzZ29m+we7KcYPZeNTzo3I3Hj3NleP8axRuZz47NZndp1q8shTRpqzTXOHhiZS7ctnoQRwtq/KbiZZPVzdQ29hC2iDfqB1tdfm4wV5Zy9pqNTy8IZdvLcnwufnzeuoGL9TuXWhoxmI1xPXx337JAEPj+/A/y8fy5LZ8sk95Z/WNNw+Usmqy79TqtZoyvD/VDc0cP+P9qcxcrbNPfpb9373APgc35WNSBkRTfM6z65q2WKw0tVgDahSTiHDZsHBe2Vvs8XPnnq7xer8uR+5emM7jW/J8vonDGMMTW49zx6WumDDAtSYNi+Ng0XmPn/eZD0/w2anJbl9z1JOS4/tQUdvk0eZI25rf/jfbgCN9IkL5n+VjWXuojI88POl3i8VKzqlqxifHefS8zrpj/kie3V5AXZPvTZfUG501475l//dZRzfPhai6I75PuEfXfP3weIXPTCzqSil9Qyg9X0+VB6e0aW3C9UWxkWFcOyWZDSd9+wL4733FrJiQRHSE75WjiDA0vg8l5z33g+xA0Xn6RIT67Bdrb3xuajKv7S/xyLmaLVZOVTeQMiBwOu+HhAjfvWI0249X8GHeWY+d9z/7irl2iu8mzeGhIXxjcQYPbcj16o9bi9Ww/ojr+vl21oz7lois7ujmsgiUSy0ZO5h3PThj/878CmaP8v3l0XriS/NG8Oz2Ao+dz1tLejlr4rB4+kWIV7oKOCP39AXO1jQyfcQAb4fSoWsmDWX1AYcTB7hcbWMLb3xU4rHF5T0tPbEvBRW1Huluse5wGSsm+MaKSa4kItyzKJ2ssmo+OOb+hK+uqYWCijrGDfWdvnqODOobyWcmJ/PYZs+3ZpRXN/D0+/k88E62S2vjO/v5+6DLzqI8Jj0xllf3e6b5sbaxhT5+tDxadyXERhIbGUbB2VpGJMS4/Xz5Z2q9NpO8s+YMDaPgXB1bcspZ6IEpTZxVVdfMC7sK+elKt6+a2Cv9YyKoqm/GajVu/9w8viWPry9K8/sBGZ1ZMSGJtYfL3Nr/yxjD4eIqn+xj5ipfuXQUT247TmiIMCfNfT/ebQOn/OPHx4RhcdQ0tvDktnzuWpDm1nOVVdXzXnY5RZX1DOobyTWTh5LY1xUz3P1XZ824W1tvwA7gHFAJ7LA/pnxUTEQotR5Ynskfl0frri/MGu6RBdjLquoZ3M8/+lR9ad5IiirreOMjzzShdaW2sYUHN+TwnctH+8VqEPPSB/LhcffWomz4+BSTU/q7/AvD10xKiedQcZVba1925lcGbOtFW1+9dBQfFZ1jT0GlW45/urqBxmarX81jNydtIBOGxfHwxlyX1iBbrIb9hef4v/eO8b/vZPPu0dNcljGI+5eN4Y75I93yue1yaJaIrACOA48C/wfkicgyl0eiXGZhZiKbc9zflJtbfsEnBxO4UlR4KJcM7ce+k+65ALZae6iMFRP9p5noljkjiIsO5w/rsz3aR7S983VN/P7tbL59eYbPLmfY3ry0BN53Y5NZeXUDB4vP+9yobndZPCaR97Ldd717L/s0i8f4Ti22u4gIdy9IY+fxCva7YdDG3z44wZd7MOm/t81NS+Azk4fy/9Yc5WRFbY+PU93QzNpDZfzvO9k8sjGXipomvjx/JD+4agy3zBnh9v6gzvRifghYZIzJAxCRNGAt8LY7A1M9d8nQfqw9XMbKie5bW/V0dQODA7zWoNXVE4fyq7VHmerGhc/P1DT6XS3MosxEJg+L55kPTtAnIozPTk1mcD/PvYbDxVW8ur+Y71+V6VfTYYSECGmDYsg97fofS8YYHt9ynPuWZrr0uL5sbtpAfr02i8VjEl3++fy4tIrRg/sGbFeV9kSEexen86dNxxBsU5G4wtbcM0xL7U+Mjw5A68qoQbH8eMVY/vFhAY0tVq6fnsKQuM6vdc0WK4eKz7Mzv5K6phZiIsO4LGMQyycM8UrXCmdKvrw10bPLBzw3AkB1m4gQGRZCQ7OFqHD3TImy5lAZV/tRTVRvhIQISy8ZwttHTrHcDZ20s09VM8YHlkbrif4xEXz3ykzO1jSy5mApZ2uaCBHoExFGfHQ40RGh9AkPJTwshIjQEMJDQ4gICyE8VD65PyA2gn5RzidrRZV1vLyniKHxffjZynF++UW8anIyj246xn1Lx7j0uM/vKuTaKck+ORrZXUSEGSMGsPtEJbNc3Ny6+kAp378qeBJnsJXnt5Zk8Of38rAaw7TU3g14qqpr5v3cM/x4xVgXRegdkWGh3LUgjaq6Zl7dX8yZmkYiQkNIiosiOjIMq9VwtqbxkxkcQkSYlBLHbXNH+MQsC85E8LGIrANeAQxwHbCndb1cY8xrboxP9dClGQl8cOwsl7upKefMhUYSPViL422zRg3kN2uPcvnYwUSEuXZi2nWHT/G1BaNcekxPS4iN5Evz/ttEU9fUQlV9M7WNFhqaLTRbrDRbbCtI1Da20GSx0myfo7GipokLjS3Q2u9KhPAQYVDfSOKjw7EaqGlooeR8Pc0WK0PiovjawjSfuID2VFR4KP2jIzhV1dBlDYGzck9foL7JwqSUeJccz59cOW4wv12X5dJk79jpC4xIiAmYiai7Q0T4xuJ0Ht9yHIsVZo7sWcJnjOHP7x3j3sX+vURfW3HR4Z80R1ushlPVDdQ3WQgRSOgbSV8fWgGpLWeullHAaWCB/f4ZYAC2dXINoMmeD5qS0p+HNua4JdnLKvPfmqjeuHHmcF7cXchtc0e47JgNzRaMMQFXExMdEdar19TUYuVMTSNVdc2EhEBMRBhD4/v4xQAMZ10/I4W/fXCC714xutfHamyx8PzOk/zs6ktcEJn/CQkRxib140hJlcvmFHx1fwnfuSLDJcfyRyLC1xem8cTWfJparMzP6P58qv/ceZKrxg8hPjrCDRF6X2iIkBzfx9thOKXLq7F9fVzlZ0JChFARmi1Wl/8y3fDxab56mf91tO2ttEGxvPlRCVV1zS4bDLDucJlbmob9XURYCMnxffzmQtoTcX3Cie8TzsmKWlIH9m5qnye25POVS0cFVDLcXddMHsoD67NdkuwdO32BlAF9