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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": [
"$$w(x)=\\frac{Ax^3}{6}+\\frac{Bx^2}{2}+Cx+D$$\n",
"\n",
"$$\\frac{d^4w}{dx^4} \\approx EI\\frac{w(x_{i+2})−4w(x_{i+1})+6w(x_i)−4w(x_{i-1})+w(x_{i-2})}{h^4}=0$$\n",
"\n",
"__Boundary Conditions:__\n",
"\n",
"* $w_0=0$\n",
"* $w'_0=0=\\frac{w_{1}-w_{-1}}{2h} \\rightarrow w_{-1} = w_1$\n",
"* $w''_L=\\frac{M}{EI} = \\frac{w_{7}-2w_{6}+w_{5}}{h^2} \\rightarrow w_{7}=\\frac{Mh^2}{EI}-w_{5}+2w_{6}$\n",
"* $w'''_L=0=\\frac{w_{8} − 2 w_{7} + 2 w_{5} − w_{4}}{2h^3} \\rightarrow w_8 = 2w_7-2w_5+w_4 = 2(\\frac{Mh^2}{EI}-w_{5}+2w_{6})-2w_5+w_4 = \\frac{2Mh^2}{EI}-4w_5+4w_6+w_4$\n",
"\n",
"__Equations:__\n",
"\n",
"1. $w_{-1} - 4w_0 +6w_1-4w_2+w_3 = 0$\n",
"\n",
"2. $w_{0} - 4w_1 +6w_2-4w_3+w_4 = 0$\n",
"\n",
"3. $w_{1} - 4w_2 +6w_3-4w_4+w_5 = 0$\n",
"\n",
"4. $w_{2} - 4w_3 +6w_4-4w_5+w_6 = 0$\n",
"\n",
"5. $w_{3} - 4w_4 +6w_5-4w_6+w_7 = 0$\n",
"\n",
"6. $w_{4} - 4w_5 +6w_6-4w_7+w_8 = 0$\n",
"\n",
"\n",
"1. $w_{1} - 4w_0 +6w_1-4w_2+w_3 = 0$\n",
"\n",
"2. $w_{0} - 4w_1 +6w_2-4w_3+w_4 = 0$\n",
"\n",
"3. $w_{1} - 4w_2 +6w_3-4w_4+w_5 = 0$\n",
"\n",
"4. $w_{2} - 4w_3 +6w_4-4w_5+w_6 = 0$\n",
"\n",
"5. $w_{3} - 4w_4 +6w_5-4w_6+\\frac{Mh^2}{EI}-w_{5}+2w_{6} = 0$\n",
"\n",
"6. $w_{4} - 4w_5 +6w_6-4(\\frac{Mh^2}{EI}-w_{5}+2w_{6})+\\frac{2Mh^2}{EI}-4w_5+4w_6+w_4 = 0$\n",
"\n",
"\n",
"1. $7w_1-4w_2+w_3 = 0$\n",
"\n",
"2. $-4w_1 +6w_2-4w_3+w_4 = 0$\n",
"\n",
"3. $w_{1} - 4w_2 +6w_3-4w_4+w_5 = 0$\n",
"\n",
"4. $w_{2} - 4w_3 +6w_4-4w_5+w_6 = 0$\n",
"\n",
"5. $w_{3} - 4w_4 +5w_5-2w_6 = -\\frac{Mh^2}{EI}$\n",
"\n",
"6. $2w_{4} - 4w_5 +2w_6 = \\frac{2Mh^2}{EI}$\n",
"\n",
"\n",
"$\\left[\\begin{array}{cccccc}\n",
"7 & -4 & 1 & 0 & 0 & 0 \\\\\n",
"-4 & 6 & -4 & 1 & 0 & 0\\\\\n",
"1 & -4 & 6 & -4 & 1 & 0\\\\\n",
"0 & 1 & -4 & 6 & -4 & 1\\\\\n",
"0 & 0 & 1 & -4 & 5 & -2\\\\\n",
"0 & 0 & 0 & 1 & -2 & 1\n",
"\\end{array}\\right]\n",
"\\left[\\begin{array}{c}\n",
"w_{1}\\\\\n",
"w_{2}\\\\\n",
"w_{3}\\\\\n",
"w_{4}\\\\\n",
"w_{5}\\\\\n",
"w_{6}\n",
"\\end{array}\\right]=\n",
"\\left[\\begin{array}{c}\n",
"0\\\\\n",
"0\\\\\n",
"0\\\\\n",
"0\\\\\n",
"-\\frac{Mh^2}{EI}\\\\\n",
"\\frac{Mh^2}{EI}\n",
"\\end{array}\\right]$"
]
},
{
"cell_type": "code",
"execution_count": 278,
"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*9.8 ; 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",
