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    "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",
    "### Class 18 - Lagrange's equation\n",
    "\n",
    "[1.   The Lagrange's equation](#section_1)  \n",
    "[2.   Example: generic s.d.o.f. system](#section_2)  \n",
    "[3.   Example: generic m.d.o.f. system](#section_3)  \n",
    "[4.   Example: simply supported beam](#section_4)  \n",
    "[4.1. Discrete flexibility and distributed mass](#section_41)  \n",
    "[4.2. Discrete mass and distributed flexibility](#section_42)  \n",
    "[4.3. Distributed mass and distributed flexibility](#section_43)  \n",
    "[5.   Example: nonlinear simple pendulum](#section_5)  \n",
    "[6.   Example: tower with flexible foundation](#section_6)  \n",
    "[7.   Example: nonlinear double pendulum](#section_7)  \n",
    "[8.   Assignments](#section_8)  \n",
    "\n",
    "---\n",
    "_Prof. Marcelo M. Rocha, Dr.techn._ [(ORCID)](https://orcid.org/0000-0001-5640-1020)  \n",
    "_Porto Alegre, RS, Brazil_ \n"
   ]
  },
  {
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   "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",
    "from   scipy.integrate import odeint\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. The Lagrange's equation <a name=\"section_1\"></a> \n"
   ]
  },
  {
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  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Example: generic s.d.o.f. system <a name=\"section_2\"></a> \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
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  },
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   "cell_type": "markdown",
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   "source": [
    "## 3. Example: generic m.d.o.f. system <a name=\"section_3\"></a> \n"
   ]
  },
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   "cell_type": "code",
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    "## 4. Example: simply supported beam <a name=\"section_4\"></a> \n",
    "\n",
    "Now we shall use the Lagrange's equation for solving a simply supported beam, considering\n",
    "three different models:\n",
    "\n",
    "1. Distributed mass and discrete flexibility,\n",
    "2. Distributed flexibility and discrete mass, and\n",
    "3. Distributed mass and distributed flexibility.\n",
    "\n",
    "<img src=\"images/simply_supported_lagrange.png\" alt=\"Simply supported beam\" width=\"360px\"/>\n",
    "\n",
    "The three beam models are useful for illustrating the use of Lagrange's equation with\n",
    "different energy evaluation approaches. At the end, the three solutions may be\n",
    "compared for evaluating the best estimates of discrete parameters $k_\\theta$ and $M$\n",
    "such that the three models give the same beam natural vibration frequency.\n",
    "\n",
    "\n",
    "### 4.1. Distributed mass and discrete flexibility <a name=\"section_41\"></a> \n",
    "\n",
    "For the sake of compatibility with the other two models, we define the generalized coordinate\n",
    "$u$ as being the vertical displacement at beam center. The potential elastic energy\n",
    "depends on the relative rotation, $\\theta$, between the two segments:\n",
    "\n",
    "$$ \\theta = \\arcsin \\left( \\frac{2u}{L}\\right) \\approx \\frac{2u}{L}$$\n",
    "\n",
    "where the small displacements assumption ($\\sin \\beta \\approx \\beta$) has been used. Hence:\n",
