{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 11: VIBRATIONS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 11.10: FREQUENCY_OF_TRANSVERSE_VIBRATION.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//CHAPTER 11 ILLUSRTATION 10 PAGE NO 296\n", "//TITLE:VIBRATIONS\n", "//FIGURE 11.18\n", "clc\n", "clear\n", "//===========================================================================================\n", "//INPUT DATA\n", "PI=3.147\n", "g=9.81// ACCELERATION DUE TO GRAVITY IN N /m^2\n", "E=200*10^9// YOUNGS MODUKUS OF SHAFT MATERIAL IN Pascals\n", "D=.03// DIAMETER OF SHAFT IN m\n", "L=.8// LENGTH OF SHAFT IN m\n", "r=40000// DENSITY OF SHAFT MATERIAL IN Kg/m^3\n", "W=10// WEIGHT ACTING AT CENTRE IN N\n", "//===========================================================================================\n", "I=PI*D^4/64// MOMENT OF INERTIA OF SHAFT IN m^4\n", "m=PI*D^2/4*r// MASS PER UNIT LENGTH IN Kg/m\n", "w=m*g\n", "DELTA=W*L^3/(48*E*I)// STATIC DEFLECTION DUE TO W\n", "DELTA1=5*w*L^4/(384*E*I)// STATIC DEFLECTION DUE TO WEIGHT OF SHAFT \n", "Fn=.4985/(DELTA+DELTA1/1.27)^.5\n", "//==========================================================================================\n", "printf('FREQUENCY OF TRANSVERSE VIBRATION = %.3f Hz',Fn)\n", "\n", "" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 11.11: CRITICAL_SPEED_OF_SHAFT.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//CHAPTER 11 ILLUSRTATION 11 PAGE NO 297\n", "//TITLE:VIBRATIONS\n", "//FIGURE 11.19\n", "clc\n", "clear\n", "//===========================================================================================\n", "//INPUT DATA\n", "PI=3.147\n", "g=9.81// ACCELERATION DUE TO GRAVITY IN N /m^2\n", "E=210*10^9// YOUNGS MODUKUS OF SHAFT MATERIAL IN Pascals\n", "D=.18// DIAMETER OF SHAFT IN m\n", "L=2.5// LENGTH OF SHAFT IN m\n", "M1=25// MASS ACTING AT E IN Kg\n", "M2=50// MASS ACTING AT D IN Kg\n", "M3=20// MASS ACTING AT C IN Kg\n", "W1=M1*g\n", "W2=M2*g\n", "W3=M3*g\n", "L1=.6// LENGTH FROM A TO E IN m\n", "L2=1.5// LENGTH FROM A TO D IN m\n", "L3=2// LENGTH FROM A TO C IN m\n", "w=1962// SELF WEIGHT OF SHAFT IN N\n", "//==========================================================================================\n", "I=PI*D^4/64// MOMENT OF INERTIA OF SHAFT IN m^4\n", "DELTA1=W1*L1^2*(L-L1)^2/(3*E*I*L)// STATIC DEFLECTION DUE TO W1\n", "DELTA2=W2*L2^2*(L-L2)^2/(3*E*I*L)// STATIC DEFLECTION DUE TO W2\n", "DELTA3=W3*L3^2*(L-L3)^2/(3*E*I*L)// STATIC DEFLECTION DUE TO W3\n", "DELTA4=5*w*L^4/(384*E*I)// STATIC DEFLECTION DUE TO w\n", "Fn=.4985/(DELTA1+DELTA2+DELTA3+DELTA4/1.27)^.5\n", "Nc=Fn*60// CRITICAL SPEED OF SHAFT IN rpm\n", "//========================================================================================\n", "printf('CRITICAL SPEED OF SHAFT = %.3f rpm',Nc)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 11.12: FREQUENCY_OF_FREE_TORSIONAL_VIBRATION.