{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1 style=\"text-align:center\">Rotating Imbalance</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/RotatingImbalance.png\" alt=\"A Mass-Spring-Damper System with a Rotating Imbalance\" width=35%/></a><br>\n",
    "    <strong> Figure 1: A Mass-Spring-Damper System with a Rotating Imbalance </strong>\n",
    "</p>\n",
    "\n",
    "This notebook simluates the frequency response of simple mass-spring-damper system with a rotating imblanace, like the one shown in Figure 1.\n",
    "\n",
    "The equation of motion for the system is:\n",
    "\n",
    "$ \\quad \\left(m_1 + m_2\\right) \\ddot{x} + c \\dot{x} + kx = m_2 e \\omega^2 \\cos{\\omega t} $\n",
    "\n",
    "We could also write this equation in terms of the damping ratio, $\\zeta$, and natural frequency, $\\omega_n$, by dividing by $(m_1 + m_2)$.\n",
    "\n",
    "$ \\quad \\ddot{x} + 2\\zeta\\omega_n\\dot{x} + \\omega_n^2x = e \\beta \\omega^2 \\cos{\\omega t}$.\n",
    "\n",
    "where\n",
    "\n",
    "$ \\quad \\beta = \\frac{m_2}{m_1 + m_2} $, $ \\quad \\omega_n^2 = \\frac{k}{m_1 + m_2} $, and $ \\quad 2 \\zeta \\omega_n = \\frac{c}{m_1 + m_2}$.    \n",
    "\n",
    "We can then write the response as:\n",
    "\n",
    "$ \\quad x(t) = \\frac{e \\beta \\omega^2}{\\sqrt{\\left(\\omega_n^2 - \\omega^2\\right)^2 + \\left(2 \\zeta \\omega \\omega_n \\right)^2}} \\cos{\\left(\\omega t - \\phi\\right)}$\n",
    "\n",
    "where\n",
    "\n",
    "$ \\quad \\phi = \\tan^{-1}\\left(\\frac{2 \\zeta \\omega \\omega_n}{\\omega_n^2 - \\omega^2}\\right) $\n",
    "\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\n",
    "\n",
    "# Import the plotting functions \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define the system pararmeters\n",
    "k = 2*(2*np.pi)**2            # Spring constant (N/m)\n",
    "m1 = 1.75                     # Sprung/main mass (kg)\n",
    "m2 = 0.25                     # rotating mass (kg)\n",
    "b = m2/(m1 + m2)              # mass ratio    \n",
    "wn = np.sqrt(k/(m1 + m2))     # natural frequency (rad/s)\n",
    "l = 0.1                       # Eccentricity\n",
    "\n",
    "\n",
    "z = 0.1                       # Damping Ratio\n",
    "c = 2*z*wn*(m1 + m2)          # Select c based on desired amping ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Set up the frequency range\n",
    "w = np.linspace(0,5*wn,2000)            # Freq range, 0-5*wn with 2000 points in-between\n",
    "\n",
    "# Look at undamped case\n",
    "z = 0.0\n",
    "x_mag_un = (l*b*w**2)/np.sqrt((wn**2-w**2)**2+(2*z*w*wn)**2)\n",
    "\n",
    "# Look at z=0.1\n",
    "z = 0.1\n",
    "x_mag_0p1 = (l*b*w**2)/np.sqrt((wn**2-w**2)**2+(2*z*w*wn)**2)\n",
    "\n",
    "# Look at z=0.2\n",
    "z = 0.2\n",
    "x_mag_0p2 = (l*b*w**2)/np.sqrt((wn**2-w**2)**2+(2*z*w*wn)**2)\n",
    "\n",
    "# Look at z=0.4\n",
    "z = 0.4\n",
    "x_mag_0p4 = (l*b*w**2)/np.sqrt((wn**2-w**2)**2+(2*z*w*wn)**2)\n",
    "\n",
    "\n",
    "w = w/wn # Scale frequency so the plot is normalized by the natural frequency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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3xn2fmfGbPm1nTePGKhQWONDk0tYJ9B5JHF5yOEBVVQCA6OnTBvda6CHTNmqR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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11168b978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's plot the magnitude of the frequency response\n",
    "\n",
    "fig = plt.figure(figsize=(6,4))\n",
    "ax = plt.gca()\n",
    "plt.subplots_adjust(bottom=0.17,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",
    "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='0.95')\n",
    "ax.set_axisbelow(True)\n",
    "\n",
    "plt.xlabel(r'Normalized Frequency $(\\Omega)$',family='Serif',fontsize=22,weight='bold',labelpad=5)\n",
    "plt.ylabel(r'Normalized Amp., $\\frac{|x|}{e \\beta}$',family='Serif',fontsize=22,weight='bold',labelpad=10)\n",
    "\n",
    "plt.plot(w,x_mag_un/(l*b),  linewidth=2, linestyle = ':',  label=r'$\\zeta = 0.0$')\n",
    "plt.plot(w,x_mag_0p1/(l*b), linewidth=2, linestyle = '-',  label=r'$\\zeta = 0.1$')\n",
    "plt.plot(w,x_mag_0p2/(l*b), linewidth=2, linestyle = '-.', label=r'$\\zeta = 0.2$')\n",
    "plt.plot(w,x_mag_0p4/(l*b), linewidth=2, linestyle = '--', label=r'$\\zeta = 0.4$')\n",
    "\n",
    "plt.xlim(0,5)\n",
    "plt.ylim(0,7)\n",
    "\n",
    "leg = plt.legend(loc='upper right', fancybox=True)\n",
    "ltext  = leg.get_texts() \n",
    "plt.setp(ltext,family='Serif',fontsize=18)\n",
    "\n",
    "# Adjust the page layout filling the page using the new tight_layout command\n",
    "plt.tight_layout(pad=0.5)\n",
    "\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('RotatingImbalance_Freq_Resp_mag.pdf')\n",
    "\n",
    "fig.set_size_inches(9,6) # 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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "    }\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": 6,
     "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
}