05 1 DOF_Mov_relat-Animation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Vibrações com excitação harmônica e Movimento relativo - 1 Grau de Liberdade\n",
    " _Prof. Tito Dias Júnior_"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Algumas vezes, a base ou suporte de um sistema de amortecimento de massa-mola sofre movimento harmônico,\n",
    "como mostrado na fig.(a). Seja $y(t)$ o deslocamento da base e $x(t)$ o deslocamento\n",
    "da massa a partir de sua posição de equilíbrio estático no tempo $t$. Então, o alongamento líquido do\n",
    "a mola é $x - y$ e a velocidade relativa entre as duas extremidades do amortecedor é $\\dot{x} - \\dot{y}$. Do diagrama de corpo livre\n",
    "mostrado na fig.(b), obtemos a equação do movimento\n",
    "\n",
    "![image.png](attachment:77a25c20-99eb-4b71-96ca-ff18f2faf68d.png)\n",
    "\n",
    "\n",
    "A equação governante é:\n",
    "\n",
    "$m\\ddot{x} + c (\\dot{x}-\\dot{y}) +k(x-y) = 0$\n",
    "\n",
    "Se $y(t) = Y sen(\\omega t)$, então \n",
    "\n",
    "$m\\ddot{x} + c \\dot{x} + kx = ky + c\\dot{y} = kY sen(\\omega t)+c \\omega Y cos(\\omega t)$, e ainda, podemos escrever\n",
    "\n",
    "$m\\ddot{x} + c \\dot{x} + kx = A sen(\\omega t- \\alpha)$\n",
    "\n",
    "Onde $A = Y \\sqrt{k^2+ (c\\omega)^2}$  e $\\alpha =  tg^{-1} [-c\\omega/k]$\n",
    "\n",
    "A resposta da massa em regime permanente pode, após manipulações algébricas, ser escrita como:\n",
    "\n",
    "$x(t) = X sen(\\omega t-\\phi)$, onde $X$ e $\\phi$ são escritos\n",
    "\n",
    "$$\n",
    "\\frac{X}{Y} = \\left[ \\frac{k^2+(c \\omega)^2}{(k-m\\omega^2)^2+(c \\omega)^2} \\right]^{1/2} = \\left[ \\frac{1+(2 \\zeta r)^2}{(1-r^2)^2+(2 \\zeta r)^2} \\right]^{1/2}\n",
    "$$\n",
    "\n",
    "e\n",
    "$$\n",
    "\\phi = tg^{-1} \\left[ \\frac{2 \\zeta r^3}{1+(4 \\zeta^2-1)r^2} \\right]\n",
    "$$\n",
    "\n",
    "A razão entre a amplitude da massa e da base $X/Y$ é denominada transmissibilidade de deslocamento. E $ r = \\omega/\\omega_n$\n",
    "\n",
    "\n"
   ]
  },
  {
   "attachments": {
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"
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exemplo - Veículo se movendo em uma via acidentada\n",
    "\n",
    "A Figura abaixo mostra um modelo simples de um veículo motorizado que pode vibrar na direção vertical enquanto viajando por uma estrada acidentada. O veículo tem uma massa de 1200 kg. O sistema de suspensão tem uma mola com constante de $400 kN / m$ e uma razão de amortecimento de $\\zeta = 0,5$. Se a velocidade do veículo for de $20 km / h$, determine a amplitude de deslocamento do veículo. A superfície da estrada varia sinusoidalmente com uma amplitude de $Y = 0,05m$ e comprimento de onda de 6 m.\n",
    "\n",
    "![image.png](attachment:e7843297-69b2-46df-87f4-ef6cd5258966.png)\n",
    "\n",
    "![image.png](attachment:dda45b5f-213a-4d6c-bc81-ebccca328f01.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### **Solução**\n",
    "\n",
    "A frequência de excitação $\\omega$ da base pode ser encontrada dividindo a velocidade do veículo ($km/h$) pelo comprimento de onde de um ciclo :\n",
    "\n",
    "$ v= \\frac{\\Delta S}{T}$, mas a $f=\\frac{1}{T}$, substituindo na fórmula anterior, obtemos\n",
    "\n",
    "$ v = f \\times \\Delta S$, e isolando a frequência, $f = v/ \\Delta S$\n",
    "\n",
    "$$\n",
    "\\omega = 2 \\pi f  = 2 \\pi \\left(\\frac{v \\times 1000}{3600} \\right) \\frac{1}{6} = 0,290889 v \\, rad/s\n",
    "$$\n",
    "\n",
    "\n",
    "e para $ v = 20 km/h$, obetmos $\\omega = 5,81778 rad/s$. A frequência natural do veículo é dada por\n",
    "\n",
    "$$\n",