iAwLnJWBekJEuHthGi/uLuTlPYXcMMP5aVPWHColPjqCGT4872UwcWY07kgReVhEXtNJlf3LrFED2ZXv2lGkLRYrTRZLwNVEOeu2uSN4dkeBy46Xc+oCY5N8e4JR5T5fmDWcF3b1bmqfbblnGJEQHVCrO/REeGgI45Pj2OuCqUNe3lPk83NeetJNM4eTHB/NH9Znc6Gh61WFXtlTRGOzlWsmuW+QoOoeZ6p83gAKgD9jG5nbelM+btbIAew6UeHSY247dobLMga59Jj+ZGBsJNERoRRV1vX6WEdKqhiTFHzN4eq/osJDGTe0Hzvze/Y5LaqsY/eJyoCe8Lc7rpk0lDWHyrBaez7v3o7jFUxL7R+UffU6Mz8jgTvmj+TP7+Xx6r5ih/POnapq4HfrskiKj+JzAbKOcKBwpnqmwRjzqNsjUS4XFhqC1RiXzta/+8Q57guy0WntfXF2Ko+8m8uPlvVudNmaQ2V878re99dS/u2aSUP55VtHmZwS363R8w3NFp56P9/vRzm6kohw9aShrD5YymemdD8BbrFYWX+kjF9cE5x9H7uSEBvJ/ywfy5GSKh55Nxew9c9tsRiaLBbi+0Rwz+L0bo2uV57hTLL3JxH5ObABaGx90Biz321RKZeZOrw/+wvPuWS90PN1TfTrE+aXU124UlR4KGOG9OWjwnM9noeqqLKOIf0itfZAISJ85dKRPL7luNODNVosVh5Yn8M9i9KDvl9Ze9NS+7Mp6zQVNY3dXlv0uR0nuXl2qk+OpvQl45PjPukb2dBsISxECNNrmU9z5n9nAvBV4Pf8twlX1831E/PSE/ggzzWz9dvm1tM+GACrJiWz+mBpj5dpemVvEddpnyBlN6x/NFOGx/OaE+tat1is/O+GHG6Zk+rRSaz9ydcWpvHE1uPd2qfgbC1NFmvArwrkalHhoZro+QFn/oeuBUYZYxYYYxbZb4vdHZhyjajwUJparL3qwwK2+ZIKK+uCvhN4q5AQ4Ypxg1l7uKzb++afqSEhNtJvZ5NX7rEoM5EWq+Gtg6UdblPT2MJv1mVx3bQURib0bgRvIOsXFc7CzET+vbfIqe0bmi088+EJ7vDD5byUcoYzyd5BIN7NcSg3mjVqINuP926gxkdF55kShJO1dmZuWgI5py5QXt3Qrf1e3F3IjTO1Vk9d7PrpKYSFCA9vzKWy9r9rDlushvVHyvjjxlzuXZROemKsF6P0D/PSE6hvtrCri8EvFqvhwXdy+PrCdO1WoQKWM1ULg4FsEdnDp/vsXeO2qJRLXZqewAPv5PRoUsxWG4+e5nsumPw10Ny9MI0H1uc4vWzXxqOnmT1qoPazUh1aNiGJ6SMG8PKeIuqaWhDAauCy0YP48Yqx2p+sG26Zncpfth6nxWqYl37x9a+pxcpDG3K4fkbXa50q5c+cSfZ+7vYolFuFhAgJsRGUX2ggsW/3L2hnaxrpFxWu/TIciI4I4/PThvHXbfncvTCt023PXGhk78nKXo/iVYFvUN/ILt9Pqmu2VSDSeWVvEX/edIybZg0nITYSYwx7Cs6x5lApX710lHZPUQHPmRU0tra9LyLzgC8AWx3voXzRqsnJvLa/mLsWdP8L5D/7ivncNJ3HqyPjk+M4VdXAS7sLuXGm4xnmG5otPLrpGPcvc+3C90qprl0/PYXyCw28vr+EC40tGGMYnxzHL66+JOhnF1DBwake4iIyGVuCdz1wAnjVjTEpNxjUN5Lz9c00NFu6NZdXbWMLdY0tPaoRDCaXjxvMxqOneWxzHndeNupTfX8qa5t4ZGMu9yxK10EZSnlJYt8ovnrZKG+HoZRXdPjNIyKjgRuBm4AK4GVAjDGLPBSbcrHPTR3Gq/uLuXlWqtP7vLyniOtn6GACZ1wxbjAjE2J4YH02iX2jGBIXRcHZWpqthh8szdSJRpVSSnlFZ9UM2cD7wNXGmDwAEfmOR6JSbpGeGMu/9xbR1GIlIqzr/nfVDc1U1jYxrL/2Z3FWemIsP14xjnO1TZytaWTxmEStzVNKKeVVnX3jfw44BWwWkadEZAmgnRv83HXTU3hh10mntv3HhwXcNneEewMKUP1jIsgY3FcTPaWUUl7XYbJnjHndGHMDMAbYAnwHGCwifxGRKz0Un3Kx9MRYqhtaupwbLqusmvjocAb17d5yQ0oppZTyLV225Rljao0xzxtjVgLDgAPA/e4OTLnPHfNH8tjmPCwdrKpR32Thpd2F3erbp5RSSinf1K2J04wxlcaYv+pyaf4tJjKMm2YN50/v5l60tmtTi5U/rM/mnkXphOqUBEoppZTf0w5FQWrMkH40tVj51ZosxoZaMcZwpKSaV/YWcedlo0jUBdaVUkqpgKDJXhCbOCyekQkxPPTvEoo25pI+uC8/u3qcrg+plFJKBRCvfKuLyAAR2Sgix+z/9u9gu6UikiMieSJyf5vHfyEiJSJywH5b7rnoA0vfqHAWpoTz3SszuWbSUE30lFJKqQDjrW/2+4FNxpgMYBMOBnyISCjwGLAMGAfcJCLj2mzyiDFmsv22zhNBK6WUUkr5G28le6uAZ+1/Pwt8xsE2M4E8Y0y+MaYJeMm+n1JKKaWUcpK3kr3BxpgyAPu/iQ62SQaK2twvtj/W6l4ROSQiz3TUDKyUUkopFeyk/dQbLjuwyLvAEAdP/Rh41hgT32bbc8aYTyVsInIdcJUx5iv2+7cAM40x3xCRwcBZwAC/ApKMMV/uII47gTsBBg0aNO2VV17p9WsLNDU1NcTGxno7DJ+iZeKYlotjWi6OablcTMvEMS0XxxYtWrTPGDO9t8dx22hcY8zlHT0nIqdFJMkYUyYiSUC5g82KgZQ294cBpfZjn25zrKeANZ3E8STwJEBmZqZZuHBhd15GUNiyZQtaLp+mZeKYlotjWi6OablcTMvEMS0X9/JWM+5q4Db737cBbzrYZg+QISIjRSQCuNG+H/YEsdW1wBE3xqqUUkop5be8Nc/e74FXROQOoBC4DkBEhgJPG2OWG2NaRORe4B0gFHjGGPOxff8HRGQytmbcAuAuD8evlFJKKeUXvJLsGWMqgCUOHi8Flre5vw64aFoVY8wtbg1QKaWUUipA6Ay6SimllFIBTJM9pZRSSqkApsmeUkoppVQA02RPKaWUUiqAabKnlFJKKRXANNlTSimllApgmuwppZRSSgUwTfaUUkoppQKYJntKKaWUUgFMkz2llFJKqQCmyZ5SSimlVADTZE8ppZRSKoBpsqeUUkopFcA02VNKKaWUCmCa7CmllFJKBTBN9pRSSimlApgme0oppZRSAUyTPaWUUkqpACbGGG/H4DEicgHI8XYcPigBOOvtIHyMloljWi6Oabk4puVyMS0Tx7RcHMs0xvTt7UHCXBGJH8kxxkz3dhC+RkT2arl8mpaJY1oujmm5OKblcjEtE8e0XBwTkb2uOI424yqllFJKBTBN9pRSSimlAliwJXtPejsAH6XlcjEtE8e0XBzTcnFMy+ViWiaOabk45pJyCaoBGkoppZRSwSbYavaUUkoppYJKQCR7IrJURHJEJE9E7nfwvIjIo/bnD4nIVGf39WdOlMvN9vI4JCLbRWRSm+cKROSwiBxw1WggX+FEuSwUkSr7az8gIj9zdl9/5kS5/KBNmRwREYuIDLA/F5DvFxF5RkTKReRIB88H67Wlq3IJumuLE2USrNeVrsol6K4rACKSIiKbRSRLRD4WkW852MZ11xdjjF/fgFDgODAKiAAOAuPabbMceBsQYDawy9l9/fXmZLnMBfrb/17WWi72+wVAgrdfh5fKZSGwpif7+uutu68NuBp4LwjeL5cBU4EjHTwfdNcWJ8slGK8tXZVJ0F1XnCmXdtsGxXXF/tqSgKn2v/sCue7MXQKhZm8mkGeMyTfGNAEvAavabbMKeM7Y7ATiRSTJyX39VZevzRiz3Rhzzn53JzDMwzF6Q2/+z4P6/dLOTcCLHonMi4wx24DKTjYJxmtLl+USjNcWJ94rHQnq90o7QXFdATDGlBlj9tv/vgBkAcntNnPZ9SUQkr1koKjN/WIuLrCOtnFmX3/V3dd2B7ZfEK0MsEFE9onInW6Iz1ucLZc5InJQRN4WkUu6ua8/cvq1iUg0sBR4tc3Dgfp+6UowXlu6K1iuLc4ItuuK04L5uiIiI4ApwK52T7ns+hIIK2iIg8faDzHuaBtn9vVXTr82EVmE7YI8v83D84wxpSKSCGwUkWz7LzR/50y57AdSjTE1IrIceAPIcHJff9Wd13Y18KExpu2v9UB9v3QlGK8tTguya0tXgvG60h1BeV0RkVhsCe63jTHV7Z92sEuPri+BULNXDKS0uT8MKHVyG2f29VdOvTYRmQg8DawyxlS0Pm6MKbX/Ww68jq3aOBB0WS7GmGpjTI3973VAuIgkOLOvH+vOa7uRdk0tAfx+6UowXlucEoTXlk4F6XWlO4LuuiIi4dgSveeNMa852MRl15dASPb2ABkiMlJEIrC9YVa322Y1cKt9ZMtsoMoYU+bkvv6qy9cmIsOB14BbjDG5bR6PEZG+rX8DVwIOR1L5IWfKZYiIiP3vmdg+JxXO7OvHnHptIhIHLADebPNYIL9fuhKM15YuBem1pVNBel1xSjBeV+zvhb8BWcaYhzvYzGXXF79vxjXGtIjIvcA72EaoPGOM+VhEvmZ//glgHbZRLXlAHXB7Z/t64WW4nJPl8jNgIPC4/RrUYmwLUQ8GXrc/Fga8YIxZ74WX4XJOlsvngbtFpAWoB240tiFQwf5+AbgW2GCMqW2ze8C+X0TkRWyjKBNEpBj4ORAOwXttAafKJeiuLU6USdBdV8CpcoEgu67YzQNuAQ6LyAH7Y/8DDAfXX190BQ2llFJKqQAWCM24SimllFKqA5rsKaWUUkoFME32lFJKKaUCmCZ7SimllFIBTJM9pZRSSqkApsmeUiroiMhAETlgv50SkRL73zUi8ribzvltEbm1k+dXisgv3XFupVRw06lXlFJBTUR+AdQYYx504znCsC2XNdUY09LBNmLfZp4xps5dsSilgo/W7CmllJ2ILBSRNfa/fyEiz4rIBhEpEJHPisgDInJYRNbblzpCRKaJyFaxLdb+jogkOTj0YmB/a6InIt8UkaMickhEXgKwT7C7BVjpkRerlAoamuwppVTH0oAVwCrgX8BmY8wEbCsgrLAnfH8GPm+MmQY8A/zGwXHmAfva3L8fmGKMmQh8rc3je4FLXf4qlFJBze+XS1NKKTd62xjTLCKHsS1L1Lpc02FgBJAJjAc22pd1CgXKHBwnCchqc/8Q8LyIvAG80ebxcmCo68JXSilN9pRSqjONAMYYq4g0m/92crZiu34K8LExZk4Xx6kHotrcXwFcBlwD/FRELrE38UbZt1VKKZfRZlyllOq5HGCQiMwBEJFwEbnEwXZZQLp9mxAgxRizGbgPiAdi7duNBo64O2ilVHDRZE8ppXrIGNMEfB74g4gcBA4Acx1s+ja2mjywNfX+y940/BHwiDHmvP25RcBad8aslAo+OvWKUkp5gIi8DtxnjDnWwfODgReMMUs8G5lSKtBpsqeUUh4gIpnAYGPMtg6enwE0G2MOeDQwpVTA02RPKaWUUiqAaZ89pZRSSqkApsmeUkoppVQA02RPKaWUUiqAabKnlFJKKRXANNlTSimllApgmuwppZRSSgWw/w+iMq6IEm988QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Cálculo dos deslocamentos por superposição modal\n",
    "\n",
    "# Mass division must be a matrix operation...\n",
    "ak1 = MRPy(np.dot(np.diag(1/Mk1), Fk1), fs=Fk1.fs)\n",
    "\n",
    "# ... and now solving\n",
    "uk1 = ak1.sdof_Duhamel(fk1, zk1)             # modal space solution\n",
    "uN1 = MRPy(np.dot(Phi1, uk1), fs=uk1.fs)     # back to nodal solution\n",
