{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Vibration Absorbers
(without damping)

\n", "\n", "

MCHE 485: Mechanical Vibrations

\n", "

Dr. Joshua Vaughan
\n", "joshua.vaughan@louisiana.edu
\n", "http://www.ucs.louisiana.edu/~jev9637/

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

\n", "\t\"
\n", " Figure 1: An Undamped Vibration Absorber System\n", "


\n", "\n", "This notebook demonstrates the analysis of a vibration absorber system like the one shown in Figure 1. The $m_2$ subsystem has been added to the system with hopes of limiting the vibration of $m_1$. For this system, to limit the vibration of $m_1$, the second mass, $m_2$, and second spring, $k_2$, must be chosen such that:\n", "\n", "$ \\quad \\frac{k_2}{m_2} = \\frac{k_1}{m_2} $\n", "\n", "Let's analyze the responses of $m_1$ and $m_2$ when this condition holds. The equations of motion for the system are:\n", "\n", "$ \\quad m_1 \\ddot{x}_1 + (k_1+k_2)x_1 - k_2 x_2 = f $\n", "\n", "$ \\quad m_2 \\ddot{x}_2 -k_2 x_1 + k_2x_2 = 0 $\n", "\n", "We could also write this equation in matrix form:\n", "\n", "$ \\quad \\begin{bmatrix}m_1 & 0 \\\\ 0 & m_2\\end{bmatrix}\\begin{bmatrix}\\ddot{x}_1 \\\\ \\ddot{x}_2\\end{bmatrix} + \\begin{bmatrix}k_1 + k_2 & -k_2 \\\\ -k_2 & \\hphantom{-}k_2\\end{bmatrix}\\begin{bmatrix}x_1 \\\\ x_2\\end{bmatrix} = \\begin{bmatrix}f \\\\ 0\\end{bmatrix}$\n", "\n", "Define\n", "\n", "$ \\quad M = \\begin{bmatrix}m_1 & 0 \\\\ 0 & m_2\\end{bmatrix} $\n", "\n", "and \n", "\n", "$ \\quad K = \\begin{bmatrix}k_1 + k_2 & -k_2 \\\\ -k_2 & \\hphantom{-}k_2\\end{bmatrix} $.\n", "\n", "Using $M$ and $K$, we want to solve:\n", "\n", "$ \\quad \\left[K - \\omega^2 M\\right]\\bar{X} = \\bar{F} $ \n", "\n", "for $\\bar{X}$. To do so, we need to take the inverse of $\\left[K - \\omega^2 M\\right]$.\n", "\n", "$ \\quad \\bar{X} = \\left[K - \\omega^2 M\\right]^{-1}\\bar{F} $ \n", "\n", "For information on how to obtain these equations, you can see the lectures at the [class website](http://www.ucs.louisiana.edu/~jev9637/MCHE485.html).\n", "\n", "We'll use the numpy tools to solve this problem and examine the response of this vibration absorber system." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "\n", "# We'll use the scipy version of the linear algebra\n", "from scipy import linalg\n", "\n", "# Import the ODE solver for our time response analysis\n", "from scipy.integrate import odeint " ] }, { "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 matrices - We'll use the values from the book example\n", "m1 = 100.0\n", "m2 = 10.0\n", "\n", "k1 = 900.0 \n", "k2 = 90.0\n", "\n", "M = np.array([[m1, 0],\n", " [0, m2]])\n", "\n", "K = np.array([[k1 + k2, -k2],\n", " [-k2, k2]])" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "F1 = 1.0\n", "F2 = 0.0\n", "\n", "F = [F1, F2]\n", "\n", "w = np.linspace(0,6,1200)\n", "X = np.zeros((len(w),2))\n", "\n", "# This is (K-w^2 M)^-1 * (w^2*F)\n", "for ii, freq in enumerate(w):\n", " X[ii,:] = np.dot(linalg.inv(K - freq**2 * M), F)\n", "\n", "# Let's mask the discontinuity, so it isn't plotted\n", "pos = np.where(np.abs(X[:,0]) >= 0.25)\n", "X[pos,:] = np.nan\n", "w[pos] = np.nan" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, 