    "\\omega_n = \\sqrt{\\frac{k}{m}} = \\left( \\frac{400 \\times 10^3}{1200} \\right)^{1/2} = 18,2574 \\, rad/s\n",
    "$$\n",
    "\n",
    "e então a razão de frequência $r$ é\n",
    "\n",
    "$$\n",
    "r = \\frac{\\omega}{\\omega_n}= \\frac{5,81778}{18,2574}=0,318653\n",
    "$$\n",
    "\n",
    "A razão de amplitudes pode ser finalmente calculada:\n",
    "\n",
    "$$\n",
    "\\frac{X}{Y} =  \\left[ \\frac{1+(2 \\zeta r)^2}{(1-r^2)^2+(2 \\zeta r)^2} \\right]^{1/2} =  \\left[ \\frac{1+(2 \\times 0,5 \\times 0,318653)^2}{(1-(0,318653^2)^2+(2 \\times 0,5 \\times 0,318653)^2} \\right]^{1/2} = 1,100964\n",
    "$$\n",
    "\n",
    "Assim, a amplitude de deslocamento do veículo é dado por\n",
    "\n",
    "$$\n",
    "X = 1,100964Y = 1,100964 \\times 0,05 = 0,055048 \\, m\n",
    "$$\n",
    "\n",
    "O que indica que uma ondulação de $5cm$ é transmitida como um solavanco de $5,5cm$ para o chassi e para os passageiros do veículo. Nesse caso, os passageiros sentem o movimento amplificado.\n",
    "\n",
    "## Como diminuir esse efeito?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para o programa, vamos precisar do módulo  _scipy_ para a integração e o _pylab_ para plotar os resultados.\n",
    "\n",
    "Inicialmente, vamos definir, como uma função, o sistema de equações que será chamado posteriormente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sistema(w, t, p):\n",
    "    import numpy as nps\n",
    "    \"\"\"\n",
    "    Define o sistema de equações diferenciais para o sistema.\n",
    "\n",
    "    Argumentos:\n",
    "        w :  vetor das variáveis de estado\n",
    "                  w = [x,y]\n",
    "        t :  tempo\n",
    "        p :  vetor de parâmetros conhecidos\n",
    "                  p = [m,k,c]\n",
    "    \"\"\"\n",
    "    x, y = w\n",
    "    m, k, c, Y, omega = p\n",
    "    F0 = Y * nps.sqrt( k**2 + (c*omega)**2 )\n",
    "    # Cria a função f = (x',y'):\n",
    "    f = [y,\n",
    "         (-c * y - k * x + F0*nps.sin(omega*t) ) / m]\n",
    "    return f"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora podemos escrever a parte do programa para efetuar a integração do sistema de EDO:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 360x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "aqui\n"
     ]
    },
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np       # Importa o módulo numpy (métodos numéricos)\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import odeint\n",
    "import matplotlib.animation as animation\n",
    "from matplotlib.patches import Circle\n",
    "\n",
    "# variáveis dos enunciado\n",
    "\n",
    "## Parâmetros da suspensão\n",
    "m = 1200.               # Massa\n",
    "k = 400000.             # Coeficiente de mola\n",
    "zeta = 0.5              # razão de amortecimento viscoso\n",
    "\n",
    "w_n = np.sqrt(k/m)      # Frequência natural\n",
    "c_critico = 2*m*w_n     # Coeficiente de amortecimento crítico\n",
    "\n",
    "c = zeta * c_critico    # Coeficiente de amortecimento\n",
    "L = 6.0                 # Comprimento de onda \n",
    "v = 20.0                # Velocidade do veículo (km/h) \n",
    "\n",
    "## Parâmetros de excitação da base\n",
    "Y = 0.05                                     # Amplitude da força de excitação\n",
    "omega = 2*np.pi*v*1000 / (L*3600)            # Frequência de excitação\n",
    "r = omega/w_n                                # Razão de frequências\n",
    "\n",
    "x0 = 0.0             # Condição inicial para x0\n",
    "y0 = 0.0             # Condição inicial para y0\n",
    "\n",
    "# Parâmetros e critérios de parada do algoritmo de integração ODE\n",