    "\n",
    "# Resultado no domínio do tempo\n",
    "f4  = uN1.plot_time(4, figsize=(10,5), axis_t=[0, uN1.Td, -0.08, 0.08])\n",
    "\n",
    "# Resultado no domínio da frequência (para confirmar picos)\n",
    "f5  = uN1.plot_freq(5, figsize=(10,5), axis_f=[0, 10, 0, 0.001])\n",
    "\n",
    "up1 = uN1.max(axis=1)\n",
    "print('Deslocamento de pico da massa 1 é {0:6.4f}m'.format(up1[0]))\n",
    "print('Deslocamento de pico da massa 2 é {0:6.4f}m'.format(up1[1]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Método 2: por condições iniciais (carga como impulso de Dirac)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mode 1 with phase -0.00rad and amplitude -0.0527m\n",
      "Mode 2 with phase  0.00rad and amplitude  0.0304m\n"
     ]
    }
   ],
   "source": [
    "I0  = 2*F0*Td/3                         # impulse is ∫F(t)dt...\n",
    "v   = I0/m                              # ... which is converted to a initial velocity\n",
    "\n",
    "u0  = np.array([[0., 0.]]).T            # column vector with the initial displacements\n",
    "v0  = np.array([[v,  0.]]).T            # column vector with the initial velocities\n",
    "\n",
    "qMu = np.dot(np.dot(Phi1.T, M1), u0)\n",
    "qMv = np.dot(np.dot(Phi1.T, M1), v0)\n",
    "\n",
    "thk = np.zeros_like(Mk1)                # phase angles to be calculated\n",
    "u0k = np.zeros_like(Mk1)                # modal response amplitude to be calculated\n",
    "\n",
    "for k in range(2):\n",
    "\n",
    "# If there are initial displacements only\n",
    "#   thk[k] = -np.pi/2\n",
    "#   u0k[k] =  qMu[k]/Mk1[k]/np.sin(thk[k])\n",
    "\n",
    "# If there are initial velocities only\n",
    "    thk[k] =  np.arctan(wk1[k]*qMu[k]/qMv[k])\n",
    "    u0k[k] =  qMv[k]/Mk1[k]/np.cos(thk[k])/wk1[k]\n",
    "\n",
    "    print('Mode {0} with phase {1:5.2f}rad and amplitude {2:7.4f}m'.format(k+1, thk[k], u0k[k]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Deslocamento de pico da massa 1 é 0.0577m\n",
      "Deslocamento de pico da massa 2 é 0.0579m\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Build the modal responses as harmonic functions with given properties\n",
    "uk  = MRPy.harmonic(NX=2, N=N, fs=F1.fs, X0=u0k, f0=fk1, phi=thk)\n",
    "\n",
    "# Calculate the NODAL responses superposing all modal responses\n",
    "uN = MRPy(np.dot(Phi1, uk), fs=F1.fs)\n",
    "\n",
    "f6  = uN.plot_time(6, figsize=(10,5), axis_t=[0, uN.Td, -0.08, 0.08])\n",
    "\n",
    "up  = uN.max(axis=1)\n",
    "print('Deslocamento de pico da massa 1 é {0:6.4f}m'.format(up[0]))\n",
    "print('Deslocamento de pico da massa 2 é {0:6.4f}m'.format(up[1]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observa-se que a hipótese de aproximação como carga impulsiva é muito ruim, pois para o segundo modo:\n",
    "\n",
    "$$\\frac{t_{\\rm d}}{T_{\\rm n}} = 0.1{\\rm s} \\times 6.16{\\rm Hz} = 0.616$$\n",
    "\n",
    "e este valor é bem maior que o valor de 25% recomendado como limite para a aproximação. Além disso, deve-se considerar que a solução acima não considera o amortecimento.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 3\n",
