diff options
Diffstat (limited to 'Engineering_Mechanics,_Schaum_Series_by_McLean/chapter19.ipynb')
| -rwxr-xr-x | Engineering_Mechanics,_Schaum_Series_by_McLean/chapter19.ipynb | 503 |
1 files changed, 0 insertions, 503 deletions
diff --git a/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter19.ipynb b/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter19.ipynb deleted file mode 100755 index d723a0d2..00000000 --- a/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter19.ipynb +++ /dev/null @@ -1,503 +0,0 @@ -{
- "metadata": {
- "name": "chapter19.ipynb"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 19: Mechanical Vibrations"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 19.19-2, Page No:465"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "#Initilization of variables\n",
- "k=18 #lb/in\n",
- "g=386 #in/s**2\n",
- "W=35 #lb\n",
- "\n",
- "#Calculations\n",
- "f=(1/(2*pi))*sqrt((k*g/W)) #cps\n",
- "period=1/f #s\n",
- "\n",
- "#Result\n",
- "print'The period of vibration is',round(period,2),\"s\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The period of vibration is 0.45 s\n"
- ]
- }
- ],
- "prompt_number": 4
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 19.19-11, Page No:471"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "ds=0.2 #m\n",
- "ts=0.05 #m\n",
- "rhos=7850 #kg/m**3 density of steel\n",
- "dw=0.002 #m\n",
- "lw=0.9 #m\n",
- "G=80*10**9 #Pa\n",
- "\n",
- "#Calculations\n",
- "#Torsional Constant\n",
- "K=(pi*dw**4*G)/(32*lw) #m/rad\n",
- "#Mass Calculations\n",
- "m=(4**-1)*pi*(ds**2)*ts*rhos #kg\n",
- "#Moment of Inertia\n",
- "Io=(0.5)*m*(ds*2**-1)**2 #kg.m**2\n",
- "#Frequency\n",
- "f=(1*(2*pi)**-1)*(sqrt(K*Io**-1)) #Hz\n",
- "\n",
- "#Result\n",
- "print'The natural frequency of the system is',round(f,2),\"Hz\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The natural frequency of the system is 0.24 Hz\n"
- ]
- }
- ],
- "prompt_number": 6
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 19.19-13, Page No 472"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "m=120 #kg\n",
- "k=0.3 #m\n",
- "ls=0.6 #m\n",
- "ds=0.05 #m\n",
- "G=80*10**9 #Pa\n",
- "\n",
- "#Calculations\n",
- "#Polar Moment of Inertia\n",
- "J1=m*k**2 #kg.m**2\n",
- "J2=J1 #kg.m**2\n",
- "J=(32**-1)*pi*(ds**4) #m**4\n",
- "#Frequency\n",
- "f=(1/(2*pi))*(sqrt((J*G*(J1+J2))/(ls*J1*J2))) #Hz\n",
- "\n",
- "#Result\n",
- "print'The natural frequency of the torsional oscillation is',round(f,1),\"Hz\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The natural frequency of the torsional oscillation is 19.6 Hz\n"
- ]
- }
- ],
- "prompt_number": 2
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 19.19-14, Page No: 473"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "ds=2 #in\n",
- "L=15 #in\n",
- "Wf1=300 #lb\n",
- "k1=6 #in\n",
- "Wf2=100 #lb\n",
- "k2=4 #in\n",
- "G=12*10**6 #Pa\n",
- "g=386 #in/s**2\n",
- "\n",
- "#Calculations\n",
- "#Moment of inertia of flywheel\n",
- "Jf=(Wf1*g**-1)*k1**2 #lb-s**2-in\n",
- "#Moment of inertia of the rotor\n",
- "Jr=(Wf2*g**-1)*k2**2 #lb-s**2-in\n",
- "#Moment of inertia of the shaft cross section\n",
- "J=(32**-1)*pi*ds**4 #in**4\n",
- "#Frequency\n",
- "f=((pi*2)**-1)*(sqrt((J*G*(Jf+Jr))*(L*Jf*Jr)**-1)) #cps\n",
- "\n",
- "#Result\n",
- "print'The natural frequency of the system is',round(f,1),\"cps\"\n",
- "\n",
- "#The answer may wary due to decimal point descrepancy"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The natural frequency of the system is 93.9 cps\n"
- ]
- }
- ],
- "prompt_number": 14
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 19.19-15, Page No: 473"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "W=10 #lb\n",
- "A=2 #in**2\n",
- "#Calculations\n",
- "\n",
- "wn=sqrt(((A*144**-1)*5*62.4*5)/2.59) #rad/s\n",
- "\n",
- "#Result\n",
- "print'The frequency of oscillation is',round(wn,2),\"rad/s\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The frequency of oscillation is 2.89 rad/s\n"
