{
 "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 (2021/1): multiple d.o.f. and continuous 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 12h de amanhã, 01 de junho de 2021.\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 scipy.linalg as sc\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from MRPy import *\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 1\n",
    "\n",
    "<img src=\"resources/tests/PEC00025A_211_P2_Q1.jpg\" alt=\"Question 1\" width=\"640px\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dados do problema:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "H  =  3.             # altura de cada pavimento (m)\n",
    "M  =  10000.         # massa de cada pavimento (kg)\n",
    "f1 =  1.             # frequência fundamental (Hz)\n",
    "zt =  0.01           # amortecimento modal (adim., mesma nos dois modos)\n",
    "g  =  9.81           # aceleração da gravidade (m/s^2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Função para cálculo dos modos de vibração:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vibration_modes(K, M):\n",
    "\n",
    "# 1. Uses scipy to solve the standard eigenvalue problem\n",
    "    w2, Phi = sc.eig(K, M)\n",
    "\n",
    "# 2. Ensure ascending order of eigenvalues\n",
    "    iw  = w2.argsort()\n",
    "    w2  = w2[iw]\n",
    "    Phi = Phi[:,iw]\n",
    "\n",
    "# 3. Eigenvalues to vibration frequencies\n",
    "    wk  = np.sqrt(np.real(w2)) \n",
    "    fk  = wk/2/np.pi\n",
    "\n",
    "# 4. Mass matrix normalization\n",
    "    Mk = np.diag(np.dot(Phi.T, np.dot(M, Phi)))\n",
    "    \n",
    "    for k in range(len(wk)):\n",
    "        Phi[:,k] = Phi[:,k]/np.sqrt(Mk[k])\n",
    "            \n",
    "# 5. Return results\n",
    "    return fk, wk, Phi\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Monta matrizes e calcula modos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rigidez individual de cada barra:  516.8kN/m.\n",
      "Frequência no primeiro modo:        1.00Hz.\n",
      "Frequência no segundo modo:         2.62Hz.\n"
     ]
    }
   ],
   "source": [
    "K  =  1.00                               # rigidez de cada coluna (incógnita)\n",
    "\n",
    "KG =  K*np.array([[2, -2], [-2, 4]])     # rigidez global\n",
    "MG =  M*np.array([[1,  0], [ 0, 1]])     # massa global\n",
    "\n",
    "fk, wk, Phi = vibration_modes(KG, MG)\n",
    "\n",
    "K  = (f1/fk[0])**2                       # determina a rigidez correta\n",
    "fk =  fk*np.sqrt(K)                      # calcula todas as frequências\n",
    "wk =  fk*2*np.pi                         # em rad/s\n",
    "\n",
    "print('Rigidez individual de cada barra: {0:6.1f}kN/m.'.format(K/1000))\n",
    "print('Frequência no primeiro modo:      {0:6.2f}Hz.'.format(fk[0]))\n",
    "print('Frequência no segundo modo:       {0:6.2f}Hz.'.format(fk[1]))\n",
    "\n",
    "#print(wk)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualiza modos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1, figsize=(12,8))\n",
    "\n",
    "x = H*np.arange(3)\n",
    "\n",
    "for k in range(2):\n",
    "    qk = np.zeros(3)\n",
    "    qk[1:] = Phi[::-1,k]\n",
    "    qk /= np.max(np.abs(qk))   # adjust scale for unity amplitude\n",
    "    \n",
    "    plt.subplot(1,2,k+1)\n",
    "    plt.plot(qk, x, 'bo')\n",
    "    plt.plot(qk, x)\n",
    "    \n",
    "    plt.xlim(-1.5, 1.5);  plt.ylabel(str(k+1));\n",
    "    plt.ylim( 0.0, 7.0);\n",
    "    plt.title('fk = {0:4.2f}Hz'.format(fk[k]));\n",
    "    plt.grid(True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 2\n",
    "\n",
    "<img src=\"resources/tests/PEC00025A_211_P2_Q2.jpg\" alt=\"Question 2\" width=\"640px\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A excitação tem mesma amplitude nas frequências de 0.5 e 3Hz. Para usar as amplificações dinâmicas, vamos admitir que o pico das respostas modais poderão estar em fase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Máximo deslocamento no pavimento superior: 0.0398m.\n"
     ]
    }
   ],
   "source": [
    "FG  =  0.1*g*np.diag(MG).reshape(2,1)                     # amplitude das forças nos pavimentos\n",