    "\n",
    "Todos os elementos do pórtico elástico linear tem rigidez à flexão \n",
    "$EI = 6.5{\\rm kN m^2}$ e massa por unidade de comprimento $\\mu = 20{\\rm kg/m}$.\n",
    "Viga e colunas tem o mesmo comprimento $L = 4{\\rm m}$.\n",
    "O amortecimento do sistema é $\\zeta = 0.01$ (razão do crítico).\n",
    "A aceleração da gravidade no local é $g = 9.81{\\rm m/s^2}$.\n",
    "\n",
    "<img src=\"resources/tests/PEC00025A_221_P2_Q3.jpg\" alt=\"Question 3\" width=\"480px\"/>  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Proponha funções adequadas para representar uma geometria deformada que aproxime o\n",
    "primeiro modo de vibração e estime a frequência fundamental de vibração livre através \n",
    "do quociente de Rayleigh. Lembre que as energias totais serão computadas somando-se\n",
    "a contribuição dos três elementos estruturais.\n",
    "_(Sugere-se o uso do software Ftool para o cálculo da energia interna de deformação.)_\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solução\n",
    "\n",
    "Fazendo-se o cálculo da estrutura acima no Ftool tem-se a seguinte deformada:\n",
    "\n",
    "<img src=\"resources/tests/PEC00025A_221_P2_Q3_Ftool.png\" alt=\"Análise pelo Ftool\" width=\"360px\"/>  \n",
    "\n",
    "Os deslocamentos nos nós superiores, calculados com o Ftool com uma carga estática $F = 1{\\rm kN}$, são:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "uA =  0.590      # deslocamento da extremidade superior esquerda (m)\n",
    "uB =  uA         # deslocamento da extremidade superior direita (m)\n",
    "\n",
    "θA = -0.0894     # rotação da extremidade superior esquerda (rad)\n",
    "θB = -0.0887     # rotação da extremidade superior direita (rad)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estes valores podem ser interpolados utilizando as funções de interpolação dadas em aula, para termos uma expressão analítica para a linha elástica, com a qual pode-se calcular a energia de deformação e a energia cinética de referência.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dados do problema\n",
    "L  = 4.           # comprimento das barras (m)\n",
    "EI = 6500.        # rigidez à flexão (Nm2)\n",
    "μ  = 20.          # massa por unidade de comprimento (kg/m)\n",
    "F  = 1000.        # carga estática arbitrária aplicada (N)\n",
    "\n",
    "# Discretização do comprimento das barras\n",
    "x  = np.linspace(0, L, 200)\n",
    "dx = L/200\n",
    "\n",
    "# Lambda functions para interpolação dos deslocamentos\n",
    "phi = []\n",
    "phi.append(lambda xi:  1 - 3*xi*xi + 2*xi*xi*xi)\n",
    "phi.append(lambda xi:  L*(xi - 2*xi*xi + xi*xi*xi))\n",
    "phi.append(lambda xi:  3*xi*xi - 2*xi*xi*xi)\n",
    "phi.append(lambda xi:  L*(-xi*xi + xi*xi*xi ))\n",
    "\n",
    "# Lambda functions para interpolação das curvaturas\n",
    "phixx = []\n",
    "phixx.append(lambda xi: (-6 + 12*xi)/L/L) \n",
