Permalink
Cannot retrieve contributors at this time
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?
compmech-project05/CompMech05-BVPs_project.ipynb
Go to fileThis commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
743 lines (743 sloc)
443 KB
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
{ | |
"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._\n", | |
"\n", | |
"__Answer__ : For all step sizes the solution converges to about y=0.0014 m." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 19, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"import matplotlib.pyplot as plt\n", | |
"from scipy import linalg\n", | |
"from IPython.display import Audio\n", | |
"plt.rcParams.update({'font.size': 22})\n", | |
"plt.rcParams['lines.linewidth'] = 3" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 27, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"\n", | |
"height= 0.004 # [m]\n", | |
"L= 0.64 # [m]\n", | |
"A= 0.002*0.004*2 # [m^2]\n", | |
"I= 4*2**3/12*(1/100)**4 # [m^4]\n", | |
"E= 10e9 # [Pa]\n", | |
"\n", | |
"mu_E1= 0.401e-3 # [kg/m]\n", | |
"mu_B= 0.708e-3 # [kg/m]\n", | |
"mu_G= 1.140e-3 # [kg/m]\n", | |
"mu_D= 2.333e-3 # [kg/m]\n", | |
"mu_A= 4.466e-3 # [kg/m]\n", | |
"mu_E2= 6.790e-3 # [kg/m]\n", | |
"\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= 9.02*9.81 # [N]\n", | |
"TE2= 7.71*9.81 # [N]\n", | |
"\n", | |
"M= (TE+TB+TG+TD+TA+TE2)*height" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 31, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"finite difference A:\n", | |
"------------------\n", | |
"[[ 7. -4. 1. 0. 0.]\n", | |
" [-4. 6. -4. 1. 0.]\n", | |
" [ 1. -4. 6. -4. 1.]\n", | |
" [ 0. 1. -4. 5. -2.]\n", | |
" [ 0. 0. 2. -4. 2.]]\n", | |
"\n", | |
"finite difference b:\n", | |
"------------------\n", | |
"[ 0. 0. 0. -0.00011322 0.00022643]\n" | |
] | |
}, | |
{ | |
"data": { | |
"image/png": "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\n", | |
"text/plain": [ | |
"<Figure size 576x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"#1.a.\n", | |
"N= 6\n", | |
"h= L/(N-1)\n", | |
"A= np.diag(np.ones(N-1)*6)\\\n", | |
"+np.diag(np.ones(N-2)*-4,-1)\\\n", | |
"+np.diag(np.ones(N-2)*-4,1)\\\n", | |
"+np.diag(np.ones(N-3),-2)\\\n", | |
"+np.diag(np.ones(N-3),2)\n", | |
"A[0,0]+= 1\n", | |
"A[-1,-1]+= -4\n", | |
"A[-1,-3]+= 1\n", | |
"A[-2,-2]+= -1\n", | |
"A[-2,-1]+= 2\n", | |
"\n", | |
"b= np.zeros(N-1)\n", | |
"b[-1]+= 2*M*h**2/E/I\n", | |
"b[-2]+= -M*h**2/E/I\n", | |
"\n", | |
"w=np.linalg.solve(A,b)\n", | |
"xnum=np.arange(0,L+h,h)\n", | |
"\n", | |
"print('finite difference A:\\n------------------')\n", | |
"print(A)\n", | |
"print('\\nfinite difference b:\\n------------------')\n", | |
"print(b)\n", | |
"\n", | |
"x_an= np.linspace(0,L,100)\n", | |
"w_an= M*x_an**2/2/E/I\n", | |
"\n", | |
"plt.figure(figsize=(8,8))\n", | |
"plt.xlabel('Position on Guitar (m)')\n", | |
"plt.ylabel('Deflection (m)')\n", | |
"plt.title('Deflection with Position')\n", | |
"plt.plot(x_an,w_an,label='Analytical Solution')\n", | |
"plt.plot(xnum, np.block([0,w]),'o',label='Finite Difference')\n", | |
"plt.legend(bbox_to_anchor=(1,1));" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 46, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "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\n", | |
"text/plain": [ | |