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//CHAPTER 11 ILLUSRTATION 12 PAGE NO 298\n", "//TITLE:VIBRATIONS\n", "//FIGURE 11.20\n", "clc\n", "clear\n", "//===========================================================================================\n", "//INPUT DATA\n", "PI=3.147\n", "g=9.81// ACCELERATION DUE TO GRAVITY IN N /m^2\n", "Na=1500// SPEED OF SHAFT A IN rpm\n", "Nb=500// SPEED OF SHAFT B IN rpm\n", "G=Na/Nb// GERA RATIO\n", "L1=.18// LENGTH OF SHAFT 1 IN m\n", "L2=.45// LENGTH OF SHAFT 2 IN m\n", "D1=.045// DIAMETER OF SHAFT 1 IN m\n", "D2=.09// DIAMETER OF SHAFT 2 IN m\n", "C=84*10^9// MODUKUS OF RIDITY OF SHAFT MATERIAL IN Pascals\n", "Ib=1400// MOMENT OF INERTIA OF PUMP IN Kg-m^2\n", "Ia=400// MOMENT OF INERTIA OF MOTOR IN Kg-m^2\n", "\n", "//======================================================================================\n", "J=PI*D1^4/32// POLAR MOMENT OF INERTIA IN m^4\n", "Ib1=Ib/G^2// MASS MOMENT OF INERTIA OF EQUIVALENT ROTOR IN m^2\n", "L3=G^2*L2*(D1/D2)^4// ADDITIONAL LENGTH OF THE EQUIVALENT SHAFT\n", "L=L1+L3// TOTAL LENGTH OF EQUIVALENT SHAFT\n", "La=L*Ib1/(Ia+Ib1)\n", "Fn=(C*J/(La*Ia))^.5/(2*PI)// FREQUENCY OF FREE TORSIONAL VIBRATION IN Hz\n", "//===================================================================================\n", "printf('FREQUENCY OF FREE TORSIONAL VIBRATION = %.2f Hz',Fn)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 11.13: THE_RANGE_OF_SPEED.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//CHAPTER 11 ILLUSRTATION 13 PAGE NO 300\n", "//TITLE:VIBRATIONS\n", "//FIGURE 11.21\n", "clc\n", "clear\n", "//===========================================================================================\n", "//INPUT DATA\n", "PI=3.147\n", "g=9.81// ACCELERATION DUE TO GRAVITY IN N /m^2\n", "D=.015// DIAMETER OF SHAFT IN m\n", "L=1.00// LENGTH OF SHAFT IN m\n", "M=15// MASS OF SHAFT IN Kg\n", "W=M*g\n", "e=.0003// ECCENTRICITY IN m\n", "E=200*10^9// YOUNGS MODUKUS OF SHAFT MATERIAL IN Pascals\n", "f=70*10^6// PERMISSIBLE STRESS IN N/m^2\n", "//============================================================================================\n", "I=PI*D^4/64// MOMENT OF INERTIA OF SHAFT IN m^4\n", "DELTA=W*L^3/(192*E*I)// STATIC DEFLECTION IN m\n", "Fn=.4985/(DELTA)^.5// NATURAL FREQUENCY OF TRANSVERSE VIBRATION\n", "Nc=Fn*60// CRITICAL SPEED OF SHAFT IN rpm\n", "M1=16*f*I/(D*g*L)\n", "W1=M1*g// ADDITIONAL LOAD ACTING\n", "y=W1/W*DELTA// ADDITIONAL DEFLECTION DUE TO W1\n", "N1=Nc/(1+e/y)^.5// MIN SPEED IN rpm\n", "N2=Nc/(1-e/y)^.5// MAX SPEED IN rpm\n", "//===========================================================================================\n", "printf('CRITICAL SPEED OF SHAFT = %.3f rpm\n THE RANGE OF SPEED IS FROM %.3f rpm TO %.3f rpm',Nc,N1,N2)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 11.1: FREQUENCY_OF_TRANSVERSE_VIBRATION.