- ]
- }
- ],
- "prompt_number": 15
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 19.19-16, Page No:474"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "f=50 #cps\n",
- "g=386 #in/s**2\n",
- "E=30*10**6 #lb/in**2\n",
- "l=4 #in\n",
- "I=2.08*10**-6 #in**4\n",
- "\n",
- "#Calculations\n",
- "W=(3*E*I*g)/(((f*2*pi)**2)*l**3) #lb\n",
- "\n",
- "#Result\n",
- "print'The value of W is',round(W,3),\"lb\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The value of W is 0.011 lb\n"
- ]
- }
- ],
- "prompt_number": 16
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 19.19-19, Page No:478"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "F=10 #lb\n",
- "v=20 #in/s\n",
- "g=386 #in/s\n",
- "W=12 #lb\n",
- "k=20 #lb/in\n",
- "\n",
- "#Calculations\n",
- "#Coefficient of damping\n",
- "c=F*(v**-1) #lb-s/in\n",
- "#Natural Frequency\n",
- "wn=sqrt((k*g)/W) #rad/s\n",
- "#Critical Damping coefficient\n",
- "cr=(2*W*(g**-1))*wn #lb-s/in\n",
- "#Damping Coefficient\n",
- "d=c*(cr**-1)\n",
- "#Frequency of damped vibrations\n",
- "wd=sqrt(1-d**2)*wn #rad/s\n",
- "\n",
- "#Result\n",
- "print'The frequency of damped vibrations is',round(wd,1),\"rad/s\"\n",
- "\n",
- "# The answer is off by 0.1 units"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The frequency of damped vibrations is 24.0 rad/s\n"
- ]
- }
- ],
- "prompt_number": 18
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 19.19-20, Page No 478"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "wn=25.4 #rad/s\n",
- "t=0.261 #s\n",
- "d=0.316\n",
- "\n",
- "#Calculations\n",
- "delta=d*t*wn #logarithmic decay\n",
- "\n",
- "#Result\n",
- "print'The rate of decay is',round(delta,3)\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The rate of decay is 2.095\n"
- ]
- }
- ],
- "prompt_number": 19
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 19.19-24, Page No 483"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "F=9 #N\n",
- "m=5 #kg\n",
- "k=6000 #N/m\n",
- "f1=1 #Hz\n",
- "f2=5.4 #Hz\n",
- "f3=50 #Hz\n",
- "\n",
- "#Calculations\n",
- "#Natural Frequency\n",
- "fn=((pi*2)**-1)*(sqrt(k/m)) #Hz\n",
- "deltaf=F*(k/1000)**-1 #mm\n",
- "#Part(a)\n",
- "r1=f1*fn**-1\n",
- "amp1=deltaf*(1-r1**2)**-1 #mm amplitude\n",
- "#Part (b)\n",
- "r2=f2*fn**-1\n",
- "amp2=deltaf/(1-r2**2) #mm amplitude\n",
- "#Part (c)\n",
- "r3=f3*fn**-1\n",
- "amp3=deltaf/(1-r3**2) #mm amplitude\n",
- "\n",
- "#Result\n",
- "print'The amplitudes in part (a),(b) and (c) respectively are',round(amp1,3),\"mm ,\",round(amp2,1),\"mm and\",round(amp3,3),\"mm\"\n",
- "\n",
- "# The answer for amp2 is incorrect in textbook"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The amplitudes in part (a),(b) and (c) respectively are 1.551 mm , 36.9 mm and -0.018 mm\n"
- ]
- }
- ],
- "prompt_number": 27
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 19.19-25, Page No 483"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of vraiables\n",
- "g=386 #in/s**2\n",
- "W=20 #lb\n",
- "w=600 #rpm\n",
- "ratio=12**-1\n",
- "\n",
- "#Calculations\n",
- "r=sqrt((1*ratio**-1)+1) \n",
- "fn=((w/60)/r) #cps\n",
- "k=((fn*2*pi)**2*W)/(g) #lb/in\n",
- "\n",
- "#Result\n",
- "print'The value of k is',round(k,1),\"lb/in\"\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The value of k is 15.7 lb/in\n"
- ]
- }
- ],
- "prompt_number": 28
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 19.19-28, Page No 487"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "import math\n",
- "\n",
- "#Initilization of variables\n",
- "X=12 #mm\n",
- "me_M=1.3 #mm\n",
- "\n",
- "#Calculations\n",
- "d=(me_M)/(2*X)\n",
- "\n",
- "#Result\n",
- "print'The damping ratio is',round(d,3)\n"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "The damping ratio is 0.054\n"
- ]
- }
- ],
- "prompt_number": 29
- }
- ],
- "metadata": {}
- }
- ]
-}
\ No newline at end of file |