    "phixx.append(lambda xi: (-4 +  6*xi)/L  ) \n",
    "phixx.append(lambda xi: ( 6 - 12*xi)/L/L) \n",
    "phixx.append(lambda xi: (-2 +  6*xi)/L  ) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Deslocamentos interpolados para as três barras\n",
    "\n",
    "# coluna da esquerda (x de baixo pra cima)\n",
    "w1 =  0*phi[0](x/L) +  0*phi[1](x/L) + uA*phi[2](x/L) - θA*phi[3](x/L)\n",
    "# viga superior (x da esquerda para direita)\n",
    "w2 =  0*phi[0](x/L) + θA*phi[1](x/L) +  0*phi[2](x/L) + θB*phi[3](x/L)\n",
    "# coluna direita (x de baixo pra cima)\n",
    "w3 =  0*phi[0](x/L) +  0*phi[1](x/L) + uB*phi[2](x/L) - θB*phi[3](x/L)\n",
    "\n",
    "f7 = plt.figure(7, figsize=(5,5))\n",
    "s  = 2   # escala das deformações\n",
    "\n",
    "plt.plot(s*w1, x, 'b', s*uA + x, L + s*w2, 'b', L + s*w3, x, 'b')\n",
    "plt.axis('equal')\n",
    "plt.grid(True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esse conjunto de linhas deformadas será utilizado como forma modal para o cálculo da respectiva frequência natural\n",
    "de vibração livre através do quociente de Rayleigh.\n",
    "\n",
    "Observe que além dos deslocamentos transversais a cada barra, tem-se\n",
    "também o deslocamento da viga para a direita, que representa a maior\n",
    "parte da energia cinética do sistema!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A energia cinética de referência é 22.58 J/m.\n",
      "A massa da viga para a direita representa 61.7%.\n"
     ]
    }
   ],
   "source": [
    "# Energia cinética de referência\n",
    "\n",
    "# Deslocamento da viga para a direita!\n",
    "Tv = μ*L*(uA**2)/2     \n",
    "\n",
    "# Deslocamentos transversais das três barras\n",
    "Tr = Tv + μ*(np.trapz(w1**2 + w2**2 + w3**2, dx=dx))/2\n",
    "\n",
    "print('A energia cinética de referência é {0:4.2f} J/m.'.format(Tr))\n",
    "print('A massa da viga para a direita representa {0:3.1f}%.'.format(100*Tv/Tr))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A energia potencial elástica pode ser calculada pelo trabalho da força externa:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A energia potencial elástica é 295.0 J.\n"
     ]
    }
   ],
   "source": [
    "# Trabalho da força externa\n",
    "V  = F*uA/2\n",
    "\n",
    "print('A energia potencial elástica é {0:4.1f} J.'.format(V))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "E finalmente o cálculo pelo quociente de Rayleigh:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A frequência fundamental do pórtico é menor que 0.575 Hz.\n"
     ]
    }
   ],
   "source": [
    "fn = np.sqrt(V/Tr)/(2*np.pi)\n",
    "\n",
    "print('A frequência fundamental do pórtico é menor que {0:5.3f} Hz.'.format(fn))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O cálculo da energia potencial elástica também pode ser feito pela curvatura:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A energia potencial elástica é 295.5 J.\n"
     ]
    }
   ],
   "source": [
    "# Curvaturas\n",
    "\n",
