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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Computational Mechanics Boundary Values - Project 05\n",
"\n",
"![6-string guitar diagram](../images/guitar.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this final project, we will consider all six strings of a guitar and the deflection of the neck of the guitar. Here are the inputs for each of the strings, all L=0.64 m:\n",
"\n",
"|string|density (g/m)|tension (kg)|\n",
"|---|---|---|\n",
"|E|0.401|7.28|\n",
"|B|0.708|7.22|\n",
"|G|1.140|7.32|\n",
"|D|2.333|8.41|\n",
"|A|4.466|9.03|\n",
"|E|6.790|7.71|"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. The neck of the guitar can be considered a cantilever beam with an applied moment, shown above. At the tip we have a moment equal to the sum of the (tensions in the strings) $\\times$ (bridge height). Here we will consider it as $h=4~mm$. \n",
"\n",
"a. Use a finite difference approximation to determine the deflection of the guitar's bridge if the Young's modulus is E=10 GPa and it is a rectangular cross-section $2\\times4~cm^2$ and $I=\\frac{4\\cdot2^3}{12}~cm^4.$\n",
"\n",
"b. Demonstrate that your finite difference solution has converged. _e.g. decrease the step size $h$ and show the solution converges to a final value._"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"E = 10e9\n",
"A = 0.02*0.04\n",
"I = 0.04*0.02**3/12\n",
"h = 0.004\n",
"L = 0.64\n",
"Te = 7.28*9.81 ; Tb = 7.22*9.8 ; Tg = 7.32*9.8 ; Td = 8.41*9.8 ; Ta = 9.03*9.8 ; TE = 7.71*9.8\n",
"T = Te + Tb + Tg + Td + Ta + TE\n",
"M = T * h\n",
"\n",
"A = 0 ; B = M/E/I ; C = 0 ; D = 0\n",
"\n",
"x=np.linspace(0,0.64,1000)\n",
"y = lambda x: M*x**2/(2*E*I)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The deflection at the end of the guitar is: 1.414 mm\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N = 3\n",
"dx = L/N\n",
"A=np.diag(np.ones(N)*6)\\\n",
"+np.diag(np.ones(N-1)*-4,-1)\\\n",
"+np.diag(np.ones(N-1)*-4,1)\\\n",
"+np.diag(np.ones(N-2),-2)\\\n",
"+np.diag(np.ones(N-2),2)\n",
"A[0,0] += 1\n",
"A[N-2,N-1] += 2\n",
"A[N-1,N-2] += 2\n",
"A[N-2,N-2] -= 1\n",
"A[N-1,N-1] -= 5\n",
"b=np.zeros(N)\n",
"b[N-2] += -M*dx**2/E/I\n",
"b[N-1] += M*dx**2/E/I\n",
"\n",
"w=np.linalg.solve(A,b)\n",
"xnum=np.linspace(0,L,N+1)\n",
"\n",
"print('The deflection at the end of the guitar is:',round(w[-1]*1000,3),'mm')\n",
"\n",
"plt.plot(xnum,np.block([0,w]),'or',label='Numerical') \n",
"plt.plot(x,y(x),label='Analytical',lw=3)\n",
"plt.plot(0,0,'b')\n",
"plt.legend(prop={'size':15});"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The deflection at the end of the guitar is: 1.414 mm\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N = 12\n",
"dx = L/N\n",
"A=np.diag(np.ones(N)*6)\\\n",
"+np.diag(np.ones(N-1)*-4,-1)\\\n",
"+np.diag(np.ones(N-1)*-4,1)\\\n",
"+np.diag(np.ones(N-2),-2)\\\n",
"+np.diag(np.ones(N-2),2)\n",
"A[0,0] += 1\n",
"A[N-2,N-1] += 2\n",
"A[N-1,N-2] += 2\n",
"A[N-2,N-2] -= 1\n",
"A[N-1,N-1] -= 5\n",
"b=np.zeros(N)\n",
"b[N-2] += -M*dx**2/E/I\n",
"b[N-1] += M*dx**2/E/I\n",
"\n",
"w=np.linalg.solve(A,b)\n",
"xnum=np.linspace(0,L,N+1)\n",
"\n",
"print('The deflection at the end of the guitar is:',round(w[-1]*1000,3),'mm')\n",
"\n",
"plt.plot(xnum,np.block([0,w]),'o',label='Numerical') \n",
"plt.plot(x,y(x),label='Analytical',lw=3)\n",
"plt.plot(0,0,'o')\n",
"plt.legend(prop={'size':15});"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The deflection at the end of the guitar is: 1.414 mm\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N = 50\n",
"dx = L/N\n",
"A=np.diag(np.ones(N)*6)\\\n",
"+np.diag(np.ones(N-1)*-4,-1)\\\n",
"+np.diag(np.ones(N-1)*-4,1)\\\n",
"+np.diag(np.ones(N-2),-2)\\\n",
"+np.diag(np.ones(N-2),2)\n",
"A[0,0] += 1\n",
