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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": "markdown",
"metadata": {},
"source": [
"**PROBLEM 1 PART A)**"
]
},
{
"cell_type": "code",
"execution_count": 87,
"metadata": {},
"outputs": [],
"source": [
"#importing libraries\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"#defining constants\n",
"E = 10e9 #Pa\n",
"A = 0.02*0.04 #m^2\n",
"I = (0.04*0.02**3)/12 #m^4\n",
"h = 0.004 #m\n",
"L = 0.64 #m\n",
"\n",
"#since EI(d4w/dx4)=0, we integrate twice to solve for the deflection\n",
"M = (TE+TB+TG+TD+TA+TE)*h"
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {},
"outputs": [],
"source": [
"#next, we need to create a laod matrix like in NB 2, except now we use new boundary conditions:\n",
"# w\"(L)= M/EI, w(0)=0, w'(0)=1, W'''(L)=0\n",
"\n",
"N = 5 #number of segments\n",
"deltax = L/N #length of each segment \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",
"\n",
"#adding in boundary conditions\n",
"A[0,0] += 1\n",
"A[-2,-1] = -2\n",
"A[-1,-2] = -4\n",
"A[-1,-3] = 2\n",
"A[-2,-2] -= 1\n",
"A[-1,-1] = 2\n",
"\n",
"#defining the solution matrix:\n",
"B = np.zeros(N)\n",
"B[-1] += 2*M*deltax**2/(E*I)\n",
"B[-2] += -M*deltax**2/(E*I) \n",
"\n",
"#solving the load matrix\n",
"solution = np.linalg.solve(A,B)"
]
},
{
"cell_type": "code",
"execution_count": 89,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"For 5 segments, the deflection at the tip is 1.428462 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": [
"#defining x array\n",
"x = np.linspace(0,L,N+1) #guitar length in N segments\n",
"\n",
"plt.plot(x,np.block([0,solution]),'-o')\n",
"plt.title(\"Deflection vs Position for {} segments\".format(N));\n",
"\n",
"print(\"For {} segments, the deflection at the tip is {:.6f} mm\".format(N,solution[-1]*1000))"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"For 20 segments, the deflection at the tip is 1.428462 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": [
"#changing number of segments to 20\n",
"N = 20 #number of segments\n",
"deltax = L/N #length of each segment \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",
"\n",
"#adding in boundary conditions\n",
"A[0,0] += 1\n",
"A[-2,-1] = -2\n",
"A[-1,-2] = -4\n",
"A[-1,-3] = 2\n",
"A[-2,-2] -= 1\n",
"A[-1,-1] = 2\n",
"\n",
"#defining the solution matrix:\n",
"B = np.zeros(N)\n",
"B[-1] += 2*M*deltax**2/(E*I)\n",
"B[-2] += -M*deltax**2/(E*I) \n",
"\n",
"#solving the load matrix\n",
"solution = np.linalg.solve(A,B)\n",
"\n",
"x = np.linspace(0,L,N+1) #guitar length in N segments\n",
"\n",
"plt.plot(x,np.block([0,solution]),'-o')\n",
"plt.title(\"Deflection vs Position for {} segments\".format(N));\n",
"\n",
"print(\"For {} segments, the deflection at the tip is {:.6f} mm\".format(N,solution[-1]*1000))"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"For 100 segments, the deflection at the tip is 1.428462 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": [
"#changing number of segments to 20\n",
"N = 100 #number of segments\n",
"deltax = L/N #length of each segment \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",
"\n",
"#adding in boundary conditions\n",
"A[0,0] += 1\n",
"A[-2,-1] = -2\n",
"A[-1,-2] = -4\n",
"A[-1,-3] = 2\n",
"A[-2,-2] -= 1\n",
"A[-1,-1] = 2\n",
"\n",
"#defining the solution matrix:\n",
"B = np.zeros(N)\n",
"B[-1] += 2*M*deltax**2/(E*I)\n",
"B[-2] += -M*deltax**2/(E*I) \n",
"\n",
"#solving the load matrix\n",
"solution = np.linalg.solve(A,B)\n",
"\n",
"x = np.linspace(0,L,N+1) #guitar length in N segments\n",
"\n",
"plt.plot(x,np.block([0,solution]),'-o')\n",
"plt.title(\"Deflection vs Position for {} segments\".format(N));\n",
"\n",