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jftitJiyuKoK5ZqYuJfcYAICVl8+3eHkL2WR2SNHlyNIyVbr8yMaVuRYp7yGb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QAAAB\nXUlEQVQf2Gjg2pOoNZyt2++smT11fHMV3ozQsYjHwv2y7GtQ87dhPytz/tlG58R8L4O9zGK/T+Z1\njZvHrd/HAte+avx1JDTuROi9GsHm3moK4J8BuNrA9qtm3FjgPYnsEYZaX7QtfcV48GjFQ1QVhBBS\nZETkArxg7LC2wCbVSRGRcQBf1AwtGcwM4KiqRs3alYJ2eI2kvWA6khBC7jDBYnOTghvNEoABgHqr\nGc+ZgK50mFToKLxGs4SUAgZhhBByBzFB0oVALd5ziFgokAYTiJ2NWdPXcqjXOiNtCxFCCgfTkYSQ\nwmMaiPYDOKq1rXdakkBq9SS81zSoquEFAYSQNoAzYYSQwmI6uCtqLRJOmSCmlbGrPY/A6wvGAIyQ\nNoUzYYQQQgghOcCZMEIIIYSQHGAQRgghhBCSAwzCCCGEEEJygEEYIYQQQkgOMAgjhBBCCMkBBmGE\nEEIIITnw/wEUzeiCiMG11gAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Set the plot size - 3x2 aspect ratio is best\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", "\n", "# Change the axis units to CMU Serif\n", "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n", "\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "# Turn on the plot grid and set appropriate linestyle and color\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "# Define the X and Y axis labels\n", "plt.xlabel('Frequency (rad/s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel('Amplitude',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "\n", "plt.plot(w,X[:,0],linewidth=2,label=r'$\\bar{x}_1$')\n", "plt.plot(w,X[:,1],linewidth=2,linestyle=\"--\",label=r'$\\bar{x}_2$')\n", "\n", "# uncomment below and set limits if needed\n", "plt.xlim(1.5,4.5)\n", "plt.ylim(-0.11,0.10)\n", "\n", "# Create the legend, then fix the fontsize\n", "leg = plt.legend(loc='upper right', fancybox=True)\n", "ltext = leg.get_texts()\n", "plt.setp(ltext,family='serif',fontsize=16)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5)\n", "\n", "# save the figure as a high-res pdf in the current folder\n", "# plt.savefig('Vibration_Absorber.pdf')\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We could also plot the magnitude of the response" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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cgCYdMPlnyJ4GTXM3aBmwnfoXdtaqCNcDqId1qh6pU9kcIDs7AeRPgzrUrHFk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the magnitude of the response\n", "\n", "# Set the plot size - 3x2 aspect ratio is best\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", "\n", "# Change the axis units to CMU Serif\n", "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n", "\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "# Turn on the plot grid and set appropriate linestyle and color\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "# Define the X and Y axis labels\n", "plt.xlabel('Frequency (rad/s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel('Magnitude',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "\n", "plt.plot(w,np.abs(X[:,0]),linewidth=2,label=r'$|\\bar{x}_1|$')\n", "plt.plot(w,np.abs(X[:,1]),linewidth=2,linestyle=\"--\",label=r'$|\\bar{x}_2|$')\n", "\n", "# uncomment below and set limits if needed\n", "plt.xlim(1.4,4.5)\n", "plt.ylim(-0.01,0.1)\n", "\n", "# Create the legend, then fix the fontsize\n", "leg = plt.legend(loc='upper right', fancybox=True)\n", "ltext = leg.get_texts()\n", "plt.setp(ltext,family='serif',fontsize=16)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5)\n", "\n", "# save the figure as a high-res pdf in the current folder\n", "# plt.savefig('Vibration_Absorber_Magnitude.pdf')\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Now, let's look at using a smaller $m_2$ and $k_2$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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jWlHP1hX5JXBfiISJtRzJ+5yk/uKdW5vVgmUNWtHpfOq+5QvvWoqC1JEvpAfA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\n+8gBNDSoapmVw6aOP9vh7cbx6kJpi38omwX8PW0ZlUu4Mie5IzryQpw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Redefine