    "abserr = 1.0e-8        # Erro absoluto\n",
    "relerr = 1.0e-6        # Erro relativo\n",
    "stoptime = 10.0        # Tempo final de integração\n",
    "numpoints = 501       # Número de pontos de integração\n",
    "\n",
    "# Cria o vetor com os valores dos tempos de integração para utiliza no plot\n",
    "t = [stoptime * float(i) / (numpoints - 1) for i in range(numpoints)]\n",
    "dt = t[1]-t[0]\n",
    "\n",
    "# Agrupando os parâmetros e condições iniciais par ao algoritmo:\n",
    "p = [m, k, c, Y, omega]\n",
    "w0 = [x0, y0]\n",
    "\n",
    "# Chamada ao algoritmo de integração \n",
    "wsol = odeint(sistema, w0, t, args=(p,),atol=abserr, rtol=relerr)\n",
    "\n",
    "# Separa a solução nos vetores x e y\n",
    "x = wsol[:,0]\n",
    "y = wsol[:,1]\n",
    "\n",
    "\n",
    "F0 = Y * np.sqrt( k**2 + (c*omega)**2 )\n",
    "\n",
    "x1 = x\n",
    "wt = [omega*stoptime * float(i) / (numpoints - 1) for i in range(numpoints)]\n",
    "y1 = Y*np.sin(wt)\n",
    "\n",
    "\n",
    "\n",
    "fig = plt.figure(figsize=(5, 4))\n",
    "ax = fig.add_subplot(111, autoscale_on=False, xlim=(-0.5,0.5), ylim=(-2*Y, 2*Y))\n",
    "ax.set_aspect('equal')\n",
    "ax.grid()\n",
    "\n",
    "line, = ax.plot([], [], 'o-', lw=2, markersize=15)\n",
    "time_template = 'time = %.1fs'\n",
    "time_text = ax.text(0.05, 0.9, '', transform=ax.transAxes)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "def animate(i):\n",
    "    thisx = [0, 0, 0]\n",
    "    thisy = [0,  x1[i], y1[i]]\n",
    "\n",
    "    line.set_data(thisx, thisy)\n",
    "    center = (x1[i], y1[i])\n",
    "   # cir  = plt.Circle(center, 0.1, color='black')\n",
    "    \n",
    "    time_text.set_text(time_template % (i*dt))\n",
    "    return  line, time_text\n",
    "\n",
    "\n",
    "ani = animation.FuncAnimation(\n",
    "    fig, animate, len(wsol), interval=dt*numpoints, blit=True)\n",
    "plt.show()\n",
    "\n",
    "ani.save('final2.mp4')\n",
    "print('aqui')\n",
    "\n",
    "from IPython.display import HTML\n",
    "HTML(ani.to_html5_video())\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print('Frequência Natural = ', w_n)\n",
    "print('Frequência da Base (Hz) = ', omega/(2*np.pi))\n",
    "print('Amplitude de x(t) = ', np.min(x))\n",
    "print('Razão de frequências r = ', r)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# Plotando o resultado\n",
    "plt.figure()         # Define uma figura para plotar\n",
    "                     # Figura é formada por dois subplots\n",
    "\n",
    "plt.subplot(211)     # Primeira forma de solução\n",
    "plt.plot(t,x, label=\"x(t)\")\n",
    "#plt.plot(t,y, label=\"x'(t)\")\n",
    "plt.legend()\n",
    "plt.xlabel('t [s]')\n",
    "plt.ylabel('x(t), y(t)')\n",
    "\n",
    "plt.subplot(212)     # Segunda forma de solução\n",
    "plt.plot(x,y)\n",
    "plt.xlabel('x(t) [m]')\n",
    "plt.ylabel('y(t) [m/s]')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
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   "source": [
    "## Referências"
   ]
  },
  {
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   "metadata": {
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     "slide_type": "fragment"
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   },
   "source": [
    "Kiusalaas, J. (2013). **Numerical Methods in Engineering With Python 3**. Cambridge: Cambridge.<br>\n",
    "S. Rao. (2012) **Vibrações Mecânicas**. Prentice Hall, 4.ª ed. "
   ]
  },
  {
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   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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