"<Figure size 576x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"N= 20\n", | |
"h= L/(N-1)\n", | |
"A= np.diag(np.ones(N-1)*6)\\\n", | |
"+np.diag(np.ones(N-2)*-4,-1)\\\n", | |
"+np.diag(np.ones(N-2)*-4,1)\\\n", | |
"+np.diag(np.ones(N-3),-2)\\\n", | |
"+np.diag(np.ones(N-3),2)\n", | |
"A[0,0]+= 1\n", | |
"A[-1,-1]+= -4\n", | |
"A[-1,-3]+= 1\n", | |
"A[-2,-2]+= -1\n", | |
"A[-2,-1]+= 2\n", | |
"\n", | |
"b= np.zeros(N-1)\n", | |
"b[-1]+= 2*M*h**2/E/I\n", | |
"b[-2]+= -M*h**2/E/I\n", | |
"\n", | |
"w=np.linalg.solve(A,b)\n", | |
"xnum=np.arange(0,L+h,h)\n", | |
"\n", | |
"x_an= np.linspace(0,L,100)\n", | |
"w_an= M*x_an**2/2/E/I\n", | |
"\n", | |
"plt.figure(figsize=(8,8))\n", | |
"plt.xlabel('Position on Guitar (m)')\n", | |
"plt.ylabel('Deflection (m)')\n", | |
"plt.title('20 Nodes')\n", | |
"plt.plot(x_an,w_an,label='Analytical Solution')\n", | |
"plt.plot(xnum, np.block([0,w]),'o',label='Finite Difference')\n", | |
"plt.legend(bbox_to_anchor=(1,1));" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 38, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "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\n", | |
"text/plain": [ | |
"<Figure size 576x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"N= 40\n", | |
"h= L/(N-1)\n", | |
"A= np.diag(np.ones(N-1)*6)\\\n", | |
"+np.diag(np.ones(N-2)*-4,-1)\\\n", | |
"+np.diag(np.ones(N-2)*-4,1)\\\n", | |
"+np.diag(np.ones(N-3),-2)\\\n", | |
"+np.diag(np.ones(N-3),2)\n", | |
"A[0,0]+= 1\n", | |
"A[-1,-1]+= -4\n", | |
"A[-1,-3]+= 1\n", | |
"A[-2,-2]+= -1\n", | |
"A[-2,-1]+= 2\n", | |
"\n", | |
"b= np.zeros(N-1)\n", | |
"b[-1]+= 2*M*h**2/E/I\n", | |
"b[-2]+= -M*h**2/E/I\n", | |
"\n", | |
"w=np.linalg.solve(A,b)\n", | |
"xnum=np.arange(0,L+h,h)\n", | |
"\n", | |
"x_an= np.linspace(0,L,100)\n", | |
"w_an= M*x_an**2/2/E/I\n", | |
"\n", | |
"plt.figure(figsize=(8,8))\n", | |
"plt.xlabel('Position on Guitar (m)')\n", | |
"plt.ylabel('Deflection (m)')\n", | |
"plt.title('40 Nodes')\n", | |
"plt.plot(x_an,w_an,label='Analytical Solution')\n", | |
"plt.plot(xnum, np.block([0,w]),'o',label='Finite Difference')\n", | |
"plt.legend(bbox_to_anchor=(1,1));" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 39, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "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\n", | |
"text/plain": [ | |
"<Figure size 576x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"N= 60\n", | |
"h= L/(N-1)\n", | |
"A= np.diag(np.ones(N-1)*6)\\\n", | |
"+np.diag(np.ones(N-2)*-4,-1)\\\n", | |
"+np.diag(np.ones(N-2)*-4,1)\\\n", | |
"+np.diag(np.ones(N-3),-2)\\\n", | |
"+np.diag(np.ones(N-3),2)\n", | |
"A[0,0]+= 1\n", | |
"A[-1,-1]+= -4\n", | |
"A[-1,-3]+= 1\n", | |
"A[-2,-2]+= -1\n", | |
"A[-2,-1]+= 2\n", | |
"\n", | |
"b= np.zeros(N-1)\n", | |
"b[-1]+= 2*M*h**2/E/I\n", | |
"b[-2]+= -M*h**2/E/I\n", | |
"\n", | |
"w=np.linalg.solve(A,b)\n", | |
"xnum=np.arange(0,L+h,h)\n", | |
"\n", | |
"x_an= np.linspace(0,L,100)\n", | |
"w_an= M*x_an**2/2/E/I\n", | |
"\n", | |
"plt.figure(figsize=(8,8))\n", | |
"plt.xlabel('Position on Guitar (m)')\n", | |
"plt.ylabel('Deflection (m)')\n", | |
"plt.title('60 Nodes')\n", | |
"plt.plot(x_an,w_an,label='Analytical Solution')\n", | |
"plt.plot(xnum, np.block([0,w]),'o',label='Finite Difference')\n", | |
"plt.legend(bbox_to_anchor=(1,1));" | |
] | |
