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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": 67,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# a. \n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy import linalg\n",
"from IPython.display import Audio\n",
"\n",
"E=10e9\n",
"I = (0.04*0.02**3)/12\n",
"L = 0.64\n",
"t=0.04 \n",
"g = 9.81\n",
"h = 0.004\n",
"\n",
"rho_e = 0.401e-3\n",
"rho_b = 0.708e-3\n",
"rho_g = 1.140e-3\n",
"rho_d = 2.333e-3\n",
"rho_a = 4.466e-3\n",
"rho_E = 6.790e-3\n",
"\n",
"T_e = 7.28*9.81\n",
"T_b = 7.22*9.81\n",
"T_g = 7.32*9.81\n",
"T_d = 8.41*9.81\n",
"T_a = 9.03*9.81\n",
"T_E = 7.71*9.81\n",
"\n",
"N = 9\n",
"h1 = L/10\n",
"\n",
"x = np.linspace(0,L,100)\n",
"xnum = np.arange(0,L+h1/2,h1)\n",
"M = (T_e+T_b+T_g+T_d+T_a+T_E)*h\n",
"w = (M*L**2/(2*E*I))*(x/L)**2\n",
"\n",
"A1 = 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",
"A1[0,0]+=1\n",
"A1[-1,-1]+=1\n",
"A1[7]= [0,0,0,0,0,1,-4,5,-2]\n",
"A1[8] = [0,0,0,0,0,0,2,-4,2]\n",
"b1=-np.zeros(N)\n",
"b1[7]=-h1**2*M/(E*I)\n",
"b1[8]=2*h1**2*M/(E*I)\n",
"w1 = np.linalg.solve(A1,b1)\n",
"\n",
"plt.figure(figsize=(8,6))\n",
"plt.plot(x,w,label='Analytical Solution')\n",
"plt.plot(xnum[:-1],np.block([0,w1]),'o',label='Numerical Solution')\n",
"plt.ylabel('Delfection (m)')\n",
"plt.xlabel('Length of Bridge (m)')\n",
"plt.title('Guitar Bridge Deflection')\n",
"plt.legend(loc='best');"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# b\n",
"w2 = []\n",
"xnum2 = []\n",
"h = np.array([L/4,L/8,L/12,L/16,L/24])\n",
"\n",
"for i in range(len(h)):\n",
" shape = int(L/h[i])\n",
" A2=np.diag(np.ones(shape)*6)+np.diag(np.ones(shape-1)*-4,-1)\\\n",
" +np.diag(np.ones(shape-1)*-4,1)+np.diag(np.ones(shape-2),-2)+np.diag(np.ones(shape-2),2)\n",
" A2[0,0]+=1\n",
" A2[-1,-1]+=1\n",
" A2[-2]= np.zeros(shape)\n",
" A2[-2,-4:]=[1,-4,5,-2]\n",
" A2[-1] = np.zeros(shape)\n",
" A2[-1,-3:] = [2,-4,2]\n",
" b2=-np.zeros(shape)\n",
" b2[-2]=-h[i]**2*M/(E*I)\n",
" b2[-1]=2*h[i]**2*M/(E*I)\n",
" w2.append(np.linalg.solve(A2,b2))\n",
" xnum2.append(np.arange(0,L+h[i]/2,h[i]))\n",
"\n",
"plt.figure(figsize=(8,6))\n",
"plt.plot(x,w,'o',label='Analytical Solution')\n",
"plt.plot(xnum2[0],np.block([0,w2[0]]),label='4')\n",
"plt.plot(xnum2[1],np.block([0,w2[1]]),label='8')\n",
"plt.plot(xnum2[2],np.block([0,w2[2]]),label='12')\n",
"plt.plot(xnum2[3],np.block([0,w2[3]]),label='16')\n",
"plt.plot(xnum2[4],np.block([0,w2[4]]),'o',label='24')\n",
"plt.ylabel('Delfection (m)')\n",
"plt.xlabel('Length of Bridge (m)')\n",
"plt.title('Bridge Deflection Convergence')\n",
"plt.legend(loc='best');"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"analytical = np.max(w)\n",
"error = []\n",
"\n",
"for i in range(len(h)):\n",
" numerical = np.max(w2[i])\n",
" error.append(np.abs(analytical-numerical))\n",
"\n",
"step = np.array([24,16,12,8,4])\n",
"plt.figure(figsize=(8,6))\n",
"plt.plot(step,error)\n",
"plt.ylabel('Absolute Error (mm)')\n",
"plt.xlabel('Number of Steps')\n",
"plt.title('Absolute Error vs Number of Steps');"
]
},
{
"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": 70,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using 6 Nodes\n",
"First 194.43600354377588\n",
"Second 379.12217397582174\n",
"Third 544.7975755283883\n",
"\n",
"Using 30 Nodes\n",
"First 195.99355421041057\n",
"Second 391.4839957781058\n",
"Third 585.969503543348\n",
"\n",
"Using 45 Nodes\n",
"First 196.0393449870616\n",