"A[N-2,N-1] += 2\n",
"A[N-1,N-2] += 2\n",
"A[N-2,N-2] -= 1\n",
"A[N-1,N-1] -= 5\n",
"b=np.zeros(N)\n",
"b[N-2] += -M*dx**2/E/I\n",
"b[N-1] += M*dx**2/E/I\n",
"\n",
"w=np.linalg.solve(A,b)\n",
"xnum=np.linspace(0,L,N+1)\n",
"\n",
"print('The deflection at the end of the guitar is:',round(w[-1]*1000,3),'mm')\n",
"\n",
"plt.plot(xnum,np.block([0,w]),'o',label='Numerical') \n",
"plt.plot(x,y(x),label='Analytical',lw=3)\n",
"plt.plot(0,0,'o')\n",
"plt.legend(prop={'size':15});"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. Here we will record the first three frequencies of the 6-string guitar. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"a. Consider the G-string on the guitar, L=0.64 m, $\\mu=1.14~g/m,$ and T=71.81 N [1]. \n",
"\n",
"__Guitar string equation:__ $\\mu\\frac{\\partial^2 y}{\\partial t^2}=T\\frac{\\partial ^2 y}{\\partial x^2}$\n",
"\n",
"a. Calculate the first, second, and third natural frequencies using 6, 30, 45, and 60 nodes. Plot the mode shapes and determine the number of nodes needed to converge for the first three modes. "
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"from scipy import linalg\n",
"L = 0.64\n",
"mu = 1.14e-3\n",
"T=71.81"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"N=6\n",
"dx=L/(N+1)\n",
"k = T/dx**2/mu\n",
"A = k*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"e,v=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e=e[isort]\n",
"v=v[:,isort]\n",
"\n",
"w1=np.sqrt(e[0].real)/2/np.pi\n",
"v1=v[:,0]/max(v[:,0])\n",
"\n",
"w2=np.sqrt(e[1].real)/2/np.pi\n",
"v2=v[:,1]/max(v[:,1])\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The natural frequencies of 30-element string (Hz) is:\n",
"[195.99464595 391.48617646 585.97276757]\n",
"\n",
"The longest time period is: 5.102 ms\n",
"shortest time period is: 0.259 ms\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N=30\n",
"dx=L/(N+1)\n",
"k = T/dx**2/mu\n",
"A = k*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"e,v=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e=e[isort]\n",
"v=v[:,isort]\n",
"\n",
"w1=np.sqrt(e[0].real)/2/np.pi\n",
"v1=v[:,0]/max(v[:,0])\n",
"w2=np.sqrt(e[1].real)/2/np.pi\n",
"v2=v[:,1]/max(v[:,1])\n",
"\n",
"x=np.linspace(0,L,N)\n",
"plt.plot(x,v[:,0],label='1')\n",
"plt.plot(x,-v[:,1],label='2')\n",
"plt.legend(prop={'size':15});\n",
"\n",
"f1=np.sqrt(e.real[0])/2/np.pi\n",
"fn=np.sqrt(e.real[-1])/2/np.pi\n",
"print('The natural frequencies of {}-element string (Hz) is:'.format(N))\n",
"print(e.real[0:3]**0.5/2/np.pi)\n",
"print('\\nThe longest time period is: {:1.3f} ms\\nshortest time period is: {:1.3f} ms'.format(1/f1*1000,1/fn*1000))"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The natural frequencies of 45-element string (Hz) is: \n",
"[196.04043699 391.85229959 587.20727994]\n",
"\n",
"The longest time period is: 5.101 ms\n",
"The shortest time period is: 0.174 ms\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N=45\n",
"dx=L/(N+1)\n",
"k = T/dx**2/mu\n",
"A = k*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"e,v=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e=e[isort]\n",
"v=v[:,isort]\n",
"\n",
"w1=np.sqrt(e[0].real)/2/np.pi\n",
"v1=v[:,0]/max(v[:,0])\n",
"w2=np.sqrt(e[1].real)/2/np.pi\n",
"v2=v[:,1]/max(v[:,1])\n",
"\n",
"x=np.linspace(0,L,N)\n",
"plt.plot(x,-v[:,0],label='1')\n",
"plt.plot(x,v[:,1],label='2')\n",
"plt.legend(prop={'size':15});\n",
"\n",
"f1=np.sqrt(e.real[0])/2/np.pi\n",
"fn=np.sqrt(e.real[-1])/2/np.pi\n",
"print('The natural frequencies of {}-element string (Hz) is: '.format(N))\n",
"print(e.real[0:3]**0.5/2/np.pi)\n",
"print('\\nThe longest time period is: {:1.3f} ms\\nThe shortest time period is: {:1.3f} ms'.format(1/f1*1000,1/fn*1000))"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The natural frequencies of 60-element string (Hz) is: \n",