"print(\"For {} segments, the deflection at the tip is {:.6f} mm\".format(N,solution[-1]*1000))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**As seen above by displaying the last number in the deflection matrix for each step size, the deflection converges to roughly y = 1.428mm**"
]
},
{
"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": 156,
"metadata": {},
"outputs": [],
"source": [
"#defining constants\n",
"L = 0.64 #m\n",
"mu = 0.00114 #kg/m\n",
"T = 71.81 #N"
]
},
{
"cell_type": "code",
"execution_count": 157,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The first three natural frequencies for 6 nodes are:\n",
" 1st: 194.4371 Hz\n",
" 2nd: 379.1243 Hz\n",
" 3rd: 544.8006 Hz\n",
"\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": [
"from scipy import linalg\n",
"\n",
"N = 6 #number of nodes\n",
"deltax = L/(N+1) #number of segments\n",
"\n",
"#defining boundary condition matrix\n",
"X = (T/((deltax**2)*mu))*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"#solving for eigen values and eigen vectors & sorting\n",
"eig_value,eig_vector=linalg.eig(X)\n",
"isort = np.argsort(eig_value.real)\n",
"eig_value=eig_value[isort]\n",
"eig_vector=eig_vector6[:,isort]\n",
"\n",
"#calculating natural frequencies\n",
"omega1 = np.sqrt(eig_value[0].real)/(2*np.pi) #first natural frequency\n",
"omega2 = np.sqrt(eig_value[1].real)/(2*np.pi) #second natural frequency\n",
"omega3 = np.sqrt(eig_value[2].real)/(2*np.pi) #third natural frequency\n",
"\n",
"print(\"The first three natural frequencies for {} nodes are:\\n 1st: {:.4f} Hz\\n 2nd: {:.4f} Hz\\n 3rd: {:.4f} Hz\\n\".format(N,omega1, omega2, omega3))\n",
"\n",
"#Plotting mode shapes\n",
"x = np.linspace(0,L,N) #node array\n",
"\n",
"plt.plot(x, eig_vector[:,0],label = 'First Mode')\n",
"plt.plot(x, eig_vector[:,1],label = 'Second Mode')\n",
"plt.plot(x, eig_vector[:,2],label = 'Third Mode')\n",
"\n",
"\n",
"plt.title('Mode Shapes for {} Nodes'.format(N))\n",
"#plt.xlabel('Node')\n",
"#plt.ylabel('Deflection [m]')\n",
"plt.legend(loc=1,fontsize=12);"
]
},
{
"cell_type": "code",
"execution_count": 158,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The first three natural frequencies for 30 nodes are:\n",
" 1st: 195.9946 Hz\n",
" 2nd: 391.4862 Hz\n",
" 3rd: 585.9728 Hz\n",
"\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 #number of nodes\n",
"deltax = L/(N+1) #number of segments\n",
"\n",
"#defining boundary condition matrix\n",
"X = (T/((deltax**2)*mu))*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"#solving for eigen values and eigen vectors & sorting\n",
"eig_value,eig_vector=linalg.eig(X)\n",
"isort = np.argsort(eig_value.real)\n",
"eig_value=eig_value[isort]\n",
"eig_vector=eig_vector[:,isort]\n",
"\n",
"#calculating natural frequencies\n",
"omega1 = np.sqrt(eig_value[0].real)/(2*np.pi) #first natural frequency\n",
"omega2 = np.sqrt(eig_value[1].real)/(2*np.pi) #second natural frequency\n",
"omega3 = np.sqrt(eig_value[2].real)/(2*np.pi) #third natural frequency\n",
"\n",
"print(\"The first three natural frequencies for {} nodes are:\\n 1st: {:.4f} Hz\\n 2nd: {:.4f} Hz\\n 3rd: {:.4f} Hz\\n\".format(N,omega1, omega2, omega3))\n",
"\n",
"#Plotting mode shapes\n",
"x = np.linspace(0,L,N) #node array\n",
"\n",
"plt.plot(x, eig_vector[:,0],label = 'First Mode')\n",
"plt.plot(x, eig_vector[:,1],label = 'Second Mode')\n",
"plt.plot(x, eig_vector[:,2],label = 'Third Mode')\n",
"\n",
"\n",
"plt.title('Mode Shapes for {} Nodes'.format(N))\n",
"#plt.xlabel('Node')\n",
"#plt.ylabel('Deflection [m]')\n",
"plt.legend(loc=1,fontsize=12);"
]
},
{
"cell_type": "code",
"execution_count": 159,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The first three natural frequencies for 45 nodes are:\n",
" 1st: 196.0404 Hz\n",
" 2nd: 391.8523 Hz\n",