    "Fk  =  np.matmul(Phi.T, FG)                               # amplitude das forças modais\n",
    "\n",
    "Mk  =  np.diag(np.dot(Phi.T, np.dot(MG, Phi)))            # massas modais\n",
    "Kk  =  wk*wk*Mk                                           # rigidezes modais\n",
    "uk  =  np.empty(2)                                        # aloca memória para respostas modais\n",
    "\n",
    "for k, fn in enumerate(fk):\n",
    "    \n",
    "    bt    = [0.5, 3.0]/fn                                 # frequências componentes da excitação\n",
    "    AD    =  np.sqrt(1/((1 - bt**2)**2 + (2*zt*bt)**2))   # respectivas amplificações dinâmicas\n",
    "    uk[k] = (Fk[k]/Kk[k])*np.sum(AD)                      # pico da resposta modal amplificada\n",
    "    \n",
    "u = np.matmul(Phi,uk)\n",
    "\n",
    "print('Máximo deslocamento no pavimento superior: {0:6.4f}m.'.format(u[0]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O mesmo cálculo agora por simulação, integrando por Fourier através do módulo ``MRPy``:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "Td  =  32.\n",
    "N   =  1024\n",
    "\n",
    "t   =  np.linspace(0, Td, N)                              # domínio do tempo\n",
    "F   =  FG*(np.sin(np.pi*t) + np.sin(6*np.pi*t))           # força dinâmica\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calcula forças modais e resolve equações de equilíbrio desacopladas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Máximo deslocamento no pavimento superior: 0.0388m.\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": [
    "Fk =  MRPy(np.matmul(Phi.T, F), Td=Td)                    # cria objeto MRPy\n",
    "\n",
    "for k in range(2):\n",
    "    Fk[k,:] /= Mk[k]                                      # prepara para solução\n",
    "\n",
    "uk =  Fk.sdof_Fourier(fk, zt)                             # calcula respostas modais\n",
    "u  =  np.matmul(Phi,uk)                                   # deslocamento nos pavimentos\n",
    "\n",
    "print('Máximo deslocamento no pavimento superior: {0:6.4f}m.'.format(u[0,:].max()))\n",
    "\n",
    "u.plot_time(1, figsize=(10,5));\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A diferença dos dois resultados se deve a que o pico das respostas modais não está perfeitamente em fase. \n",
    "Portanto a solução numérica, que é a mais precisa, apresenta amplitude ligeiramente menor.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 3\n",
    "\n",
    "<img src=\"resources/tests/PEC00025A_211_P2_Q3.jpg\" alt=\"Question 3\" width=\"640px\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Primeiro vamos calcular a resposta exata, aplicando as condições de contorno na solução geral:\n",
    "\n",
    "$$ \\varphi(x) = C_1 \\left(\\cos px + \\cosh px \\right) + \n",
    "                C_2 \\left(\\cos px - \\cosh px \\right) + \n",
    "                C_3 \\left(\\sin px + \\sinh px \\right) + \n",
    "                C_4 \\left(\\sin px - \\sinh px \\right) $$  \n",
    "\n",
    "onde:\n",
    "\n",
    "$$ p^4 = \\left(\\frac{\\mu}{EI}\\right) \\omega^2 $$\n",
    "\n",
    "As condições de contorno são:\n",
    "\n",
    "\\begin{align*}\n",
    " \\varphi(0)                      &= 0 \\\\\n",
    " \\varphi^{\\prime\\prime}(0)       &= 0 \\\\\n",
    " \\varphi^{\\prime}(L)             &= 0 \\\\\n",
    " \\varphi^{\\prime\\prime\\prime}(L) &= 0\n",
    "\\end{align*}\n",
    "\n",
    "Aplicando essas condições na solução geral temos, para $x = 0$:\n",
    "\n",
    "\\begin{align*}\n",
    "\\varphi(0)                &=  C_1 \\left( 1 + 1 \\right) + \n",
    "                              C_2 \\left( 1 - 1 \\right) + \n",
    "                              C_3 \\left( 0 + 0 \\right) + \n",
    "                              C_4 \\left( 0 - 0 \\right) = 0 \\\\\n",
    "\\varphi^{\\prime\\prime}(0) &=  C_1 \\left(-1 + 1 \\right) + \n",
    "                              C_2 \\left(-1 - 1 \\right) + \n",
    "                              C_3 \\left(-0 + 0 \\right) + \n",
    "                              C_4 \\left(-0 - 0 \\right) = 0\n",
    "\\end{align*}\n",
    "\n",
    "Portanto $C_1 = 0$ e $C_2 = 0$. Por outro lado, para $x = L$:\n",