the matrices with the new parameters\n", "m1 = 100.0\n", "m2 = 3.0\n", "\n", "k1 = 900.0 \n", "k2 = 27.0\n", "\n", "M = np.asarray([[m1, 0],\n", " [0, m2]])\n", "\n", "K = np.asarray([[k1 + k2, -k2],\n", " [-k2, k2]])\n", "\n", "F1 = 1.0\n", "F2 = 0.0\n", "\n", "F = [F1,F2]\n", "\n", "w = np.linspace(0,6,1200)\n", "X = np.zeros((len(w),2))\n", "\n", "for ii, freq in enumerate(w):\n", "\tX[ii,:] = np.dot(linalg.inv(K - freq**2 * M), F)\n", "\n", "# Let's mask the discontinuity, so it isn't plotted\n", "pos = np.where(np.abs(X[:,0]) >= 0.25)\n", "X[pos,:] = np.nan\n", "w[pos] = np.nan\n", "\n", "\n", "\n", "# Set the plot size - 3x2 aspect ratio is best\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", "\n", "# Change the axis units to CMU Serif\n", "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n", "\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "# Turn on the plot grid and set appropriate linestyle and color\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "# Define the X and Y axis labels\n", "plt.xlabel('Frequency (rad/s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel('Amplitude',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "\n", "plt.plot(w,X[:,0],linewidth=2,label=r'$\\bar{x}_1$')\n", "plt.plot(w,X[:,1],linewidth=2,linestyle=\"--\",label=r'$\\bar{x}_2$')\n", "\n", "# uncomment below and set limits if needed\n", "plt.xlim(1.5,4.5)\n", "plt.ylim(-0.11,0.10)\n", "\n", "# Create the legend, then fix the fontsize\n", "leg = plt.legend(loc='upper right', fancybox=True)\n", "ltext = leg.get_texts()\n", "plt.setp(ltext,family='serif',fontsize=16)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5)\n", "\n", "# save the figure as a high-res pdf in the current folder\n", "# plt.savefig('Vibration_Absorber_SmallerM2K2.pdf')\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the two natural frequencies are closer together than the previous case. This leads to a smaller range over which there is low vibration in $x_1$. \n", "\n", "The amplitude of $x_2$ is also increased from the previous case.\n", "\n", "We could again plot the magnitude of the response." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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GgnxkrfSctRPnpzA1m8Gx02MaLXUGB02jhmjKF3HWfCSdTgdtQuQQTfXDWlMN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot the magnitude of the response\n", "\n", "# Set the plot size - 3x2 aspect ratio is best\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", "\n", "# Change the axis units to CMU Serif\n", "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n", "\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "# Turn on the plot grid and set appropriate linestyle and color\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "# Define the X and Y axis labels\n", "plt.xlabel('Frequency (rad/s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel('Magnitude',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "\n", "plt.plot(w,np.abs(X[:,0]),linewidth=2,label=r'$|\\bar{x}_1|$')\n", "plt.plot(w,np.abs(X[:,1]),linewidth=2,linestyle=\"--\",label=r'$|\\bar{x}_2|$')\n", "\n", "# uncomment below and set limits if needed\n", "plt.xlim(1.4,4.5)\n", "plt.ylim(-0.01,0.1)\n", "\n", "# Create the legend, then fix the fontsize\n", "leg = plt.legend(loc='upper