    "\n",
    "$$ V = \\frac{1}{2} k_\\theta \\theta^2 \\approx \n",
    "                 \\frac{2 k_\\theta}{L^2} u^2$$\n",
    "\n",
    "The kinetic energy is obtained by integrating the velocities along the two bars:\n",
    "\n",
    "$$ T = 2 \\cdot \\frac{1}{2} \\int_0^{L/2} {\\left( \\dot{r}_x^2 + \\dot{r}_y^2 \\right) \\; \\mu d\\xi} $$\n",
    "\n",
    "with:\n",
    "\n",
    "\\begin{align*}\n",
    " r_x &= \\xi \\cos\\left( \\frac{2u}{L}\\right) \\\\\n",
    " r_y &= \\xi \\sin\\left( \\frac{2u}{L}\\right)\n",
    "\\end{align*}\n",
    "\n",
    "Observe that, without the small displacements assumption, the dummy variable $\\xi$ \n",
    "is a line differential, not the projection in $x$ direction.\n",
    "Corresponding time derivatives are:\n",
    "\n",
    "\\begin{align*}\n",
    "\\dot{r}_x &= \\frac{dr_x}{du} \\; \\frac{du}{dt} =\n",
    "            -\\frac{2\\xi}{L} \\sin\\left( \\frac{2u}{L}\\right) \\, \\dot{u}\n",
    "    \\approx -\\frac{4 u \\dot{u}}{L^2} \\xi \\approx 0 \\\\\n",
    "\\dot{r}_y &= \\frac{dr_y}{du} \\; \\frac{du}{dt} = \n",
    "             \\frac{2\\xi}{L} \\cos\\left( \\frac{2u}{L}\\right) \\, \\dot{u}\n",
    "    \\approx  \\frac{2\\dot{u}}{L} \\xi \\\\\n",
    "\\end{align*}\n",
    "\n",
    "where the small displacements assumption is made ($\\sin \\beta \\approx \\beta$ and\n",
    "$\\cos \\beta \\approx 1$) and the velocity in direction $x$ is\n",
    "neglected. Replacing these results in the kinetic energy yields:\n",
    "\n",
    "$$ T \\approx \\frac{4\\dot{u}^2}{L^2} \\int_0^{L/2} {\\xi^2 \\; \\mu d\\xi}\n",
    "           = \\frac{\\mu L}{6} \\, \\dot{u}^2 $$\n",
    "\n",
    "Now the two terms of Lagrange's equation can be calculated. Firstly the kinectic energy:\n",
    "\n",
    "$$ \\frac{\\partial T}{\\partial \\dot{u}} = \\frac{\\mu L}{3} \\, \\dot{u} $$\n",
    "\n",
    "and then for the potential elastic energy:\n",
    "\n",
    "$$ \\frac{\\partial V}{\\partial u} = \\frac{4 k_\\theta }{L^2} \\, u $$\n",
    "\n",
    "Applying Lagrange's equation gives finally the equilibrium equation:\n",
    "\n",
    "$$ \\frac{\\mu L}{3} \\, \\ddot{u} +  \\frac{4 k_\\theta }{L^2} \\, u = 0 $$\n",
    "\n",
    "which means that the natural vibration frequency is:\n",
    "\n",
    "$$ \\omega_{\\rm n} = \\sqrt{\\frac{12 k_\\theta}{\\mu L^3}} $$\n"
   ]
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    "\n",
    "### 4.2. Distributed flexibility and discrete mass <a name=\"section_42\"></a> \n",
    "\n",
    "In this case we must assume a deflected shape. A good option is the elastic line resulting\n",
    "from a point load at beam center:\n",
    "\n",
    "$$ w(\\xi) = \\frac{P L^3}{12 EI} \\left( \\frac{3}{4} \\xi - \\xi^3 \\right), \n",
    "            \\hspace{1cm} \\xi \\leq \\frac{1}{2} $$\n",
    "            \n",
    "where the variable $\\xi$ is a non-dimensional coordinate, $\\xi = x/L$.\n",
    "This function is valid up to beam center and its symmetry must be accounted for. \n",
    "The assumed shape must be rescaled, such that the displacement at beam center is our generalized\n",
    "coordinate, $u$. The maximumum central deflection from the function above is:\n",
    "\n",
    "$$ w_{\\rm max} = \\frac{P L^3}{48 EI} $$\n",
    "\n",
    "Re-scaling gives:\n",
    "\n",
    "$$ w(\\xi) = 4 u \\left( \\frac{3}{4} \\xi - \\xi^3 \\right), \n",
    "            \\hspace{1cm} \\xi \\leq \\frac{1}{2} $$\n",
