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+{
+"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
+}
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