{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lab 1: Identification of Damping Using Log Decrement" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Interactive iPython tools will not work without IPython.display and ipywidgets installed.\n", "Interactive iPython tools will not work without IPython.display and ipywidgets installed.\n" ] } ], "source": [ "%load_ext autoreload\n", "%autoreload 2\n", "import vibration_toolbox as vtb\n", "from vibration_toolbox import time_plot\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import scipy.io as sio\n", "import math as math" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Beam Properties\n", "---------------------" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "l=21.75*0.0254;# length in meters\n", "h=0.5*0.0254;# height in meters\n", "w=1*0.0254;# width in meters\n", "rho=2700;# density in kg/cubicmeter\n", "E=7.31e10;# youngs modulus in Pa\n", "I = (1/12)*w*h**3; # moment of inertia (m^4)\n", "k = (3*E*I)/l**3; # stiffness (N/m)\n", "V = l*w*h;# volume (m^3)\n", "m = rho*V;# mass (kg)\n", "wn = math.sqrt(k/m) # analytical natural frequency of massless beam with concentrated mass\n", "wn2=(1.875)**(2)*math.sqrt((E*I)/(m*(l)**3)) #natural freqency of a uniform section beam\n", "#c_cr = 2*math.sqrt(k*m); # critical damping coefficient" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "108.259140771331" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wn" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "219.7386705465195" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wn2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Acceleration vs Time plot\n", "------------------------------------" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "<matplotlib.text.Text at 0x7f719edf9438>" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEXCAYAAACtTzM+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDHBBMDOzzAXBzMwAFwQzM8v+A/1SGptdbihpAAAAAElFTkSuQmCC\n", "text/plain": [ "<matplotlib.figure.Figure at 0x7f71a0e2a668>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Acc vs Time\n", "\n", "%matplotlib inline\n", "mat_contents=sio.loadmat('Case1-2.mat')\n", "Time_domain = mat_contents['Time_domain']\n", "Time_chan_2 = mat_contents['Time_chan_2']\n", "Time_chan_2 = Time_chan_2*(9.81);\n", "mean=sum(Time_chan_2)/np.size(Time_chan_2);\n", "Accel = Time_chan_2-mean;\n", "# The acceleration values from Bobcat will be in Gs. So, to convert them to m/s^2,\n", "# we will have to multiply the vector by 9.81\n", "plt.plot(Time_domain, Accel)\n", "plt.grid('on')\n", "plt.ylabel('$Acc(m/s^2)$')\n", "plt.xlabel('$Time(sec)$')\n", "plt.title('$Acc$ versus $Time$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Data Analysis\n", " --------------------" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Enter values from plots for calculations. Use data cursor to\n", "# obtain x and t values.\n", "x1 = 81.45;\n", "t1 = 0.007031;\n", "x2 = 15.44;\n", "t2 = 3.181;\n", "n = 106;\n", "time = t2-t1;\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Log Decrement Method\n", "--------------------------" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.015688941419353057" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d = (1/n)*math.log(x1/x2) # delta\n", "d" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0024969647946533331" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "z= d/np.sqrt(4*math.pi**2+d**2) # zeta\n", "z" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.029943103773584907" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Td = (time/n)#damped time period\n", "Td" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "209.83747559003763" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wd = 2*math.pi/Td #damped natural frequency\n", "wd" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "209.83812974392472" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wne = wd/np.sqrt(1-z**2) # natural frequency in rad/sec\n", "wne" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "21186.684200875719" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k2=(wne**2)*m # one way to use experimental zeta and nat freq to calculate C\n", "k2" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "c_cr = 2*np.sqrt(k2*m) # critical\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.50422108345689065" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c=c_cr*z # damping constant\n", "c" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0.00126369], dtype=float32)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = Accel*(1/-(wd**2))\n", "x[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using Vibration toolbox for comparison\n", "------------------------------------------------------" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "<matplotlib.figure.Figure at 0x7f719ece0320>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZQAAAEgCAYAAACTnoXDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nWCwWS1WwBsVisVgsVcEaFIvFYrFUhf8fgzhwts9iK6cAAAAASUVORK5CYII=\n", "text/plain": [ "<matplotlib.figure.Figure at 0x7f719ec00898>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "[<matplotlib.lines.Line2D at 0x7f719ea01438>]" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAD1CAYAAAC/duk9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMBQkScFQkCSFFwMQ3Loohjj+AAAAAElFTkSuQmCC\n", "text/plain": [ "<matplotlib.figure.Figure at 0x7f719ec08160>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "mat_contents=sio.loadmat('Case1-2.mat')\n", "Time_domain = mat_contents['Time_domain']\n", "Time_chan_2 = mat_contents['Time_chan_2']\n", "Time_chan_2 = Time_chan_2*(9.81);\n", "mean=sum(Time_chan_2)/np.size(Time_chan_2);\n", "Accel = Time_chan_2-mean;\n", "ax=max(x);\n", "x = Accel*(1/-(wd**2))# max amplitude\n", "initialvel=-ax*wne;\n", "plt.figure()\n", "vtb.time_plot(m=rho*V, c=c_cr*z, k=(wne**2)*m, x0=0.00126369, v0=-ax*wne, max_time=3.2)\n", "#ax=fig.add_subplot(111)\n", "plt.plot(Time_domain, x)\n", "#grid minor\n", "#plt.title('Case 2: position vs time')\n", "#plt.xlabel('t(s)')\n", "#plt.ylabel('Position (m)')\n", "#plt.legend('Estimated Displacement','Experimental Displacement')\n", "#x[0]" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "[t,x,v,zeta,omega,omega_d,A]=vtb.free_response(m=rho*V, c=c_cr*z, k=(wne**2)*m, x0=0.00126369, v0=-ax*wne, max_time=3.2);\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0024969647946533327" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zeta" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "209.83812974392472" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "omega" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "209.83747559003763" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "omega_d" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3 Mode shapes\n", "---------------------" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAETCAYAAAA23nEoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "<matplotlib.figure.Figure at 0x7f719ecda278>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# first three mode shapes\n", "%matplotlib inline\n", "beta = np.array([1.87510407, 4.69409113, 7.85475744])\n", "alpha = np.array([0.7341, 1.0185, 0.9992])\n", "x = np.linspace(0, 1, num=1000)\n", "for i in range(0, 3):\n", " X=np.cosh(beta[i]*x)-np.cos(beta[i]*x)-alpha[i]*(np.sinh(beta[i]*x)-np.sin(beta[i]*x))\n", " plt.plot(x, X)\n", " plt.grid('on')\n", " plt.ylabel('$X$')\n", " plt.xlabel('$x$')\n", " plt.title('$X$ versus $x$')\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "hide_input": false, "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 2 }