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//CHAPTER 11 ILLUSRTATION 1 PAGE NO 290\n", "//TITLE:VIBRATIONS\n", "clc\n", "clear\n", "//===========================================================================================\n", "//INPUT DATA\n", "PI=3.147\n", "D=.1// DIAMETER OF SHAFT IN m\n", "L=1.10// LENGTH OF SHAFT IN m\n", "W=450// WEIGHT ON THE OTHER END OF SHAFT IN NEWTONS\n", "E=200*10^9// YOUNGS MODUKUS OF SHAFT MATERIAL IN Pascals\n", "// =========================================================================================\n", "A=PI*D^2/4// AREA OF SHAFT IN mm^2\n", "I=PI*D^4/64// MOMENT OF INERTIA \n", "delta=W*L/(A*E)// STATIC DEFLECTION IN LONGITUDINAL VIBRATION OF SHAFT IN m\n", "Fn=0.4985/(delta)^.5// FREQUENCY OF LONGITUDINAL VIBRATION IN Hz\n", "delta1=W*L^3/(3*E*I)// STATIC DEFLECTION IN TRANSVERSE VIBRATION IN m\n", "Fn1=0.4985/(delta1)^.5// FREQUENCY OF TRANSVERSE VIBRATION IN Hz\n", "//============================================================================================\n", "//OUTPUT\n", "printf('FREQUENCY OF LONGITUDINAL VIBRATION =%.3f Hz\n FREQUENCY OF TRANSVERSE VIBRATION =%.3f Hz',Fn,Fn1)\n", "\n", "\n", "" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 11.2: NATURAL_FREQUENCY_OF_TRANSVERSE_VIBRATION.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//CHAPTER 11 ILLUSRTATION 2 PAGE NO 290\n", "//TITLE:VIBRATIONS\n", "//FIGURE 11.10\n", "clc\n", "clear\n", "//===========================================================================================\n", "//INPUT DATA\n", "PI=3.147\n", "L=.9// LENGTH OF THE SHAFT IN m\n", "m=100// MASS OF THE BODY IN Kg\n", "L2=.3// LENGTH WHERE THE WEIGHT IS ACTING IN m\n", "L1=L-L2// DISTANCE FROM THE OTHER END\n", "D=.06// DIAMETER OF SHAFT IN m\n", "W=9.81*m// WEGHT IN NEWTON\n", "E=200*10^9// YOUNGS MODUKUS OF SHAFT MATERIAL IN Pascals\n", "//==========================================================================================\n", "//CALCULATION\n", "I=PI*D^4/64// MOMENT OF INERTIA IN m^4\n", "delta=W*L1^2*L2^2/(3*E*I*L)// STATIC DEFLECTION\n", "Fn=.4985/(delta)^.5// NATURAL FREQUENCY OF TRANSVERSE VIBRATION\n", "//=========================================================================================\n", "//OUTPUT\n", "printf('NATURAL FREQUENCY OF TRANSVERSE VIBRATION=%.3f Hz',Fn)" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 11.3: FREQUENCY_OF_TORSIONAL_VIBRATION.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//CHAPTER 11 ILLUSRTATION 3 PAGE NO 291\n", "//TITLE:VIBRATIONS\n", "//FIGURE 11.11\n", "clc\n", "clear\n", "//===========================================================================================\n", "//INPUT DATA\n", "PI=3.147\n", "g=9.81// ACCELERATION DUE TO GRAVITY IN N /m^2\n", "D=.050// DIAMETER OF SHAFT IN m\n", "m=450// WEIGHT OF FLY WHEEL IN IN Kg\n", "K=.5// RADIUS OF GYRATION IN m\n", "L2=.6// FROM FIGURE IN m\n", "L1=.9// FROM FIGURE IN m\n", "L=L1+L2\n", "E=200*10^9// YOUNGS