{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 style=\"text-align:center\">Undamped Response to Harmonic Seismic Inputs<br>Transfer Function Form</h1>\n",
    "<h3 style=\"text-align:center\">MCHE 485: Mechanical Vibrations</h3> \n",
    "<p style=\"text-align:center\">Dr. Joshua Vaughan <br>\n",
    "<a href=\"mailto:joshua.vaughan@louisiana.edu\">joshua.vaughan@louisiana.edu</a><br>\n",
    "http://www.ucs.louisiana.edu/~jev9637/   </p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center\">\n",
    "\t<img src=\"http://shared.crawlab.org/MassSpring_Seismic_Horiz.png\" alt=\"A Mass-Spring-Damper System\" width=50%/></a><br>\n",
    "    <strong> Figure 1: A Mass-Spring System </strong>\n",
    "</p>\n",
    "\n",
    "This notebook examines the frequency response of a simple mass-spring system like the one shown in Figure 1. It has a position input, $ y(t) $, that is known to be harmonic connected to the mass, $ m $, via a spring of stiffness $ k $. The position of the mass is defined by $ x(t) $.\n",
    "\n",
    "The equation of motion for the system is:\n",
    "\n",
    "<!-- the \\quad commmand just adds a space in the math mode -->\n",
    "$ \\quad m \\ddot{x} + kx = ky $\n",
    "\n",
    "We could also write this equation in terms of the damping ratio, $\\zeta$, and natural frequency, $\\omega_n$.\n",
    "\n",
    "$ \\quad \\ddot{x} + \\omega_n^2x = \\omega_n^2 y$\n",
    "\n",
    "For information on how to obtain this equation, you can see the lectures at the [class website](http://www.ucs.louisiana.edu/~jev9637/MCHE485.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np              # Grab all of the NumPy functions with nickname np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# We want our plots to be displayed inline, not in a separate window\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import the plotting functions \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the System Parameters\n",
    "m = 1.0                 # kg\n",
    "k = (2.0 * np.pi)**2.      # N/m (Selected to give an undamped natural frequency of 1Hz)\n",
    "wn = np.sqrt(k / m)       # Natural Frequency (rad/s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use the closed-form, steady-state solution we developed in lecture:\n",
    "\n",
    "Assume:\n",
    "\n",
    "$ \\quad y(t) = \\bar{y} \\sin{\\omega t} $\n",
    "\n",
    "Then, the solution $x(t)$ should have the form:\n",
    "\n",
    "$ \\quad x(t) = a \\sin{\\omega t} + b \\cos{\\omega t} $\n",
    "\n",
    "We saw that when we substituted this assumed solution into the equations of motion for this undamped system, the $b$ constant was elimiinated, leaving:\n",
    "\n",
    "$ \\quad x(t) = \\frac{\\omega_n^2}{\\omega_n^2 - \\omega^2}\\bar{y} \\sin{\\omega t} $\n",
    "\n",
    "or \n",
    "\n",
    "$ \\quad x(t) = \\frac{\\omega_n^2}{\\omega_n^2 - \\omega^2} y(t) $\n",
    "\n",
    "So, $ \\frac{\\omega_n^2}{\\omega_n^2 - \\omega^2} $ gives us the relationship between the input $ y(t) $ and the system response $ x(t) $. <br><br>\n",
    "\n",
    "### Transfer Function Form\n",
    "We can then write the transfer function (which represents the \"tranformation\" of the input to the output) as:\n",
    "\n",
    "$ \\quad \\frac{\\mbox{Output}}{\\mbox{Input}} \\equiv \\frac{x(t)}{y(t)} = \\frac{\\omega_n^2}{\\omega_n^2 - \\omega^2} $\n",
    "\n",
    "So our transfer funciton is then:\n",
    "\n",
    "$ \\quad G(\\omega) = \\frac{\\omega_n^2}{\\omega_n^2 - \\omega^2} $\n",
    "\n",
    "We can also normalize this according to $ \\Omega = \\frac{\\omega}{\\omega_n} $:\n",
    "\n",
    "$ \\quad G(\\Omega) = \\frac{1}{1 - \\Omega^2} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Set up input parameters\n",
    "wnorm = np.linspace(0.01,3,1000)            # Frequency range for freq response plot, 0-3x wn with 1000 points in-between\n",
    "\n",
    "TFnorm_amp = (1) / (1 - wnorm**2)\n",
    "\n",
    "# Let's mask the discontinuity, so it isn't plotted\n",
    "pos = np.where(np.abs(TFnorm_amp) >= 50)\n",
    "TFnorm_amp[pos] = np.nan\n",
    "wnorm[pos] = np.nan\n",
    "\n",
    "# Now define the magnitude and phase of this TF\n",
    "TFnorm_mag = np.sqrt(TFnorm_amp**2)\n",
    "TFnorm_phase = -np.arctan2(0,TFnorm_amp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmsAAAGJCAYAAADVKHTwAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nGgAAwIBRrAEAAAzYPzgCsg24NtlDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110eb4a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make the figure pretty, then plot the results\n",
    "#   \"pretty\" parameters selected based on pdf output, not screen output\n",