    "w1xx =  0*phixx[0](x/L) +  0*phixx[1](x/L) + uA*phixx[2](x/L) - θA*phixx[3](x/L)\n",
    "w2xx =  0*phixx[0](x/L) + θA*phixx[1](x/L) +  0*phixx[2](x/L) + θB*phixx[3](x/L)\n",
    "w3xx =  0*phixx[0](x/L) +  0*phixx[1](x/L) + uB*phixx[2](x/L) - θB*phixx[3](x/L)\n",
    "\n",
    "V    = EI*(np.trapz(w1xx**2 + w2xx**2 + w3xx**2, dx=dx))/2\n",
    "\n",
    "print('A energia potencial elástica é {0:4.1f} J.'.format(V))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Que resulta muito próximo do valor calculado pelo trabalho das forças externas, respeitando portanto a conservação de energia."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 4\n",
    "\n",
    "O topo do pórtico é submetido a uma força horizontal estocástica, $F(t)$, com densidade \n",
    "espectral $S_F(f)$, ilustrada abaixo. A força tem média zero e valor r.m.s. \n",
    "$\\sigma_F = 50{\\rm N}$. A banda de frequências excitada é definida por $r = 10$\n",
    "(eixo das frequências em hertz). \n",
    "\n",
    "<img src=\"resources/tests/PEC00025A_221_P2_Q4.jpg\" alt=\"Question 4\" width=\"420px\"/>  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estime o valor r.m.s. e o valor de pico do deslocamento horizontal $u(t)$ na\n",
    "extremidade esquerda da viga. Calcule a correspondente _força estática equivalente_.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solução\n",
    "\n",
    "Inicialmente vamos calcular as propriedades modais no primeiro \n",
    "(e único) modo de vibração que foi estimado. Neste caso, a \n",
    "configuração deformada aproxima a forma modal, cuja escala vamos\n",
    "manter com o deslocamento horizontal $u_A$ na extremidade esquerda \n",
    "da viga.\n",
    "\n",
    "Definida essa escala para a forma modal, a massa modal iguala \n",
    "a energia cinética de referência sem o fator 1/2.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Massa modal:            45.2 kg.\n",
      "Rigidez modal:         590.0 N/m.\n",
      "Deslocamento estático: 0.590 m.\n"
     ]
    }
   ],
   "source": [
    "# Cálculo das propriedades modais\n",
    "\n",
    "Mk = 2*Tr\n",
    "wk = 2*np.pi*fn\n",
    "Kk = wk*wk*Mk\n",
    "zk = 0.01\n",
    "\n",
    "# Deslocamento estático a partir da rigidez modal\n",
    "Fk = 1000*uA      # força modal\n",
    "uk = Fk/Kk        # deslocamento estático modal\n",
    "ue = uA*uk        # deslocamento nodal\n",
    "\n",
    "print('Massa modal:           {0:5.1f} kg.'.format(Mk))\n",
    "print('Rigidez modal:         {0:4.1f} N/m.'.format(Kk))\n",
    "print('Deslocamento estático: {0:5.3f} m.'.format(ue))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A força (definida pelo espectro) é aplicada na extremidade\n",
    "esquerda da viga, na horizontal, onde o deslocamento na forma\n",
    "modal tem amplitude $u_A$. Portanto o espectro da força modal é:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Amplitude r.m.s. pela integral do espectro é 50.0 N.\n",
      "\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "M  =  4097             # discretização do domínio da frequência\n",
