Skip to content
Permalink
master
Switch branches/tags

Name already in use

A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?
Go to file
 
 
Cannot retrieve contributors at this time
{
"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": 53,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"finite difference A:\n",
"------------------\n",
"[[ 7 -4 1 0 0 0]\n",
" [-4 6 -4 1 0 0]\n",
" [ 1 -4 6 -4 1 0]\n",
" [ 0 1 -4 6 -4 1]\n",
" [ 0 0 1 -4 5 -2]\n",
" [ 0 0 0 2 -4 2]]\n",
"\n",
"finite difference b:\n",
"------------------\n",
"[ 0. 0. 0. 0. -0.00050101 0.00100203]\n",
"\n",
"deflection of beam (m)\n",
"-------------\n",
" [0. 0.00025051 0.00100203 0.00225456 0.00400811 0.00626267\n",
" 0.00901824]\n",
"39 39\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": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy import linalg\n",
"plt.rcParams.update({'font.size': 12})\n",
"plt.rcParams['lines.linewidth'] = 2\n",
"\n",
"#define constants \n",
"L = 0.64 #m\n",
"h = 4e-3 #m\n",
"E = 10e9 #Pa\n",
"I = ((4*2)**3/12)*1e-8 #m^4\n",
"\n",
"#define densities and tensions (units: g/m and g)\n",
"mu_E_high = 0.401\n",
"T_E_high = 7.28e3\n",
"mu_B = 0.708\n",
"T_B = 7.22e3\n",
"mu_G = 1.140\n",
"T_G = 7.32e3\n",
"mu_D = 2.333\n",
"T_D = 8.41e3\n",
"mu_A = 4.466\n",
"T_A = 9.03e3\n",
"mu_E_low = 6.790\n",
"T_E_low = 7.71e3\n",
"\n",
"#Integrate with 6 elements\n",
"\n",
"A=np.array([[7, -4, 1, 0, 0, 0],\n",
" [-4, 6, -4, 1, 0, 0],\n",
" [1, -4, 6, -4, 1, 0],\n",
" [0, 1, -4, 6, -4, 1],\n",
" [0, 0, 1, -4, 5, -2],\n",
" [0, 0, 0, 2, -4, 2]])\n",
"\n",
"M = (T_E_high + T_E_low + T_B + T_G + T_D + T_A) * h\n",
"hh = L/6\n",
"b=np.array([0, 0, 0, 0, -M*hh**2/E/I, 2*M*hh**2/E/I])\n",
"\n",
"w=np.linalg.solve(A,b)\n",
"\n",
"w = np.append(0, w)\n",
"\n",
"x=np.array([0, hh, 2*hh, 3*hh, 4*hh, 5*hh, 6*hh])\n",
"\n",
"plt.title('w vs. x, 6 & 40 segments')\n",
"plt.plot(x,w,label='finite differences 6 segments')\n",
"\n",
"w_analytic=lambda x: M*L**2/(2*E*I)*(x/L)**2\n",
"#plt.plot(x,w_analytic(x),'ro', label='analytic')\n",
"\n",
"#print(w)\n",
"print('finite difference A:\\n------------------')\n",
"print(A)\n",
"print('\\nfinite difference b:\\n------------------')\n",
"print(b)\n",
"print('\\ndeflection of beam (m)\\n-------------\\n',w)\n",
"\n",
"# 40 elements\n",
"numelem = 40\n",
"hh=L/(numelem-1)\n",
"A40=np.diag(np.ones(39)*6)\\\n",
"+np.diag(np.ones(38)*-4,-1)\\\n",
"+np.diag(np.ones(38)*-4,1)\\\n",
"+np.diag(np.ones(37),-2)\\\n",
"+np.diag(np.ones(37),2)\n",
"\n",
"A40[0,0]+=1\n",
"A40[-1,-1]+=-1\n",
"A40[numelem-2,numelem-2]=2\n",
"A40[numelem-3,numelem-2]=-2\n",
"A40[numelem-2,numelem-4]=2\n",
"A40[numelem-3,numelem-3]=5\n",
"\n",
"b40 = np.zeros(numelem-1)\n",
"\n",
"b40[numelem-2] = 2*M*hh**2/E/I\n",
"b40[numelem-3] = -M*hh**2/E/I\n",
"\n",
"print(len(A40),len(b40))\n",
"w40=np.linalg.solve(A40,b40)\n",
"x40 = np.linspace(0,L,num=numelem-1)\n",
"\n",
"plt.plot(x40,w40,label='finite differences 40 segments')\n",
"plt.plot(x40,w_analytic(x40),'r.', label='analytic solution')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"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": 80,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First three natural frequencies, 6 element = 194.4360035437754 379.12217397582145 544.797575528388\n",
"First three natural frequencies, 30 elements = 195.99355421041057 391.4839957781058 585.969503543348\n",
"First three natural frequencies, 45 elements = 196.03934498705303 391.8501168671653 587.2040090393828\n",