    "#   Many of these setting could also be made default by the .matplotlibrc file\n",
    "fig = plt.figure(figsize=(6,4))\n",
    "ax = plt.gca()\n",
    "plt.subplots_adjust(bottom=0.23,left=0.15,top=0.96,right=0.96)\n",
    "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n",
    "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "ax.grid(True,linestyle=':',color='0.75')\n",
    "ax.set_axisbelow(True)\n",
    "\n",
    "plt.xlabel(r'Normalized Frequency $\\left(\\Omega = \\frac{\\omega}{\\omega_n}\\right)$',family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel(r'$ |G(\\Omega)| $',family='serif',fontsize=22,weight='bold',labelpad=15)\n",
    "plt.ylim(0.0,5.0)\n",
    "# yticks([0,1])\n",
    "plt.xticks([0,1],['0','$\\Omega = 1$'])\n",
    "\n",
    "plt.plot(wnorm,TFnorm_mag,linewidth=2)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# If you want to save the figure, uncomment the commands below. \n",
    "# The figure will be saved in the same directory as your IPython notebook.\n",
    "# Save the figure as a high-res pdf in the current folder\n",
    "# plt.savefig('MassSpring_SeismicTF_NormAmp.pdf',dpi=300)\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAl0AAAGLCAYAAAD9DSeEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAGrw/wE4h0SwBjsWPAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1199729b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make the figure pretty, then plot the results\n",
    "#   \"pretty\" parameters selected based on pdf output, not screen output\n",
    "#   Many of these setting could also be made default by the .matplotlibrc file\n",
    "fig = plt.figure(figsize=(6,4))\n",
    "ax = plt.gca()\n",
    "plt.subplots_adjust(bottom=0.23,left=0.15,top=0.96,right=0.96)\n",
    "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n",
    "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.xaxis.set_ticks_position('bottom')\n",
    "ax.yaxis.set_ticks_position('left')\n",
    "ax.grid(True,linestyle=':',color='0.75')\n",
    "ax.set_axisbelow(True)\n",
    "\n",
    "plt.xlabel(r'Normalized Frequency $\\left(\\Omega = \\frac{\\omega}{\\omega_n}\\right)$',family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel(r'$ \\phi $ (deg)',family='serif',fontsize=22,weight='bold',labelpad=15)\n",
    "plt.ylim(-200.0,20.0,)\n",
    "plt.yticks([0,-30, -60, -90, -120, -150,-180])\n",
    "plt.xticks([0,1],['0','$\\Omega = 1$'])\n",
    "\n",
    "plt.plot(wnorm,TFnorm_phase*180/np.pi,linewidth=2)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# If you want to save the figure, uncomment the commands below. \n",
    "# The figure will be saved in the same directory as your IPython notebook.\n",
    "# Save the figure as a high-res pdf in the current folder\n",
    "# plt.savefig('MassSpring_SeismicTF_Phase.pdf',dpi=300)\n",
    "\n",
    "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoEAAAKCCAYAAACuxwMWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAACYQBSBAAAAE+j/AbQOX+T/IRLbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1170e9c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's plot the magnitude and phase as subplots, to make it easier to compare\n",
    "\n",
    "# Make the figure pretty, then plot the results\n",
    "#   \"pretty\" parameters selected based on pdf output, not screen output\n",
    "#   Many of these setting could also be made default by the .matplotlibrc file\n",
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex = True, figsize=(8,8))\n",
    "\n",
    "plt.subplots_adjust(bottom=0.12,left=0.17,top=0.96,right=0.96)\n",
    "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n",
    "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n",
    "\n",
    "ax1.spines['right'].set_color('none')\n",
    "ax1.spines['top'].set_color('none')\n",
    "ax1.xaxis.set_ticks_position('bottom')\n",
    "ax1.yaxis.set_ticks_position('left')\n",
    "ax1.grid(True,linestyle=':',color='0.75')\n",
    "ax1.set_axisbelow(True)\n",
    "\n",
    "ax2.spines['right'].set_color('none')\n",
    "ax2.spines['top'].set_color('none')\n",
    "ax2.xaxis.set_ticks_position('bottom')\n",
    "ax2.yaxis.set_ticks_position('left')\n",
    "ax2.grid(True,linestyle=':',color='0.75')\n",
    "ax2.set_axisbelow(True)\n",
    "\n",
    "plt.xlabel(r'Normalized Frequency $\\left(\\Omega = \\frac{\\omega}{\\omega_n}\\right)$',family='serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.xticks([0,1],['0','$\\Omega = 1$'])\n",
    "\n",
    "# Magnitude plot\n",
    "ax1.set_ylabel(r'$ |G(\\Omega)| $',family='serif',fontsize=22,weight='bold',labelpad=40)\n",