}, | |
{ | |
"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. \n", | |
"\n", | |
"__Answer__: 60 nodes needed to converge. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 48, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"L = 0.64 #m\n", | |
"mu= 0.00114 #kg/m\n", | |
"T = 71.81" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 51, | |
"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 \n", | |
"deltax = L/(N+1) \n", | |
"\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", | |
"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", | |
"omega1 = np.sqrt(eig_value[0].real)/(2*np.pi) \n", | |
"omega2 = np.sqrt(eig_value[1].real)/(2*np.pi) \n", | |
"omega3 = np.sqrt(eig_value[2].real)/(2*np.pi) \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", | |
"x = np.linspace(0,L,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", | |
"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": 52, | |
"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": [ | |
"from scipy import linalg\n", | |
"\n", | |
"N = 30\n", | |
"deltax = L/(N+1) \n", | |
"\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", | |
"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", | |
"omega1 = np.sqrt(eig_value[0].real)/(2*np.pi) \n", | |
"omega2 = np.sqrt(eig_value[1].real)/(2*np.pi) \n", | |
"omega3 = np.sqrt(eig_value[2].real)/(2*np.pi) \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", | |
"x = np.linspace(0,L,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", | |
"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": 53, | |
"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": [ | |
"from scipy import linalg\n", | |
"\n", | |
"N = 45\n", | |
"deltax = L/(N+1) \n", | |
"\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", | |
"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", | |
"omega1 = np.sqrt(eig_value[0].real)/(2*np.pi) \n", | |
"omega2 = np.sqrt(eig_value[1].real)/(2*np.pi) \n", | |
"omega3 = np.sqrt(eig_value[2].real)/(2*np.pi) \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", | |
"x = np.linspace(0,L,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", | |
"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": 54, | |
"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": { | |
"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 = 60\n", | |
"deltax = L/(N+1) \n", | |
"\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", | |
"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", | |
"omega1 = np.sqrt(eig_value[0].real)/(2*np.pi) \n", | |
"omega2 = np.sqrt(eig_value[1].real)/(2*np.pi) \n", | |
"omega3 = np.sqrt(eig_value[2].real)/(2*np.pi) \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", | |
"x = np.linspace(0,L,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", | |
"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": [ | |
"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": 65, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"First three natural frequencies of the first E string:\n", | |
"First= 324.258563803387 Hz\n", | |
"Second= 648.3021231114291 Hz\n", | |
"Third= 971.9158159907618 Hz\n", | |
"\n", | |
"First three natural frequencies of the B string:\n", | |
"First= 243.02442340154545 Hz\n", | |
"Second= 485.8877058207245 Hz\n", | |
"Third= 728.4288131221649 Hz\n", | |