"First three natural frequencies, 60 elements = 196.05578023030412 391.98156274026314 587.6474360065606\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": [
"N=6# N-node guitar string\n",
"dx=L/(N+1)\n",
"\n",
"k = T_G*9.81/dx**2/mu_G\n",
"\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,v6=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e=e[isort]\n",
"v6=v6[:,isort]\n",
"\n",
"print(\"First three natural frequencies, 6 element = \", e.real[0]**0.5/2/np.pi, e.real[1]**0.5/2/np.pi, e.real[2]**0.5/2/np.pi)\n",
"\n",
"N=30# N-node guitar string\n",
"dx=L/(N+1)\n",
"\n",
"k = T_G*9.81/dx**2/mu_G\n",
"\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,v30=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e=e[isort]\n",
"v30=v30[:,isort]\n",
"\n",
"print(\"First three natural frequencies, 30 elements = \", e.real[0]**0.5/2/np.pi, e.real[1]**0.5/2/np.pi, e.real[2]**0.5/2/np.pi)\n",
"\n",
"N=45# N-node guitar string\n",
"dx=L/(N+1)\n",
"\n",
"k = T_G*9.81/dx**2/mu_G\n",
"\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,v45=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e=e[isort]\n",
"v45=v45[:,isort]\n",
"\n",
"print(\"First three natural frequencies, 45 elements = \", e.real[0]**0.5/2/np.pi, e.real[1]**0.5/2/np.pi, e.real[2]**0.5/2/np.pi)\n",
"\n",
"\n",
"N=60# N-node guitar string\n",
"dx=L/(N+1)\n",
"\n",
"k = T_G*9.81/dx**2/mu_G\n",
"\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,v60=linalg.eig(A)\n",
"isort = np.argsort(e.real)\n",
"e=e[isort]\n",
"v60=v60[:,isort]\n",
"\n",
"print(\"First three natural frequencies, 60 elements = \", e.real[0]**0.5/2/np.pi, e.real[1]**0.5/2/np.pi, e.real[2]**0.5/2/np.pi)\n",
"\n",
"\n",
"plt.figure(1)\n",
"plt.title('First Mode')\n",
"x60=np.linspace(0,L,N)\n",
"y0=0.1*np.sin(np.pi*x/L)\n",
"plt.plot(x60,v60[:,0],'o-',label='60 segments')\n",
"x45=np.linspace(0,L,45)\n",
"plt.plot(x45,v45[:,0],'g.',label='45 segments')\n",
"x30=np.linspace(0,L,30)\n",
"plt.plot(x30,v30[:,0],'r.',label='30 segments')\n",
"x6=np.linspace(0,L,6)\n",
"plt.plot(x6,v6[:,0],'b+',label='6 segments')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');\n",
"\n",
"\n",
"plt.figure(2)\n",
"plt.title('Second Mode')\n",
"plt.plot(x60,v60[:,1],'o-',label='60 segments')\n",
"plt.plot(x45,v45[:,1],'g.',label='45 segments')\n",
"plt.plot(x30,v30[:,1],'r.',label='30 segments')\n",
"plt.plot(x6,v6[:,1],'b+',label='6 segments')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');\n",
"\n",
"plt.figure(3)\n",
"plt.title('Third Mode')\n",
"plt.plot(x60,v60[:,2],'o-',label='60 segments')\n",
"plt.plot(x45,v45[:,2],'g.',label='45 segments')\n",
"plt.plot(x30,v30[:,2],'r.',label='30 segments')\n",
"plt.plot(x6,v6[:,2],'b+',label='6 segments')\n",
"plt.legend(bbox_to_anchor=(1,0.5),loc='center left');"
]
},
{
"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": 89,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"First three natural frequencies, 80 elements, high E string = 329.6786446859916 659.2333107162825 988.5400660592479\n",
"First three natural frequencies, 80 elements, B string = 247.0866508282831 494.0803824723907 740.8883106909918\n",
"First three natural frequencies, 80 elements, G string = 196.06515978493042 392.056587481797 587.9005787300415\n",
"First three natural frequencies, 80 elements, D string = 146.90546131081632 293.7556774856881 440.49542416393336\n",
"First three natural frequencies, 80 elements, A string = 110.02258094973527 220.00378690639837 329.90225843629725\n",
"First three natural frequencies, 80 elements, low E string = 82.44980154949074 164.86859710057612 247.2253923149307\n",