" 3rd: 587.2073 Hz\n",
"\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 #number of nodes\n",
"deltax = L/(N+1) #number of segments\n",
"\n",
"#defining boundary condition matrix\n",
"X = (T/((deltax**2)*mu))*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"#solving for eigen values and eigen vectors & sorting\n",
"eig_value,eig_vector=linalg.eig(X)\n",
"isort = np.argsort(eig_value.real)\n",
"eig_value=eig_value[isort]\n",
"eig_vector=eig_vector[:,isort]\n",
"\n",
"#calculating natural frequencies\n",
"omega1 = np.sqrt(eig_value[0].real)/(2*np.pi) #first natural frequency\n",
"omega2 = np.sqrt(eig_value[1].real)/(2*np.pi) #second natural frequency\n",
"omega3 = np.sqrt(eig_value[2].real)/(2*np.pi) #third natural frequency\n",
"\n",
"print(\"The first three natural frequencies for {} nodes are:\\n 1st: {:.4f} Hz\\n 2nd: {:.4f} Hz\\n 3rd: {:.4f} Hz\\n\".format(N,omega1, omega2, omega3))\n",
"\n",
"#Plotting mode shapes\n",
"x = np.linspace(0,L,N) #node array\n",
"\n",
"plt.plot(x, eig_vector[:,0],label = 'First Mode')\n",
"plt.plot(x, eig_vector[:,1],label = 'Second Mode')\n",
"plt.plot(x, eig_vector[:,2],label = 'Third Mode')\n",
"\n",
"\n",
"plt.title('Mode Shapes for {} Nodes'.format(N))\n",
"#plt.xlabel('Node')\n",
"#plt.ylabel('Deflection [m]')\n",
"plt.legend(loc=1,fontsize=12);"
]
},
{
"cell_type": "code",
"execution_count": 160,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The first three natural frequencies for 60 nodes are:\n",
" 1st: 196.0569 Hz\n",
" 2nd: 391.9837 Hz\n",
" 3rd: 587.6507 Hz\n",
"\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 = 60 #number of nodes\n",
"deltax = L/(N+1) #number of segments\n",
"\n",
"#defining boundary condition matrix\n",
"X = (T/((deltax**2)*mu))*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
"#solving for eigen values and eigen vectors & sorting\n",
"eig_value,eig_vector=linalg.eig(X)\n",
"isort = np.argsort(eig_value.real)\n",
"eig_value=eig_value[isort]\n",
"eig_vector=eig_vector[:,isort]\n",
"\n",
"#calculating natural frequencies\n",
"omega1 = np.sqrt(eig_value[0].real)/(2*np.pi) #first natural frequency\n",
"omega2 = np.sqrt(eig_value[1].real)/(2*np.pi) #second natural frequency\n",
"omega3 = np.sqrt(eig_value[2].real)/(2*np.pi) #third natural frequency\n",
"\n",
"print(\"The first three natural frequencies for {} nodes are:\\n 1st: {:.4f} Hz\\n 2nd: {:.4f} Hz\\n 3rd: {:.4f} Hz\\n\".format(N,omega1, omega2, omega3))\n",
"\n",
"#Plotting mode shapes\n",
"x = np.linspace(0,L,N) #node array\n",
"\n",
"plt.plot(x, eig_vector[:,0],label = 'First Mode')\n",
"plt.plot(x, eig_vector[:,1],label = 'Second Mode')\n",
"plt.plot(x, eig_vector[:,2],label = 'Third Mode')\n",
"\n",
"\n",
"plt.title('Mode Shapes for {} Nodes'.format(N))\n",
"#plt.xlabel('Node')\n",
"#plt.ylabel('Deflection [m]')\n",
"plt.legend(loc=1,fontsize=12);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**From the results above, it takes roughly 30 nodes for the first three nodes to converge**"
]
},
{
"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": 161,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"For T = 75.635 N The first three natural frequencies are:\n",
" 1st: 201.1469 Hz\n",
" 2nd: 401.7775 Hz\n",
" 3rd: 601.3768 Hz\n",
"\n",
"For T = 70.828 N The first three natural frequencies are:\n",
" 1st: 194.6502 Hz\n",
" 2nd: 388.8007 Hz\n",
" 3rd: 581.9532 Hz\n",
"\n",
"For T = 82.502 N The first three natural frequencies are:\n",
" 1st: 210.0798 Hz\n",
" 2nd: 419.6203 Hz\n",
" 3rd: 628.0836 Hz\n",
"\n",
"For T = 88.584 N The first three natural frequencies are:\n",
" 1st: 217.6858 Hz\n",
" 2nd: 434.8128 Hz\n",
" 3rd: 650.8237 Hz\n",
"\n",
"For T = 75.635 N The first three natural frequencies are:\n",
" 1st: 201.1469 Hz\n",