"Second 391.8501168671646\n",
"Third 587.2040090393817\n",
"\n",
"Using 60 Nodes\n",
"First 196.05578023030412\n",
"Second 391.98156274026314\n",
"Third 587.6474360065606\n",
"\n",
"THERE NEEDS TO BE AT LEAST 30 NODES FOR CONVERGENCE\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"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"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": [
"L = 0.64\n",
"N = np.array([6,30,45,60])\n",
"\n",
"for i in range(len(N)):\n",
" dx = L/(N[i]+1)\n",
" k = T_g/(dx**2*rho_g)\n",
" A = k*(np.diag(np.ones(N[i])*2)\\\n",
" -np.diag(np.ones(N[i]-1),-1)\\\n",
" -np.diag(np.ones(N[i]-1),1))\n",
" e,v = linalg.eig(A)\n",
" isort = np.argsort(e.real)\n",
" e = e.real[isort]\n",
" v = v.real[:,isort]\n",
" x = np.linspace(0,L,N[i]+2)\n",
" v = np.pad(v,((1,1),(0,0)))\n",
" \n",
" print('Using {} Nodes'.format(N[i]))\n",
" print('First', (e[0]**0.5/(2*np.pi)))\n",
" print('Second', (e[1]**0.5/(2*np.pi)))\n",
" print('Third', (e[2]**0.5/(2*np.pi)))\n",
" print()\n",
" \n",
" plt.figure(1);\n",
" plt.xlabel('Time (s)')\n",
" plt.ylabel('Amplitude (m)')\n",
" plt.title('First Mode Convergence')\n",
" if N[i] == 45:\n",
" plt.plot(x,v[:,0]/np.max(v[:,0]),'o',label = 'N ='+ str(N[i]))\n",
" else:\n",
" plt.plot(x,-v[:,0]/np.max(-v[:,0]),'o',label = 'N ='+ str(N[i]))\n",
" plt.legend(bbox_to_anchor=(1,0.5),loc='best');\n",
" \n",
" plt.figure(2);\n",
" plt.xlabel('Time (s)')\n",
" plt.ylabel('Amplitude (m)')\n",
" plt.title('Second Mode Convergence')\n",
" if N[i] == 45 or N[i] == 6:\n",
" plt.plot(x,v[:,1]/np.max(v[:,1]),'o',label = 'N ='+ str(N[i]))\n",
" else:\n",
" plt.plot(x,-v[:,1]/np.max(v[:,1]),'o',label = 'N ='+ str(N[i]))\n",
" plt.legend(bbox_to_anchor=(1,0.5),loc='best');\n",
" \n",
" plt.figure(3);\n",
" plt.xlabel('Time (s)')\n",
" plt.ylabel('Amplitude (m)')\n",
" plt.title('Third Mode Convergence')\n",
" if N[i] == 45:\n",
" plt.plot(x,v[:,2]/np.max(v[:,2]),'o',label = 'N ='+ str(N[i]))\n",
" else:\n",
" plt.plot(x,-v[:,2]/np.max(-v[:,2]),'o',label = 'N =' + str(N[i]))\n",
" plt.legend(bbox_to_anchor=(1,0.5),loc='best');\n",
" \n",
"print('THERE NEEDS TO BE AT LEAST 30 NODES FOR CONVERGENCE')"
]
},
{
"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": 71,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using 30 nodes for convergence to calculate natural frequencies\n",
"\n",
"3 modes of vibration with 30 nodes on E string\n",
"First: 329.5582417096158\n",
"Second: 658.2705121393185\n",
"Third: 985.2930116053444\n",
"\n",
"3 modes of vibration with 30 nodes on B string\n",
"First: 246.99641153429778\n",
"Second: 493.35878682265803\n",
"Third: 738.4547171810427\n",
"\n",
"3 modes of vibration with 30 nodes on D string\n",
"First: 146.85180950460807\n",
"Second: 293.32665252038413\n",
"Third: 439.048530226062\n",
"\n",
"3 modes of vibration with 30 nodes on A string\n",
"First: 109.98239925642233\n",
"Second: 219.68247527133062\n",
"Third: 328.81862952292795\n",
"\n",
"3 modes of vibration with 30 nodes on High E string\n",
"First: 82.41968979777636\n",
"Second: 164.6278094339143\n",
"Third: 246.41333184434473\n"
]
}
],
"source": [
"N = 30\n",
"x = np.linspace(0,L,N)\n",
"dx = L/(N+1)\n",
"k_e = T_e/(dx**2*rho_e)\n",
"k_b = T_b/(dx**2*rho_b)\n",
"k_d = T_d/(dx**2*rho_d)\n",
"k_a = T_a/(dx**2*rho_a)\n",
"k_E = T_E/(dx**2*rho_E)\n",
"\n",