MODUKUS OF SHAFT MATERIAL IN Pascals\n", "C=84*10^9// MODUKUS OF RIDITY OF SHAFT MATERIAL IN Pascals\n", "//=========================================================================================\n", "A=PI*D^2/4// AREA OF SHAFT IN mm^2\n", "I=PI*D^4/64// \n", "m1=m*L2/(L1+L2)// MASS OF THE FLYWHEEL CARRIED BY THE LENGTH L1 IN Kg\n", "DELTA=m1*g*L1/(A*E)// EXTENSION OF LENGTH L1 IN m\n", "Fn=0.4985/(DELTA)^.5// FREQUENCY OF LONGITUDINAL VIBRATION IN Hz\n", "DELTA1=(m*g*L1^3*L2^3)/(3*E*I*L^3)// STATIC DEFLECTION IN TRANSVERSE VIBRATION IN m\n", "Fn1=0.4985/(DELTA1)^.5// FREQUENCY OF TRANSVERSE VIBRATION IN Hz\n", "J=PI*D^4/32// POLAR MOMENT OF INERTIA IN m^4\n", "Q1=C*J/L1// TORSIONAL STIFFNESS OF SHAFT DUE TO L1 IN N-m\n", "Q2=C*J/L2// TORSIONAL STIFFNESS OF SHAFT DUE TO L2 IN N-m\n", "Q=Q1+Q2// TORSIONAL STIFFNESS OF SHAFT IN Nm\n", "Fn2=(Q/(m*K^2))^.5/(2*PI)// FREQUENCY OF TORSIONAL VIBRATION IN Hz\n", "//=======================================================================================\n", "printf('FREQUENCY OF LONGITUDINAL VIBRATION = %.3f Hz\n FREQUENCY OF TRANSVERSE VIBRATION = %.3f Hz\n FREQUENCY OF TORSIONAL VIBRATION = %.3f Hz',Fn,Fn1,Fn2)\n", "" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 11.6: FREQUENCY_OF_TRANSVERSE_VIBRATION.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//CHAPTER 11 ILLUSRTATION 6 PAGE NO 294\n", "//TITLE:VIBRATIONS\n", "//FIGURE 11.14\n", "clc\n", "clear\n", "//===========================================================================================\n", "//INPUT DATA\n", "PI=3.147\n", "g=9.81// ACCELERATION DUE TO GRAVITY IN N /m^2\n", "D=.06// DIAMETER OF SHAFT IN m\n", "L=3// LENGTH OF SHAFT IN m\n", "W1=1500// WEIGHT ACTING AT C IN N\n", "W2=2000// WEIGHT ACTING AT D IN N\n", "W3=1000// WEIGHT ACTING AT E IN N\n", "L1=1// LENGTH FROM A TO C IN m\n", "L2=2// LENGTH FROM A TO D IN m\n", "L3=2.5// LENGTH FROM A TO E IN m\n", "I=PI*D^4/64\n", "E=200*10^9// YOUNGS MODUKUS OF SHAFT MATERIAL IN Pascals\n", "//===========================================================================================\n", "DELTA1=W1*L1^2*(L-L1)^2/(3*E*I*L)// STATIC DEFLECTION DUE TO W1\n", "DELTA2=W2*L2^2*(L-L2)^2/(3*E*I*L)// STATIC DEFLECTION DUE TO W2\n", "DELTA3=W2*L3^2*(L-L3)^2/(3*E*I*L)// STATIC DEFLECTION DUE TO W2\n", "Fn=.4985/(DELTA1+DELTA2+DELTA3)^.5// FREQUENCY OF TRANSVERSE VIBRATION IN Hz\n", "//==========================================================================================\n", "printf('FREQUENCY OF TRANSVERSE VIBRATION = %.3f Hz',Fn)" ] } ], "metadata": { "kernelspec": { "display_name": "Scilab", "language": "scilab", "name": "scilab" }, "language_info": { "file_extension": ".sce", "help_links": [ { "text": "MetaKernel Magics", "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" } ], "mimetype": "text/x-octave", "name": "scilab", "version": "0.7.1" } }, "nbformat": 4, "nbformat_minor": 0 }