    "                              \n",
    "\\begin{align*}                              \n",
    "\\varphi^\\prime(L)               &= C_3 \\left( \\cos pL + \\cosh pL \\right) + \n",
    "                                   C_4 \\left( \\cos pL - \\cosh pL \\right) = 0 \\\\\n",
    "\\varphi^{\\prime\\prime\\prime}(L) &= C_3 \\left(-\\cos pL + \\cosh pL \\right) + \n",
    "                                   C_4 \\left(-\\cos pL - \\cosh pL \\right) = 0\n",
    "\\end{align*}\n",
    "\n",
    "Colocando as equações acima em forma matricial temos:\n",
    "\n",
    "$$ \\left[ \\begin{array}{cc}\n",
    "                 \\left( \\cos pL + \\cosh pL \\right) & \\left( \\cos pL - \\cosh pL \\right) \\\\\n",
    "                 \\left(-\\cos pL + \\cosh pL \\right) & \\left(-\\cos pL - \\cosh pL \\right) \n",
    "          \\end{array} \\right] \n",
    " \\left[ \\begin{array}{c}\n",
    "                  C_3 \\\\\n",
    "                  C_4 \n",
    "        \\end{array} \\right]  =                \n",
    " \\left[ \\begin{array}{c}\n",
    "                  0 \\\\\n",
    "                  0 \n",
    "        \\end{array} \\right] $$\n",
    "\n",
    "Fazendo o determinante da matrix de coeficientes igual a zero temos as frequência naturais.\n",
    "Estas frequências podem ser calculadas numericamente, como mostrado abaixo.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cantilever beam frequency parameter is 1.570796...\n"
     ]
    }
   ],
   "source": [
    "def char_eq(x):\n",
    "    \n",
    "    x = x[0]\n",
    "    A = np.array([[ np.cos(x)+np.cosh(x),  np.cos(x)-np.cosh(x)], \n",
    "                  [-np.cos(x)+np.cosh(x), -np.cos(x)-np.cosh(x)]])\n",
    " \n",
    "    return np.linalg.det(A)\n",
    "\n",
    "#-----------------------------------------------------------------------\n",
    "\n",
    "from scipy.optimize import fsolve\n",
    "\n",
    "p = fsolve(char_eq, 1.0)\n",
    "\n",
    "print('Cantilever beam frequency parameter is {0:8.6f}...'.format(p[0]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ou seja, o parâmetro de frequência parece ser $\\pi/2$ e a frequência fundamental resulta:\n",
    "\n",
    "$$ \\omega_1 = \\left(\\frac{\\pi}{2L} \\right)^2 \\sqrt{\\frac{EI}{\\mu}} $$\n",
    "\n",
    "que coerentemente corresponde à frequência fundamental de uma viga bi-apoiada com vão $2L$. \n",
    "Isso está correto já que a condição de apoio da direita equivale a uma condição de simetria para uma viga com o \n",
    "dobro do vão!\n",
    "\n",
    "Agora vamos refazer o cálculo propondo a seguinte função aproximada para a forma modal:\n",
    "\n",
    "$$ \\varphi(x) = \\frac{1}{L^2}\\left( 2Lx - x^2 \\right) $$\n",
    "\n",
    "ou seja, uma parábola que apresenta derivada nula para $x = L$, e portanto respeita _algumas_ condições de contorno. A escala desta forma modal é intencionalmente escolhida como sendo unitária. As derivadas dessa forma modal aproximada são:\n",
    "\n",
    "\\begin{align*}\n",
    " \\varphi^{\\prime}(x)       &=  (2L - 2x)\\,/L^2 \\\\\n",
    " \\varphi^{\\prime\\prime}(x) &=  -2\\,/L^2\n",
    "\\end{align*}\n",
    "\n",
    "Observa-se que a função proposta não cumpre a condição de momento nulo na extremidade da esquerda, mas vamos em frente.\n",
    "A correspondente energia cinética de referência é:\n",
    "\n",
    "$$ T_{\\rm ref} = \\frac{1}{2} \\int_0^L {\\mu \\varphi ^2(x) \\, dx} \n",
    "               = \\frac{4}{15} \\, \\mu L   $$\n",
    "\n",
    "enquanto a energia potencial elástica resulta:\n",
    "\n",
    "$$ V = \\frac{1}{2} \\int_0^L {EI \\left[ \\varphi^{\\prime\\prime}(x) \\right] ^2 \\, dx}\n",
    "     = \\frac{2EI}{L^3}  $$\n",
    "\n",
    "Portanto o quociente de Rayleigh resulta:\n",
    "\n",
    "$$ \\omega_1 = \\sqrt{\\frac{V}{T_{\\rm ref}}}\n",
    "            = \\sqrt{\\frac{2EI \\cdot 15}{4\\mu L^4}} \n",
    "            = \\left(\\frac{120^{1/4}}{2L} \\right)^2 \\sqrt{\\frac{EI}{\\mu}} $$\n",
    "\n",
    "onde $120^{1/4} \\approx 3.31$ e portanto esse valor apresenta um erro de aproximadamente 5.4%, esperado em relação ao valor correto, $\\pi$, e um erro de aproximadamente 11% em relação à \n",