"[196.05687232 391.9837462 587.65070938]\n",
"\n",
"The longest time period =5.101 ms\n",
"The shortest time period is: 0.131 ms\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N=60\n",
"dx=L/(N+1)\n",
"k = T/dx**2/mu\n",
"A = k*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"e,v=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e=e[isort]\n",
"v=v[:,isort]\n",
"\n",
"w1=np.sqrt(e[0].real)/2/np.pi\n",
"v1=v[:,0]/max(v[:,0])\n",
"w2=np.sqrt(e[1].real)/2/np.pi\n",
"v2=v[:,1]/max(v[:,1])\n",
"\n",
"x=np.linspace(0,L,N)\n",
"plt.plot(x,v[:,0],label='1')\n",
"plt.plot(x,-v[:,1],label='2')\n",
"plt.legend(prop={'size':15});\n",
"\n",
"f1=np.sqrt(e.real[0])/2/np.pi\n",
"fn=np.sqrt(e.real[-1])/2/np.pi\n",
"print('The natural frequencies of {}-element string (Hz) is: '.format(N))\n",
"print(e.real[0:3]**0.5/2/np.pi)\n",
"print('\\nThe longest time period ={:1.3f} ms\\nThe shortest time period is: {:1.3f} ms'.format(1/f1*1000,1/fn*1000))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"b. Use the number of nodes necessary for convergence to calculate the first 3 modes of vibration for the other 5 strings on the guitar. Display the first three natural frequencies for all six strings. "
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The natural frequencies of 71.42 N string (Hz) is:\n",
" 195.503\n",
" 390.778\n",
" 585.597\n",
"\n",
"The natural frequencies of 70.76 N string (Hz) is:\n",
" 194.596\n",
" 388.966\n",
" 582.882\n",
"\n",
"The natural frequencies of 71.74 N string (Hz) is:\n",
" 195.939\n",
" 391.65\n",
" 586.905\n",
"\n",
"The natural frequencies of 82.42 N string (Hz) is:\n",
" 210.022\n",
" 419.799\n",
" 629.086\n",
"\n",
"The natural frequencies of 88.49 N string (Hz) is:\n",
" 217.626\n",
" 434.998\n",
" 651.862\n",
"\n",
"The natural frequencies of 75.56 N string (Hz) is:\n",
" 201.091\n",
" 401.948\n",
" 602.337\n",
"\n"
]
}
],
"source": [
"\n",
"N = 45\n",
"tension = np.array([Te,Tb, Tg, Td, Ta, TE])\n",
"signal = np.zeros(18)\n",
"i=0\n",
"for T in tension:\n",
" dx=L/(N+1)\n",
" k = T/dx**2/mu\n",
" A = k*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
" e,v=linalg.eig(A)\n",
" isort = np.argsort(e.real)\n",
" e=e[isort]\n",
" v=v[:,isort]\n",
"\n",
" w1=np.sqrt(e[0].real)/2/np.pi\n",
" v1=v[:,0]/max(v[:,0])\n",
" w2=np.sqrt(e[1].real)/2/np.pi\n",
" v2=v[:,1]/max(v[:,1])\n",
" \n",
" print('The natural frequencies of {:.4} N string (Hz) is:'.format(T))\n",
" print(' ',round(e.real[0]**0.5/2/np.pi,3))\n",
" print(' ',round(e.real[1]**0.5/2/np.pi,3))\n",
" print(' ',round(e.real[2]**0.5/2/np.pi,3))\n",
" print()\n",
" signal[i]=e.real[0]**0.5/2/np.pi\n",
" i+=1\n",
" signal[i]=e.real[1]**0.5/2/np.pi\n",
" i+=1\n",
" signal[i]=e.real[2]**0.5/2/np.pi\n",
" i+=1 \n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"c. Create an audio signal that has the 18 frequencies (6 strings $\\times$ 3 modes) in an array and display it using the `from IPython.display import Audio` library. \n",
"\n",
"_Hint: you don't need to solve the differential equations here. You can use the calculated frequencies to add sine-waves together:_ $\\sin(f_12\\pi t)+\\sin(f_22\\pi t)+...$"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
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\" type=\"audio/wav\" />\n",
" Your browser does not support the audio element.\n",
" </audio>\n",
" "
],
"text/plain": [
"<IPython.lib.display.Audio object>"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Audio\n",
"r=20000\n",
"tsig=np.arange(0,5,1/r)\n",
"data = 0\n",
"for i in range(0,18):\n",
" data += np.sin(signal[i]*2*np.pi*tsig)\n",
"Audio(data=data,rate=r)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}