{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lab 2: Frequency Domain Identification Techniques\n" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear all\n", "close all\n", "clc\n", "imatlab_export_fig('print-png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Beam Properties\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "wn =\n", "\n", " 17.2300\n", "\n", "\n", "wnunibeam =\n", "\n", " 34.9725\n", "\n" ] } ], "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", "A=w*h;\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 = (sqrt(k/m))/(2*pi) % analytical natural frequency of massless beam with concentrated mass in Hz\n", "wnunibeam=((1.875)^(2)*sqrt((E*I)/(m*(l)^3)))/(2*pi) % natural freqency of a uniform section beam in Hz\n", "%c_cr = 2*sqrt(k*m); % critical damping coefficient" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Freq versus Magnitude plot\n" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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Wbayrq3M6nQMGDDDHSyAx4V1ChAVJAEQaeQMSEeXl5a1evbqxsZGIvvzyy8bG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\nDwsQgSACEVlfBIwhAQAAAIKweUCSYe4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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "load('Case2-2.mat')\n", "H=20*log10(abs(Hf_chan_2));% in dB\n", "f=Freq_domain; % in Hz\n", "figure\n", "plot(f, H)\n", "grid on\n", "grid minor\n", "title('Case 2: Freqency vs Magnitude')\n", "xlabel('f(Hz)')\n", "%imatlab_export_fig('print-png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Quadrature peak picking\n" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "fd =\n", "\n", " 34.0600\n", "\n", "\n", "zeta =\n", "\n", " 0.0103\n", "\n", "\n", "fn =\n", "\n", " 34.0618\n", "\n" ] } ], "source": [ "hpeak=85.23;% obtained from plot\n", "fd=34.06 %obtained from plot\n", "thredb=(hpeak)/sqrt(2);\n", "fda=33.65;%obtained from plot\n", "fdb=34.35;%obtained from plot\n", "zeta=(fdb-fda)/(2*fd)\n", "fn=fd/sqrt(1-zeta^2) % in hertz" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using Vibration Toolbox\n" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "> In vtb7_4 (line 132)\n", "Warning: Rank deficient, rank = 4, tol = 4.511444e+02.\n", "> In vtb7_4 (line 162)\n", "Warning: Rank deficient, rank = 2, tol = 6.684570e-04.\n", "DOF 1 of 1. Press return to plot next curve-fit FRF or end.\n", "\n", "z =\n", "\n", " single\n", "\n", " 5.5664e-04\n", "\n", "\n", "nf =\n", "\n", " single\n", "\n", " 34.0605\n", "\n" ] }, { "data": { "image/png": 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gUwMAQJkiIiK8vLzc3NxE0sPCwhBCR44c6VBuKSkpU6ZMGThwIP44bNiw5OTkGTNm3Lt3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\n6Oiguqa6p/ajv3///tDQEEKIw+GMjo7eu0fDdSLUfr1pcrmj+p6h7v3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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "load('Case2-2')\n", "Fmin=30;\n", "Fmax=40;\n", "\n", "[z,nf]=vtb7_4(Freq_domain,Hf_chan_2,Fmin,Fmax)\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Closed form solution\n" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Beta1 =\n", "\n", " 3.3942\n", "\n", "\n", "Beta2 =\n", "\n", " 8.4969\n", "\n", "\n", "w1 =\n", "\n", " 219.7631\n", "\n", "\n", "f1 =\n", "\n", " 34.9764\n", "\n", "\n", "w2 =\n", "\n", " 1.3772e+03\n", "\n", "\n", "f2 =\n", "\n", " 219.1932\n", "\n" ] } ], "source": [ "Beta1= 1.87510407/l\n", "Beta2= 4.69409133/l\n", "\n", "w1=Beta1^2*sqrt((E*I)/(rho*A))\n", "f1=((Beta1^2)/(2*pi))*sqrt((E*I)/(rho*A))\n", "w2=Beta2^2*sqrt((E*I)/(rho*A))\n", "f2=((Beta2^2)/(2*pi))*sqrt((E*I)/(rho*A))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Beam Deflection at center due to an excitation on the tip with specified frequency (using vibration toolbox)\n" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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zGCaucnNzExIS6HZhYaG6xLK0tOTxeOHh4XQHf39/BweH69ev0xVai4uL/f39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\nTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xin=l; %excitation location\n", "xout=l/2; % interested Deflection \n", "freq=100; % in Hz\n", "F=100; % in Newtons\n", "fmin=0;\n", "fmax=100;% \n", "bctype=2;% for cantilever beam\n", "beamparams=[E I rho A l];\n", "[fout,H]=vtb6_5(xin,xout,fmin,fmax,beamparams,bctype);" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "displacement =\n", "\n", " 2.0861e-07\n", "\n" ] } ], "source": [ "find(fout==100);\n", "admittance=abs(H(2001));\n", "displacement=admittance*F % in meters" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "hide_input": false, "kernelspec": { "display_name": "MATLAB", "language": "matlab", "name": "imatlab" }, "language_info": { "codemirror_mode": "octave", "file_extension": ".m", "mimetype": "text/x-matlab", "name": "matlab", "nbconvert_exporter": "imatlab._exporter.MatlabExporter", "pygments_lexer": "matlab", "version": "9.2.0.556344 (R2017a)" } }, "nbformat": 4, "nbformat_minor": 2 }