    "frequência correta. \n",
    "Observe que o quociente de Rayleigh sempre fornece frequência igual ou maior que a exata.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Questão 4\n",
    "\n",
    "<img src=\"resources/tests/PEC00025A_211_P2_Q4.jpg\" alt=\"Question 4\" width=\"640px\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dados do problema:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "L  =  6.             # comprimento da viga (m)\n",
    "m  =  80.            # massa da pessoa (kg)\n",
    "mu =  200.           # massa por unidade de comprimento (kg/m)\n",
    "EI =  36.e6          # rigidez à flexão (Nm^2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos considerar a resposta apenas no primeiro modo. A dissipação de energia por amortecimento\n",
    "é desprezada e a energia total do sistema deve se manter constante e igual à a energia potencial \n",
    "gravitacional da pessoa no início da queda:\n",
    "\n",
    "$$ E = mgh = 784.8{\\rm J}$$\n",
    "\n",
    "Por questão de simplicidade, admite-se que a viga já está deformada por peso próprio quando se \n",
    "determina a altura de queda da pessoa. Também vamos considerar que o choque é perfeitamente inelástico, \n",
    "ou seja, a viga e a pessoa seguem unidos após o contato.\n",
    "\n",
    "Observe que forma modal proposta é normalizada pela unidade, de modo que ela tem valor unitário na \n",
    "extremidade da direita, $\\varphi(L) = 1$. \n",
    "Desta forma, deslocamento vertical e deslocamento modal tem mesmo valor numérico\n",
    "no ponto B.\n",
    "\n",
    "A energia cinética total do sistema após o choque é calculada como:\n",
    "\n",
    "$$ T = \\frac{1}{2} \\int_0^L {\\mu \\left[ v_0 \\varphi(x) \\right]^2 \\, dx}\n",
    "     + \\frac{1}{2} m\\left[ v_0 \\varphi(L) \\right] ^2  = 360v_0^2$$\n",
    "\n",
    "onde $v_0$ é a velocidade inicial da extremidade direita da viga logo após o choque, que é numericamente\n",
    "igual à velocidade inicial no espaço modal. Igualando-se as energias, $E = T$, chega-se a:\n",
    "\n",
    "$$ v_0 = \\sqrt{\\frac{784.8}{360}} \\approx 1.48{\\rm m/s}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A frequência natural no primeiro modo precisa ser re-calculada, pois agora a viga tem também a massa\n",
    "da pessoa incorporada na extremidade direita. A nova energia cinética de referência é:\n",
    "\n",
    "$$ T_{\\rm ref} = \\frac{1}{2} \\int_0^L {\\mu \\varphi^2(x) \\, dx} + \\frac{1}{2} m \\varphi^2(L)  = 360 $$\n",
    "\n",
    "A energia potencial elástica, $V$, permanece a mesma e, portanto, a frequência natural resulta menor:\n",
    "\n",
    "$$ \\omega_{\\rm n} = \\sqrt{\\frac{V}{T_{\\rm ref}}}\n",
    "                  = \\sqrt{\\frac{2\\cdot 36\\times 10^6}{360 \\cdot 6^3}} \\approx 30.42{\\rm rad/s} $$\n",
    "\n",
    "Sem a massa da pessoa incorporada, a frequência natural calculada na seção anterior seria de $32.27{\\rm rad/s}$.\n",
    "\n",
    "A amplitude total do delocamento modal é a soma da amplitude devida à velocidade inicial \n",
    "com o deslocamento  devido à carga impulsiva. \n",
    "Dada a escala unitária da forma modal, a força modal tem o mesmo módulo da força aplicada na \n",
    "extremidade da direita.\n",
    "O formato retangular da carga impulsiva (choque inelástico) implica que o fator de amplificação dinâmica, \n",
    "$A$, da resposta estática, $u_{B, \\rm est}$, é igual a 2. \n",
    "\n",
    "$$ u_{B, \\rm max} = \\frac{v_0}{\\omega_{\\rm n}} + A \\, u_{B, \\rm est} $$\n",
    "\n",
    "Para calcular a resposta estática é necessário conhecer a massa modal:\n",
    "\n",
    "$$ M = \\int_0^L {\\mu \\varphi^2(x) \\, dx} + m \\varphi^2(L) = 720{\\rm kg}$$\n",
    "\n",
    "Lembrando que a rigidez modal é dada por $K = \\omega^2_{\\rm n} M$, a resposta estática é calculada como:\n",
    "\n",
    "$$ u_{B, \\rm est} = \\frac{mg \\varphi(L)}{K} = \\frac{80 \\cdot 9.81 \\cdot 1}{30.42^2 \\cdot 720} \\approx 1.18{\\rm mm}$$ \n",
    "\n",
    "Substituindo valores:\n",
    "\n",
    "$$ u_{B, \\rm max} = \\frac{1.48}{30.42} + 2 \\cdot 0.00118 \\approx  5.1{\\rm cm}$$\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
}