" 2nd: 401.7775 Hz\n",
" 3rd: 601.3768 Hz\n",
"\n",
"For T = 71.809 N The first three natural frequencies are:\n",
" 1st: 195.9936 Hz\n",
" 2nd: 391.4840 Hz\n",
" 3rd: 585.9695 Hz\n",
"\n"
]
}
],
"source": [
"#defining tensions of each string\n",
"TE = 7.28*9.81 #N\n",
"TB = 7.22*9.81 #N\n",
"TG = 7.32*9.81 #N\n",
"TD = 8.41*9.81 #N\n",
"TA = 9.03*9.81 #N\n",
"TE = 7.71*9.81 #N\n",
"\n",
"#creating array to loop through\n",
"Tension = np.array([TE,TB,TD,TA,TE,TG])\n",
"\n",
"#creating a for loop to calcluate the three neatural frequency for each string tension\n",
"for T in Tension:\n",
" N = 30 #converged number of nodes\n",
" deltax = L/(N+1) #number of segments\n",
"\n",
" #defining boundary condition matrix\n",
" X = (T/((deltax**2)*mu))*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
" #solving for eigen values and eigen vectors & sorting\n",
" eig_value,eig_vector=linalg.eig(X)\n",
" isort = np.argsort(eig_value.real)\n",
" eig_value=eig_value[isort]\n",
" eig_vector=eig_vector[:,isort]\n",
"\n",
" #calculating natural frequencies\n",
" omega1 = np.sqrt(eig_value[0].real)/(2*np.pi) #first natural frequency\n",
" omega2 = np.sqrt(eig_value[1].real)/(2*np.pi) #second natural frequency\n",
" omega3 = np.sqrt(eig_value[2].real)/(2*np.pi) #third natural frequency\n",
"\n",
" print(\"For T = {:.3f} N The first three natural frequencies are:\\n 1st: {:.4f} Hz\\n 2nd: {:.4f} Hz\\n 3rd: {:.4f} Hz\\n\".format(T,omega1, omega2, omega3)) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**The following list is based off of tension, but can easily be refered back to the table for which string it is**"
]
},
{
"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": 151,
"metadata": {},
"outputs": [],
"source": [
"from IPython.display import Audio\n",
"\n",
"r=20000\n",
"tsig=np.arange(0,3,1/r) #3 seconds"
]
},
{
"cell_type": "code",
"execution_count": 155,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[201.14694323 401.77754514 601.37678986 194.65019668 388.80072909\n",
" 581.95321561 210.07977615 419.62028053 628.08362567 217.68581154\n",
" 434.81282672 650.82368361 201.14694323 401.77754514 601.37678986\n",
" 195.99355421 391.48399578 585.96950354]\n"
]
}
],
"source": [
"signal = np.zeros(18)\n",
"i=0\n",
"\n",
"#creating a for loop to add each frequency to signal array\n",
"for T in Tension:\n",
" N = 30 #converged number of nodes\n",
" deltax = L/(N+1) #number of segments\n",
"\n",
" #defining boundary condition matrix\n",
" X = (T/((deltax**2)*mu))*(np.diag(np.ones(N)*2)\\\n",
" -np.diag(np.ones(N-1),-1)\\\n",
" -np.diag(np.ones(N-1),1))\n",
"\n",
" #solving for eigen values and eigen vectors & sorting\n",
" eig_value,eig_vector=linalg.eig(X)\n",
" isort = np.argsort(eig_value.real)\n",
" eig_value=eig_value[isort]\n",
" eig_vector=eig_vector[:,isort]\n",
"\n",
" #adding frequencies to signal array\n",
" signal[i] = np.sqrt(eig_value[0].real)/(2*np.pi) #first natural frequency\n",
" i+=1\n",
" signal[i] = np.sqrt(eig_value[1].real)/(2*np.pi) #second natural frequency\n",
" i+=1\n",
" signal[i] = np.sqrt(eig_value[2].real)/(2*np.pi) #third natural frequency\n",
" i+=1\n",
" \n",
"print(signal)"
]
},
{
"cell_type": "code",
"execution_count": 153,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" <audio controls=\"controls\" >\n",
" <source 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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": 153,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#adding a data array for each signal\n",
"data = 0\n",
"for i in range(len(signal)):\n",
" data += np.sin(signal[i]*2*np.pi*tsig)\n",
"\n",
" #creating audio\n",
"Audio(data=data,rate=r)"
]
},
{
"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
}