"\n", | |
"First three natural frequencies of the G string:\n", | |
"First= 192.8417510461769 Hz\n", | |
"Second= 385.5556354822231 Hz\n", | |
"Third= 578.0138714818675 Hz\n", | |
"\n", | |
"First three natural frequencies of the D string:\n", | |
"First= 144.49026246426672 Hz\n", | |
"Second= 288.88471849683754 Hz\n", | |
"Third= 433.0876251917709 Hz\n", | |
"\n", | |
"First three natural frequencies of the A string:\n", | |
"First= 108.15381937904385 Hz\n", | |
"Second= 216.2359257489487 Hz\n", | |
"Third= 324.17465365093324 Hz\n", | |
"\n", | |
"First three natural frequencies of the second E string:\n", | |
"First= 81.09428580605798 Hz\n", | |
"Second= 162.13480083184666 Hz\n", | |
"Third= 243.06780995055306 Hz\n", | |
"\n" | |
] | |
} | |
], | |
"source": [ | |
"N = 60\n", | |
"L= 0.64 # [m]\n", | |
"dx= L/N\n", | |
"tensions= np.array([T_E1,T_B,T_G,T_D,T_A,T_E2])\n", | |
"mus= np.array([mu_E1,mu_B,mu_G,mu_D,mu_A,mu_E2])\n", | |
"names= np.array(['first E','B','G','D','A','second E'])\n", | |
"frequencies= np.zeros(3*len(tensions))\n", | |
"for i in range(0,len(tensions)):\n", | |
" T= tensions[i]\n", | |
" mu= mus[i]\n", | |
" k= T/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", | |
" e, v= linalg.eig(A)\n", | |
" isort = np.argsort(e.real)\n", | |
" e=e.real[isort]\n", | |
" v=v.real[:,isort]\n", | |
" print('First three natural frequencies of the {} string:'.format(names[i]))\n", | |
" print('First= {} Hz'.format(e[0]**0.5/2/np.pi))\n", | |
" print('Second= {} Hz'.format(e[1]**0.5/2/np.pi))\n", | |
" print('Third= {} Hz\\n'.format(e[2]**0.5/2/np.pi))\n", | |
" if i == 0:\n", | |
" frequencies[0]= e[0]**0.5/2/np.pi\n", | |
" frequencies[1]= e[1]**0.5/2/np.pi\n", | |
" frequencies[2]= e[2]**0.5/2/np.pi\n", | |
" if i == 1:\n", | |
" frequencies[3]= e[0]**0.5/2/np.pi\n", | |
" frequencies[4]= e[1]**0.5/2/np.pi\n", | |
" frequencies[5]= e[2]**0.5/2/np.pi\n", | |
" if i == 2:\n", | |
" frequencies[6]= e[0]**0.5/2/np.pi\n", | |
" frequencies[7]= e[1]**0.5/2/np.pi\n", | |
" frequencies[8]= e[2]**0.5/2/np.pi\n", | |
" if i == 3:\n", | |
" frequencies[9]= e[0]**0.5/2/np.pi\n", | |
" frequencies[10]= e[1]**0.5/2/np.pi\n", | |
" frequencies[11]= e[2]**0.5/2/np.pi\n", | |
" if i == 4:\n", | |
" frequencies[12]= e[0]**0.5/2/np.pi\n", | |
" frequencies[13]= e[1]**0.5/2/np.pi\n", | |
" frequencies[14]= e[2]**0.5/2/np.pi\n", | |
" if i == 5:\n", | |
" frequencies[15]= e[0]**0.5/2/np.pi\n", | |
" frequencies[16]= e[1]**0.5/2/np.pi\n", | |
" frequencies[17]= e[2]**0.5/2/np.pi" | |
] | |
}, | |
{ | |
"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": 66, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"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 IPython.display import Audio\n", | |
"N= 10000\n", | |
"dt= 2/N\n", | |
"t= np.linspace(0,2,N)\n", | |
"out_file=0\n", | |
"\n", | |
"for n in range(0,18):\n", | |
" out_file+= np.sin(2*np.pi*frequencies[n]*t)\n", | |
" \n", | |
"samplerate= int(1/dt)\n", | |
"Audio(data=out_file,rate=samplerate)\n", | |
"\n", | |
"plt.plot(np.arange(0,len(out_file))*dt*1000,out_file)\n", | |
"plt.xlim((0,200))\n", | |
"plt.xlabel('Time (ms)')\n", | |
"plt.ylabel('Input Signal (a.u.)')\n", | |
"plt.title('Audio Signal of the 18 Frequencies\\n');" | |
] | |
} | |
], | |
"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 | |
} |