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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
}
|