    "σF =  50               # valor r.m.s. da força\n",
    "r  =  10.\n",
    "f  =  np.linspace(0, 2*r, M)\n",
    "fs =  2*f[-1]\n",
    "\n",
    "SF =  np.zeros_like(f)\n",
    "\n",
    "SF[f > 1/r] = (σF**2)/(2*np.log(r))*(1/f[f > 1/r])\n",
    "SF[f < 1/r] =  0.\n",
    "SF[f >  r ] =  0.\n",
    "\n",
    "sF2 =  np.trapz(SF, f)\n",
    "sF  =  np.sqrt(sF2)\n",
    "\n",
    "print('Amplitude r.m.s. pela integral do espectro é {0:4.1f} N.\\n'.format(sF))\n",
    "\n",
    "SFk = uA*uA*SF      # espectro da força modal Fk(t)\n",
    "\n",
    "plt.figure(3, figsize=(8,4), clear=True)\n",
    "plt.semilogy(f, SFk);\n",
    "plt.grid(True)\n",
    "plt.axis([0, 1.2*r, 1e01, 1e04])\n",
    "plt.xlabel('Frequência (Hz)')\n",
    "plt.ylabel('Espectro da força modal [N²/Hz]');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Uma vez definido o espectro da força modal, podemos calcular a \n",
    "resposta modal no domínio da frequência.\n",
    "\n",
    "O espectro do deslocamento NODAL (extremidade esquerda da viga)\n",
    "é obtido multiplicando-se o espectro do deslocamento MODAL por \n",
    "$u_A^2$, da mesma forma como foi feito para a força modal.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Hf2 =  lambda fi: 1/( (1 - (fi/fn)**2)**2 + (2*zk*(fi/fn))**2 )/(Kk**2)\n",
    "\n",
    "SU  =  uA*uA*Hf2(f)*SFk\n",
    "\n",
    "plt.figure(4, figsize=(8,4), clear=True)\n",
    "plt.semilogy(f, SU);\n",
    "plt.grid(True)\n",
    "plt.axis([0, 1.2*r, 1e-10, 1e02])\n",
    "plt.xlabel('Frequência (Hz)')\n",
    "plt.ylabel('Espectro do deslocamento [m²/Hz]');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finalmente, faz-se a análise estatística da resposta em deslocamento\n",
    "a partir do espectro.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fator de pico da resposta em deslocamento é      2.87.\n",
      "Amplitude r.m.s. da resposta em deslocamento é  123mm.\n",
      "Valor de pico da resposta em deslocamento é     353mm.\n"
     ]
    }
   ],
   "source": [
    "sU2 =  np.trapz(    SU, f)\n",
    "sU4 =  np.trapz(f*f*SU, f)\n",
    "\n",
    "nu  =  np.sqrt(sU4/sU2)\n",
    "lnu =  np.sqrt(2*np.log(60*nu))  # Tempo de excitação é 60 segundos!\n",
    "g   =  lnu + 0.5772/lnu\n",
    "\n",
    "sU  =  np.sqrt(sU2)\n",
    "up  =  g*sU\n",
    "\n",
    "print('Fator de pico da resposta em deslocamento é    {0:6.2f}.'.format(g))\n",
    "print('Amplitude r.m.s. da resposta em deslocamento é {0:4.0f}mm.'.format(1000*sU))\n",
    "print('Valor de pico da resposta em deslocamento é    {0:4.0f}mm.'.format(1000*up))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos usar a rigidez aparente da análise do Ftool para \n",
    "calcular a força estática equivalente. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Força estática equivalente é 598.2N.\n"
     ]
    }
   ],
   "source": [
    "k   = 1000/uA\n",
    "Feq = up*k\n",
    "\n",
    "print('Força estática equivalente é {0:4.1f}N.'.format(Feq))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}