    "\n",
    "The rotation and the curvature functions are, respectively:\n",
    "\n",
    "\\begin{align*}\n",
    " w^{\\prime}(\\xi)       &=  \\frac{ 4}{L  } u \\left( \\frac{3}{4} - 3\\xi^2 \\right) \\\\\n",
    " w^{\\prime\\prime}(\\xi) &= -\\frac{24}{L^2} u \\xi \n",
    "\\end{align*}\n",
    "\n",
    "where one must be aware that:\n",
    "\n",
    "$$ \\frac{d}{dx} = \\frac{d}{d\\xi}\\,\\frac{d\\xi}{dx} = \\frac{1}{L} \\, \\frac{d}{d\\xi}$$\n",
    "\n",
    "The potential elastic energy is then given by:\n",
    "\n",
    "$$ V = 2 \\cdot \\frac{1}{2} \\int_{0}^{1/2} {EI \\left[ w^{\\prime\\prime}(\\xi) \\right]^2 \\, L d\\xi}\n",
    "     = \\frac{24 EI}{L^3} \\, u^2 $$\n",
    "\n",
    "On the other hand, the kinetic energy evaluation is straighforward:\n",
    "\n",
    "$$ T = \\frac{1}{2} M\\dot{u}^2 $$\n",
    "\n",
    "Now we calculate the two terms of Lagrange's equation, starting with the kinectic energy:\n",
    "\n",
    "$$ \\frac{\\partial T}{\\partial \\dot{u}} = M \\, \\dot{u} $$\n",
    "\n",
    "and then for the potential elastic energy:\n",
    "\n",
    "$$ \\frac{\\partial V}{\\partial u} = \\frac{48 EI}{L^3} \\, u $$\n",
    "\n",
    "Applying Lagrange's equation gives finally the equilibrium equation:\n",
    "\n",
    "$$ M \\, \\ddot{u} +  \\frac{48 EI}{L^3} \\, u = 0 $$\n",
    "\n",
    "which means that the natural vibration frequency is:\n",
    "\n",
    "$$ \\omega_{\\rm n} = \\sqrt{\\frac{48 EI}{ML^3}} $$\n"
   ]
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    "\n",
    "### 4.3. Distributed mass and distributed flexibility <a name=\"section_43\"></a> \n",
    "\n",
    "Here we assume a half-sine as the deflected shape (that we _know_ to be the right solution):\n",
    "\n",
    "$$ w(\\xi) = u \\sin\\left( \\pi \\xi \\right) $$\n",
    "            \n",
    "The rotation and the curvature functions are, respectively:\n",
    "\n",
    "\\begin{align*}\n",
    " w^{\\prime}(\\xi)       &=  \\frac{\\pi   u}{L  } \\, \\cos \\left(\\pi \\xi \\right) \\\\\n",
    " w^{\\prime\\prime}(\\xi) &= -\\frac{\\pi^2 u}{L^2} \\, \\sin \\left(\\pi \\xi \\right)\n",
    "\\end{align*}\n",
    "\n",
    "The velocity is assumed (small displacements) to have only the vertical component,\n",
    "which is then calculated as:\n",
    "\n",
    "$$ \\dot{w}(\\xi) = \\frac{dw}{du} \\, \\frac{du}{dt} = \\dot{u} \\sin\\left( \\pi \\xi \\right)$$\n",
    "\n",
    "The potential elastic energy is then given by:\n",
    "\n",
    "$$ V = \\frac{1}{2} \\int_{0}^{1} {EI \\left[ w^{\\prime\\prime}(\\xi) \\right]^2 \\; L d\\xi}\n",
    "     = \\frac{\\pi^4 EI}{4 L^3} \\, u^2 $$\n",
    "\n",
    "A comparison with the previous model leads to $\\pi^4/4 \\approx 24$, such\n",
    "that the potential energy for both models are quite close (error is $\\approx 1.5$%)\n",
    "even by using different functions for the deflected shape. \n",
    "Comparison with the discrete flexibility model demands that:\n",
    "\n",
    "$$ \\frac{2 k_\\theta}{L^2} = \\frac{\\pi^4 EI}{4 L^3} $$\n",
    "\n",
    "and consequently the hinge flexibility to match the continuous beam flexibility\n",
    "must be:\n",
    "\n",
    "$$ k_\\theta = \\frac{\\pi^4 EI}{8 L}$$\n",
    "\n",
    "On the other hand, the kinetic energy is given by:\n",
    "\n",
    "$$ T = \\frac{1}{2} \\int_{0}^{1} {\\mu \\left[ \\dot{w}(\\xi) \\right]^2 \\; L d\\xi}\n",