    "ax1.plot(wnorm,TFnorm_mag,linewidth=2)\n",
    "ax1.set_ylim(0.0,5.0)\n",
    "ax1.set_yticks([0, 1, 2, 3, 4, 5])\n",
    "ax1.set_yticklabels(['$0$', '$1$', '', '', '', ''])\n",
    "\n",
    "# Phase plot \n",
    "ax2.set_ylabel(r'$ \\phi $ (deg)',family='serif',fontsize=22,weight='bold',labelpad=10)\n",
    "ax2.plot(wnorm,TFnorm_phase*180/np.pi,linewidth=2)\n",
    "ax2.set_ylim(-200.0,20.0,)\n",
    "ax2.set_yticks([0, -90, -180])\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\n",
    "# If you want to save the figure, uncomment the commands below. \n",
    "# The figure will be saved in the same directory as your IPython notebook.\n",
    "# Save the figure as a high-res pdf in the current folder\n",
    "# plt.savefig('MassSpring_SeismicTF.pdf',dpi=300)\n",
    "\n",
    "fig.set_size_inches(9,9) # Resize the figure for better display in the notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr style=\"border: 0px;\n",
    "        height: 1px;\n",
    "        text-align: center;\n",
    "        background: #333;\n",
    "        background-image: -webkit-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:    -moz-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:     -ms-linear-gradient(left, #ccc, #333, #ccc); \n",
    "        background-image:      -o-linear-gradient(left, #ccc, #333, #ccc);\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Licenses\n",
    "Code is licensed under a 3-clause BSD style license. See the licenses/LICENSE.md file.\n",
    "\n",
    "Other content is provided under a [Creative Commons Attribution-NonCommercial 4.0 International License](http://creativecommons.org/licenses/by-nc/4.0/), CC-BY-NC 4.0.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n",
       "\n",
       "<style>\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunsx.otf');\n",
       "        font-weight: bold;\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunsi.otf');\n",
       "        font-style: oblique;\n",
       "    }\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunso.otf');\n",
       "        font-weight: bold;\n",
       "        font-style: oblique;\n",
       "    }\n",
       "\n",
       "    div.cell {\n",
       "        max-width: 1100px;\n",
       "    }\n",
       "    \n",
       "    h1 {\n",
       "        font-family: Computer Modern;\n",
       "    }\n",
       "    \n",
       "    h4 {\n",
       "        margin-top: 12px;\n",
       "        margin-bottom: 3px;\n",
       "    }\n",
       "\n",
       "    div.text_cell_render {\n",
       "        font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "        line-height: 145%;\n",
       "        font-size: 130%;\n",
       "        width: 100%;\n",
       "        max-width: 1100px;\n",
       "    }\n",
       "    \n",
       "    .CodeMirror {\n",
       "        font-family: \"Source Code Pro\", source-code-pro, Consolas, monospace;\n",
       "    }\n",
       "    \n",
       "    .warning {\n",
       "        color: rgb( 240, 20, 20 )\n",
       "    }  \n",
       "  \n",
       "   \n",
       "    hr.style-end {\n",
       "        border: 0px !important;\n",
       "        height: 1px !important;\n",
       "        text-align: center !important;\n",
       "        background: #333 !important;\n",
       "        background-image: -webkit-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:    -moz-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:     -ms-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "        background-image:      -o-linear-gradient(left, #ccc, #333, #ccc) !important; \n",
       "    }\n",
       "\n",
       "    hr.style-end:after {\n",
       "        content: &#x269C !important;\n",
       "        left: 50% !important;\n",
       "        position: absolute !important;\n",
       "        /* Controls the whitespace around the symbol */\n",
       "        padding: 0px !important;\n",
       "        background: #fff !important;\n",
       "    }\n",
       "    \n",
       "/*  Center figures, etc\n",
       "    .ui-wrapper {\n",
       "        margin-left: auto !important;\n",
       "        margin-right: auto !important;\n",
       "    }\n",
       "*/\n",
       "    \n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This cell will just improve the styling of the notebook\n",
    "# You can ignore it, if you are okay with the default sytling\n",
    "from IPython.core.display import HTML\n",
    "import urllib.request\n",
    "response = urllib.request.urlopen(\"https://cl.ly/1B1y452Z1d35\")\n",
    "HTML(response.read().decode(\"utf-8\"))"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}