right', fancybox=True)\n", "ltext = leg.get_texts()\n", "plt.setp(ltext,family='serif',fontsize=16)\n", "\n", "# Adjust the page layout filling the page using the new tight_layout command\n", "plt.tight_layout(pad=0.5)\n", "\n", "# save the figure as a high-res pdf in the current folder\n", "# plt.savefig('Vibration_Absorber_Magnitude.pdf')\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Time Response\n", "Let's take a look at the time response to confirm this phenomenon. To do so, we'll have to represent our equations of motion as a system of first order ODEs, rather than two second-order ODEs. This is the beginning of putting the equations into state space form.\n", "\n", "Define a state vector $\\mathbf{w} = \\left[x \\quad \\dot{x_1} \\quad x_2 \\quad \\dot{x_2}\\right]^T $\n", "\n", "*Note*: We'll most often see the state space form writen as:\n", "\n", "$ \\quad \\dot{w} = Aw + Bu $\n", "\n", "where $x$ is the state vector, $A$ is the state transition matrix, $B$ is the input matrix, and $u$ is the input. We'll use w here and in the code to avoid confusion with our state $x$, the position of $m_1$.\n", "\n", "To begin, let's write the two equations of motion as:\n", "\n", "$ \\quad \\ddot{x}_1 = \\frac{1}{m_1} \\left(-(k_1 + k_2)x_1 + k_2 x_2 + f \\right)$\n", "\n", "$ \\quad \\ddot{x}_2 = \\frac{1}{m_2} \\left(k_2 x_1 - k_2 x_2 \\right)$\n", "\n", "After some algebra and using the state vector defined above, we can write our equations of motion as:\n", "\n", "$ \\quad \\dot{\\mathbf{w}} = \\begin{bmatrix}0 & 1 & 0 & 0\\\\ -\\frac{k_1 + k_2}{m_1} & 0 & \\frac{k_2}{m_1} & 0 \\\\ 0 & 0 & 0 & 1 \\\\ \\frac{k_2}{m_2} & 0 & -\\frac{k_2}{m_2} & 0 \\end{bmatrix}\\mathbf{w} + \\begin{bmatrix}0 \\\\ \\frac{1}{m_1} \\\\ 0 \\\\ 0 \\end{bmatrix} f $\n", "\n", "Now, let's write this in a way that our ODE solver can use it." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Define the equations of motion\n", "\n", "# Define the system as a series of 1st order ODEs (beginnings of state-space form)\n", "def eq_of_motion(w, t, p):\n", " \"\"\"\n", " Defines the differential equations for the coupled spring-mass system.\n", "\n", " Arguments:\n", " w : vector of the state variables:\n", " w = [x1, x1_dot, x2, x2_dot]\n", " t : time\n", " p : vector of the parameters:\n", " p = [m1, m2, k1, k2, wf]\n", " \"\"\"\n", " \n", " x1, x1_dot, x2, x2_dot = w\n", " m1, m2, k1, k2, wf = p\n", "\n", " # Create sysODE = (x1', x1_dot', x2', x2_dot')\n", " sysODE = [x1_dot,\n", " (-(k1 + k2) * x1 + k2 * x2 + f(t, p)) / m1,\n", " x2_dot,\n", " (k2 * x1 - k2 * x2) / m2]\n", " \n", " return sysODE\n", "\n", "\n", "# Define the forcing function\n", "def f(t, p):\n", " \"\"\" \n", " Defines the forcing function\n", " \n", " Arguments:\n", " t : time\n", " p : vector of the parameters:\n", " p = [m1, m2, k1, k2, wf]\n", " \n", " Returns:\n", " f : forcing function at current timestep\n", " \"\"\"\n", " \n", " m1, m2, k1, k2, wf = p\n", " \n", " # Uncomment below for no force input - use for initial condition response\n", " #f = 0.0 \n", " \n", " # Uncomment below for sinusoidal forcing input at frequency wf rad/s\n", " f = 10 * np.sin(wf * t)\n", " \n", " return f" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Set up simulation parameters \n", "\n", "# ODE solver parameters\n", "abserr = 1.0e-9\n", "relerr = 1.0e-9\n", "max_step = 0.01\n", "stoptime = 100.0\n", "numpoints = 10001\n", "\n", "# Create the time samples for the output of the ODE