"A_e = k_e*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"A_b = k_b*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"A_d = k_d*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"A_a = k_a*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"A_E = k_E*(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_e,v_e = linalg.eig(A_e)\n",
"isort_e = np.argsort(e_e.real)\n",
"e_e = e_e.real[isort_e]\n",
"v_e = v_e.real[:,isort_e]\n",
"e_b,v_b = linalg.eig(A_b)\n",
"isort_b = np.argsort(e_b.real)\n",
"e_b = e_b.real[isort_b]\n",
"v_b = v_b.real[:,isort_b]\n",
"e_d,v_d = linalg.eig(A_d)\n",
"isort_d = np.argsort(e_d.real)\n",
"e_d = e_d.real[isort_d]\n",
"v_d = v_d.real[:,isort_d]\n",
"e_a,v_a = linalg.eig(A_a)\n",
"isort_a = np.argsort(e_a.real)\n",
"e_a = e_a.real[isort_a]\n",
"v_a = v_a.real[:,isort_a]\n",
"e_E,v_E = linalg.eig(A_E)\n",
"isort_E = np.argsort(e_E.real)\n",
"e_E = e_E.real[isort_E]\n",
"v_E = v_E.real[:,isort_E]\n",
"\n",
"print('Using {} nodes for convergence to calculate natural frequencies'.format(N))\n",
"print()\n",
"\n",
"print('3 modes of vibration with {} nodes on E string'.format(N))\n",
"f_e = np.array([e_e[0],e_e[1],e_e[2]])**0.5/ (2*np.pi)\n",
"print('First:', f_e[0])\n",
"print('Second:', f_e[1])\n",
"print('Third:', f_e[2])\n",
"print()\n",
"\n",
"print('3 modes of vibration with {} nodes on B string'.format(N))\n",
"f_b = np.array([e_b[0],e_b[1],e_b[2]])**0.5/ (2*np.pi)\n",
"print('First:', f_b[0])\n",
"print('Second:', f_b[1])\n",
"print('Third:', f_b[2])\n",
"print()\n",
"\n",
"print('3 modes of vibration with {} nodes on D string'.format(N))\n",
"f_d = np.array([e_d[0],e_d[1],e_d[2]])**0.5/ (2*np.pi)\n",
"print('First:', f_d[0])\n",
"print('Second:', f_d[1])\n",
"print('Third:', f_d[2])\n",
"print()\n",
"\n",
"print('3 modes of vibration with {} nodes on A string'.format(N))\n",
"f_a = np.array([e_a[0],e_a[1],e_a[2]])**0.5/ (2*np.pi)\n",
"print('First:', f_a[0])\n",
"print('Second:', f_a[1])\n",
"print('Third:', f_a[2])\n",
"print()\n",
"\n",
"print('3 modes of vibration with {} nodes on High E string'.format(N))\n",
"f_E = np.array([e_E[0],e_E[1],e_E[2]])**0.5/ (2*np.pi)\n",
"print('First:', f_E[0])\n",
"print('Second:', f_E[1])\n",
"print('Third:', f_E[2])"
]
},
{
"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": 72,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
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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": 72,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"N = 30\n",
"k_g = T_g/(dx**2*rho_g)\n",
"A_g = k_g*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"e_g,v_g = linalg.eig(A_g)\n",
"isort_g = np.argsort(e_g.real)\n",
"e_g = e_g.real[isort_g]\n",
"v_g = v_g.real[:,isort_g]\n",
"\n",
"samplerate=20000\n",
"t=np.arange(0,3,1/samplerate)\n",
"data = 100*(np.sin(t*e_e[0].real**0.5)+np.sin(t*e_b[0].real**0.5)+np.sin(t*e_g[0].real**0.5)+\n",
" np.sin(t*e_d[0].real**0.5)+np.sin(t*e_a[0].real**0.5)+np.sin(t*e_E[0].real**0.5)+\n",
" np.sin(t*e_e[1].real**0.5)+np.sin(t*e_b[1].real**0.5)+np.sin(t*e_g[1].real**0.5)+\n",
" np.sin(t*e_d[1].real**0.5)+np.sin(t*e_a[1].real**0.5)+np.sin(t*e_E[1].real**0.5)+\n",
" np.sin(t*e_e[2].real**0.5)+np.sin(t*e_b[2].real**0.5)+np.sin(t*e_g[2].real**0.5)+\n",
" np.sin(t*e_d[2].real**0.5)+np.sin(t*e_a[2].real**0.5)+np.sin(t*e_E[2].real**0.5))\n",
"Audio(data=data,rate=samplerate)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
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