    "     = \\frac{\\mu L}{4} \\, \\dot{u}^2 $$\n",
    "\n",
    "A comparison with the discrete mass model demands that:\n",
    "\n",
    "$$ \\frac{M}{2} = \\frac{\\mu L}{4}$$\n",
    "\n",
    "and consequently the discrete mass must be $M = \\mu L/2$, which is half the total beam mass.\n",
    "\n",
    "Finally, taking derivatives and applying Lagrange's equation gives the equilibrium equation:\n",
    "\n",
    "$$ \\frac{\\mu L}{2} \\, \\ddot{u} +  \\frac{\\pi^4 EI}{2 L^3} \\, u = 0 $$\n",
    "\n",
    "and the natural vibration frequency results as :\n",
    "\n",
    "$$ \\omega_{\\rm n} = \\left( \\frac{\\pi}{L} \\right)^2 \\sqrt{\\frac{EI}{\\mu}} $$\n",
    "\n",
    "which is the _exact_ solution for the first natural frequency of a simply supported beam.\n"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Example: simple pendulum <a name=\"section_5\"></a> \n",
    "\n",
    "\n",
    "<img src=\"images/simple_pendulum.png\" alt=\"Simple pendulum\" width=\"240px\"/>\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Example: tower with flexible foundation <a name=\"section_6\"></a> \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. Example: nonlinear double pendulum <a name=\"section_7\"></a> \n",
    "\n",
    "\n",
    "<img src=\"images/double_pendulum.png\" alt=\"Double pendulum\" width=\"240px\"/>\n",
    "\n",
    "\n",
    "Define $d\\vec{y}/dt$ function:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def double_pendulum(y, t, m1, h1, m2, h2, g):\n",
    "    \n",
    "    th1, w1, th2, w2 = y\n",
    "    \n",
    "    mt  = m1  + m2\n",
    "    dth = th1 - th2\n",
    "    \n",
    "    cd  = np.cos(dth)\n",
    "    sd  = np.sin(dth)\n",
    "    s1  = np.sin(th1)\n",
    "    s2  = np.sin(th2)\n",
    "    \n",
    "    A   = np.array([[mt*h1,    m2*h2*cd], \n",
    "                    [m2*h1*cd, m2*h2  ]])\n",
    "\n",
    "    B   = np.array([-m2*h2*w2*w2*sd - g*mt*s1,\n",
    "                     m2*h1*w1*w1*sd - g*m2*s2])\n",
    "    \n",
    "    a   = np.linalg.solve(A, B)\n",
    "    \n",
    "    return [w1, a[0], w2, a[1]]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Call ```scipy``` for differential equation solution:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x396 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t  =  np.linspace(0, 4, 16384)\n",
    "\n",
    "m1 =  1.0;   h1 = 1.0\n",
    "m2 =  1.5;   h2 = 0.5\n",
    "\n",
    "g  =  9.81\n",
    "\n",
    "Y0 = [np.pi+0.001, 0., np.pi/2, 0.]\n",
    "\n",
    "plt.figure(1, figsize=(12, 5.5), clear=True)\n",
    "\n",
    "for k in range(2):\n",
    "    \n",
    "    Y  =  odeint(double_pendulum, Y0, t, args=(m1, h1, m2, h2, g))\n",
    "\n",
    "    x1 =  h1*np.sin(Y[:,0])\n",
    "    y1 = -h1*np.cos(Y[:,0])\n",
    "\n",
    "    x2 =  x1 + h2*np.sin(Y[:,1])\n",
    "    y2 =  y1 - h2*np.cos(Y[:,1])\n",
    "\n",
    "    plt.subplot(1,2,k+1)\n",
    "    plt.plot(x1,y1, 'r:')\n",
    "    plt.plot(x2,y2, 'b', linewidth=0.5)\n",
    "\n",
    "    plt.xlim(-2, 2);   plt.xlabel('X2 (m)') \n",
    "    plt.ylim(-2, 2);   plt.ylabel('Y2 (m)') \n",
    "    plt.title('Simulation {0}'.format(k+1))\n",
    "\n",
    "    plt.grid(True) \n",
    "    \n",
    "    Y0 = [np.pi+0.002, 0, np.pi/2, 0.]   # repeat with butterfly wing flap\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8. Assignments <a name=\"section_8\"></a> \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}