solver\n", "t = np.linspace(0.0, stoptime, numpoints)\n", "\n", "# Initial conditions\n", "x1_init = 0.0 # initial position\n", "x1_dot_init = 0.0 # initial velocity\n", "x2_init = 0.0 # initial angle\n", "x2_dot_init = 0.0 # initial angular velocity\n", "\n", "wf = np.sqrt(k1 / m1) # forcing function frequency\n", "\n", "# Pack the parameters and initial conditions into arrays \n", "p = [m1, m2, k1, k2, wf]\n", "x0 = [x1_init, x1_dot_init, x2_init, x2_dot_init]" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Call the ODE solver.\n", "resp = odeint(eq_of_motion, x0, t, args=(p,), atol=abserr, rtol=relerr, hmax=max_step)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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Qkz2lFHc++Bqu/vZzcE9aw1U0G+Bz3hysIneupGU5nZ2dZg8hYfzBMG77ycv4wTMHNLfR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\nHLt375auxb79+8HzPA7Vt+Dr7zbGfD/brv5Ig+nv31fTiihPsau6RdIic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pr5lRewp3pg+65tXgFd29/zQkpDQ1Nak+hIQx5yA5PcyffLUVv3nzRCoPyZFs0D0d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\nAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Set the plot size - 3x2 aspect ratio is best\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", "\n", "# Change the axis units to serif\n", "plt.setp(ax.get_ymajorticklabels(),family='serif',fontsize=18)\n", "plt.setp(ax.get_xmajorticklabels(),family='serif',fontsize=18)\n", "\n", "ax.spines['right'].set_color('none')\n", "ax.spines['top'].set_color('none')\n", "\n", "ax.xaxis.set_ticks_position('bottom')\n", "ax.yaxis.set_ticks_position('left')\n", "\n", "# Turn on the plot grid and set appropriate linestyle and color\n", "ax.grid(True,linestyle=':',color='0.75')\n", "ax.set_axisbelow(True)\n", "\n", "# Define the X and Y axis labels\n", "plt.xlabel('Time (s)',family='serif',fontsize=22,weight='bold',labelpad=5)\n", "plt.ylabel('Position (m)',family='serif',fontsize=22,weight='bold',labelpad=10)\n", "\n", "plt.plot(t, resp[:,0],linewidth=2,label=r'$x_1$')\n", "plt.plot(t, resp[:,2],linewidth=2,linestyle=\"--\",label=r'$x_2$')\n", "\n", "# uncomment below and set limits if needed\n", "# plt.xlim(0,5)\n", "plt.ylim(-1,1)\n", "\n", "\n", "# Create the legend, then fix the fontsize\n", "leg = plt.legend(loc='upper right', ncol=2, 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", "# save the figure as a high-res pdf in the current folder\n", "# It's saved at the original 6x4 size\n", "# plt.savefig('Undamped_VibAbsorber_TimeResponse.pdf')\n", "\n", "fig.set_size_inches(9,6) # Resize the figure for better display in the notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Wait... It's *NOT* a Vibration Absorber?!?!?\n", "Remember that our frequency domain analysis assumes steady-state responses. In this simulation, that is not the case. We have some *transient* oscillation that occurs as our system transitions from rest to being forced according to $f(t)$. If the system has no damping, like this one, then this transient response never decays.\n", "\n", "Notice, however, that the ampliude of $x(t)$ is bounded. It would not be without the attached mass, $m_2$. We're forcing at the original $m_1,k_1$ subystem's natural frequency, so it would grow to inifinity." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "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": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 13, "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 }