"[329.67864469 659.23331072 988.54006606 247.08665083 494.08038247\n",
" 740.88831069 196.06515978 392.05658748 587.90057873 146.90546131\n",
" 293.75567749 440.49542416 110.02258095 220.00378691 329.90225844\n",
" 82.44980155 164.8685971 247.22539231]\n"
]
}
],
"source": [
"def string_wave(N,T,mu):\n",
" dx=L/(N+1)\n",
" k = T*9.81/dx**2/mu\n",
"\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",
" return e,v\n",
"\n",
"N = 80\n",
"\n",
"eigval,eigvec = string_wave(N,T_E_high,mu_E_high)\n",
"print(\"First three natural frequencies, 80 elements, high E string = \", eigval.real[0]**0.5/2/np.pi, eigval.real[1]**0.5/2/np.pi, eigval.real[2]**0.5/2/np.pi)\n",
"freq = np.array([eigval.real[0]**0.5/2/np.pi, eigval.real[1]**0.5/2/np.pi, eigval.real[2]**0.5/2/np.pi])\n",
"\n",
"eigval,eigvec = string_wave(N,T_B,mu_B)\n",
"print(\"First three natural frequencies, 80 elements, B string = \", eigval.real[0]**0.5/2/np.pi, eigval.real[1]**0.5/2/np.pi, eigval.real[2]**0.5/2/np.pi)\n",
"freq = np.append(freq, np.array([eigval.real[0]**0.5/2/np.pi, eigval.real[1]**0.5/2/np.pi, eigval.real[2]**0.5/2/np.pi]))\n",
"\n",
"eigval,eigvec = string_wave(N,T_G,mu_G)\n",
"print(\"First three natural frequencies, 80 elements, G string = \", eigval.real[0]**0.5/2/np.pi, eigval.real[1]**0.5/2/np.pi, eigval.real[2]**0.5/2/np.pi)\n",
"freq = np.append(freq, np.array([eigval.real[0]**0.5/2/np.pi, eigval.real[1]**0.5/2/np.pi, eigval.real[2]**0.5/2/np.pi]))\n",
"\n",
"eigval,eigvec = string_wave(N,T_D,mu_D)\n",
"print(\"First three natural frequencies, 80 elements, D string = \", eigval.real[0]**0.5/2/np.pi, eigval.real[1]**0.5/2/np.pi, eigval.real[2]**0.5/2/np.pi)\n",
"freq = np.append(freq, np.array([eigval.real[0]**0.5/2/np.pi, eigval.real[1]**0.5/2/np.pi, eigval.real[2]**0.5/2/np.pi]))\n",
"\n",
"eigval,eigvec = string_wave(N,T_A,mu_A)\n",
"print(\"First three natural frequencies, 80 elements, A string = \", eigval.real[0]**0.5/2/np.pi, eigval.real[1]**0.5/2/np.pi, eigval.real[2]**0.5/2/np.pi)\n",
"freq = np.append(freq, np.array([eigval.real[0]**0.5/2/np.pi, eigval.real[1]**0.5/2/np.pi, eigval.real[2]**0.5/2/np.pi]))\n",
"\n",
"eigval,eigvec = string_wave(N,T_E_low,mu_E_low)\n",
"print(\"First three natural frequencies, 80 elements, low E string = \", eigval.real[0]**0.5/2/np.pi, eigval.real[1]**0.5/2/np.pi, eigval.real[2]**0.5/2/np.pi)\n",
"freq = np.append(freq, np.array([eigval.real[0]**0.5/2/np.pi, eigval.real[1]**0.5/2/np.pi, eigval.real[2]**0.5/2/np.pi]))\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": 115,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" <audio controls=\"controls\" >\n",
" <source src=\"data:audio/wav;base64,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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": 115,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import Audio\n",
"r=20000\n",
"tsig=np.arange(0,1,1/r)\n",
"signal = np.sin(freq[0]*2*np.pi*tsig) + np.sin(freq[1]*2*np.pi*tsig) + np.sin(freq[2]*2*np.pi*tsig) + np.sin(freq[3]*2*np.pi*tsig) + np.sin(freq[4]*2*np.pi*tsig) + np.sin(freq[5]*2*np.pi*tsig) + np.sin(freq[6]*2*np.pi*tsig) + np.sin(freq[7]*2*np.pi*tsig)+ np.sin(freq[8]*2*np.pi*tsig)+ np.sin(freq[9]*2*np.pi*tsig)+ np.sin(freq[10]*2*np.pi*tsig)+ np.sin(freq[11]*2*np.pi*tsig)+ np.sin(freq[12]*2*np.pi*tsig)+ np.sin(freq[13]*2*np.pi*tsig)+ np.sin(freq[14]*2*np.pi*tsig)+ np.sin(freq[15]*2*np.pi*tsig)+ np.sin(freq[16]*2*np.pi*tsig)+ np.sin(freq[17]*2*np.pi*tsig)\n",
"Audio(data=100*signal,rate=r)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"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
}