"# Solving for constants:\n",
"A = 0 ; B = M/E/I ; C = 0 ; D = 0\n",
"# y = Mx^2/(2EI)\n",
"x=np.linspace(0,0.64,1000)\n",
"y = lambda x: M*x**2/(2*E*I)"
]
},
{
"cell_type": "code",
"execution_count": 279,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Deflection at end of guitar neck: 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('Deflection at end of guitar neck:',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": 280,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Deflection at end of guitar neck: 1.414 mm\n"
]
},
{
"data": {
"image/png": 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0xvnBA6FxpftFN2vWLKKioujWrRthYWF07tyZ2bNn8+yzz+ZbkvPRRx9lyJAhAFx99dXUq1ePJUuW8NBDDwEwYsSInLbZ2dnccsstbN68mf/+979cf/31RR57yJAhTJgwgY8++ohbbrkFcK5UoqOj6d69OyEhITRp0gSAa665psTzmD59Ops3b+brr7/mqquuAqBjx/zjDl56KXc8eFZWVs6VzqJFixg4cKCbb5cx5S9lD8+mPUe4ZADwQ3YMD2f8mSyC2ZuS6uPgSsfNlcN6IFZEmopIGNAfWFygzWJgoGfU0jXAUVXd57JvPiISBSwFxqhq0X/KVkJpaWksXLiQO++8k7CwMAAGDBjATz/9xLp16/K17dKlS87XtWvXJjo6Ot+VQ1JSEoMGDSImJoaQkBBCQ0N5//33+eGHH4o9fmxsLDfddBNTp04FnFFT06dP54EHHiAkpHQLCq5Zs4bWrVvnJIairFu3js6dO1O7dm1CQkKoUqUKJ06cKDFGY3wq7Ti8ew915BgAh/UChmY8znGqANAgyreL95SW1+SgqpnACGAlsBWYo6qbReQhEXnI02wZsBPYAbwF/KGkvgAicqeIJAHXAktF5MxwlhHAxcCTIvKN58P/Jh4pZ8uXLyclJYUePXqQkpJCSkoKHTp0IDw8vNCtpaioqHzlsLAwTp92xlhnZ2dzxx138Pnnn/P000/z4Ycfsn79erp3757TpjhDhw5l3rx5HD9+nDVr1rB7924GDx5c6nM5fPgw9evXL3b7nj176NKlC6rK//3f/7F27VrWr19PdHS01xiN8YnsLJg3FA5sASBdQxie/ig/az0AIkODGdW1uS8jLDVXf/Kp6jKcBJC3bnKerxV4uGC/4vp66hfi3DoqWP8P4B9u4jonpbyl42tnEkC/fv0KbZszZ06+2zAl2bFjB4mJiSxfvpxu3brl1Kemer/k7devH3/605+YO3cuH374Ie3bt6dFi4Kjmr2rXbt2iQ+XV6xYwalTp1i0aBFVq1YFnIfiR44cKfWxjCkX7z8J23OHa29q8wz7tl6KpKTSICqSUV2b+83a826V7n6A8YkTJ06wZMkSBgwYwLBhw/JtS0xM5LHHHuPDDz90ta8zSSA8PHd08O7du1m7di1XXHFFiX0jIyMZMGAAr732Gt9//z0vvvhivu1nbnedPn2aiIiIYvdz6623MnfuXDZu3FjkMVNTUwkKCsp3u2rOnDlkZmZ6P0FjylvCFFj3Wm75hse4utMfWFtwwH+AsekzAsCiRYs4deoUf/7zn+nQoUO+jxEjRlC7dm3X7zxceumlNGzYkJEjR7J06VJmz55Nly5diIlx91fN0KFD+frrr1FV+vfvX2jfAJMmTWL9+vVs21b06IyBAwfSqlUrunTpwuTJk/nwww95++23GT3aeYG+Y8eOZGVlMXjwYFavXs0rr7zC6NGjC90uM8bndqyCpSNzy5f19Ps5k9yy5BAAZs2aRWxsLO3bty+0LTQ0lLvvvpsFCxaQllbodZBCwsPDWbBgASEhIfTt25cnn3ySMWPGcPPN7tatjYuLIyYmhj59+lCjRv4RXzfeeCOjRo1i0qRJtG/fnuHDixyFTEREBGvWrKFnz578/e9/p3v37jz//PM0aNAAgFatWjFlyhS+/PJLbr/9dt59913mzp1b6HjG+NQvm2DOb0GznHL9K+HO/4OgivFrVfKOWw9UcXFxmpCQUOz2rVu3ctlll5VjRBXXli1baNmyJatWreLWW2/1dTilZj8LpkwcTYb/dILjnpH51RvCg6ugevEDLfyRiGxQ1biittkzB+PK4cOH2bZtG08++SSXX355ofcSjKk0Th+Dd+/OTQzh1eG+uQGXGLypGNc/5rz73//+xw033MC+fftypukwptLJyoC5v4X93znloBC4ZwbUK/2oPX9nycG48tvf/pbs7Gy2bNlik+iZykkVlj4GP67OrbvjVWjWwVcRnVeWHIwxxo1PX4Cvp+eWbx4NV93ru3jOs0qTHCrCg3dzbuxnwJy1jXNhzTO55SsHQIdC655VKJUiOYSGhrp6A9hUbKmpqYSGhvo6DBNofloLi/6QW25yI/R8BSr4c7dKkRyio6NJTk7m1KlT9tdjJaSqnDp1iuTkZKKjK/00XaY0Dv7gLPOZle6U614K98yEkDDfxlUOKsVQ1urVqwOwd+9eMjIyfByN8YXQ0FDq1auX87NgjFfHf4F37oLTKU65Wj1nyGpk5XhTv1IkB3AShP1iMMa4cvoozOwLKXuccmgVuPc9iGrs27jKUaW4rWSMMa5lpsHs+2D/JqcswdBvGjRo7du4ypklB2OMOSM7GxYOh58+za2741W4pEvxfSooSw7GGAPOS24rx8DmPMvM3DoWWt/nu5h8yJKDMcYArJ0EX07OLbcbDjc86rt4fMySgzHGfDMLVo3NLbfoDd2eq/DvMpTEkoMxpnLbvgoWj8gtN7nRsy5DsO9i8gOukoOIdBORbSKyQ0QKvTMujlc82zeKSBtvfUWkn4hsFpFsEYkrsL8xnvbbRKTruZygMcYUK3kDzBkI2Z4laOtdDv3fgdDil7mtLLwmBxEJBl4DugMtgAEiUnB+2u5ArOdjGPCGi77fAX2ATwocrwXQH2gJdANe9+zHGGPKzuEf4Z1+kHHSKddoBPfNgwhbcRDcXTm0A3ao6k5VTQdmAwWXzu4FTFfHOiBKROqX1FdVt6pqUYsM9wJmq2qaqu4Cdnj2Y4wxZePYXpjeG04ddsqRNeH+BRVuwZ5z4SY5xAA/5ykneerctHHT92yOh4gME5EEEUk4ePCgl10aYwzEJybT47l4tv+rExz1vP0cEgn3zoG6l/g2OD/jJjkU9bi+4Ox1xbVx0/dsjoeqvqmqcaoaV7duXS+7NMZUdvGJyTyz4CueS32K2KBkANI1mM/jXoZGdnOiIDfJIQlolKfcENjrso2bvmdzPGOMKZVJKzbxKs9zZdBOALJVeCzjD4z6xmbqLYqb5LAeiBWRpiIShvOweHGBNouBgZ5RS9cAR1V1n8u+BS0G+otIuIg0xXnI/VUpzskYY/LLymTMqee5LnhLTtXfMoewJPta9qbYWi9F8Torq6pmisgIYCUQDLytqptF5CHP9snAMqAHzsPjU8DgkvoCiMidwKtAXWCpiHyjql09+54DbAEygYdVNatMz9oYU3lkZ8PiEXQJ3pBT9c+M/rybdSsADaIifRWZX5OKsPhNXFycJiQk+DoMY4y/UYUVo/NNizE5sycTMgcAEBkazHN9WtG7tbdxMhWTiGxQ1biittkb0saYiuvj5/Mlhp8u6suMqoMRICYqslInBm8qzWI/xphKZt1k+OjZ3HKL3jTp+yZrK/m0GG7ZlYMxpuL55l1Y8URu+Tcdoc+blX6+pNKw5GCMqVi+mw+LHs4tN2wH98yEkHDfxRSALDkYYyqOrUtg/u9As51yvVZw3xwIq+rbuAKQJQdjTMWwfRXMGwxnRr7XaQ4D4515k0ypWXIwxgS+nR/De/dBVrpTrtUMBi2GqnV8G1cAs+RgjAlse9bBrAGQedop12gMAxfDBRf6Nq4AZ8nBGBO4kr/OvybDBQ2cK4aoRiX3M15ZcjDGBKZfNsGMOyHtmFOuWtdJDLWa+jauCsKSgzEm8Bz43lms53SKU46sCQMXQZ1Y38ZVgVhyMMYElkPbYXovOHXIKYfXgAfioV5L38ZVwVhyMMYEjkPbYertcOIXpxxWDe6fDw2u8m1cFZAlB2NMYCiYGEKrOMt7Nmrr27gqKEsOxhj/d2hH4cRw3zxocr1v46rALDkYY/zboR0w9TZLDOXMkoMxxn9ZYvAZSw7GGP90aAdMK3graa4lhnJiycEY43/OJIbj+5xyTmK4wbdxVSKukoOIdBORbSKyQ0RGF7FdROQVz/aNItLGW18RqSUiH4jIds/nmp76UBGZJiKbRGSriIwpixM1xgSIohLDvXMsMZQzr8lBRIKB14DuQAtggIi0KNCsOxDr+RgGvOGi72hgtarGAqs9ZYB+QLiqtgKuBoaLSJOzPD9jTICIT0zm/mencvDVjoUTQ9MbfRtcJeTmyqEdsENVd6pqOjAb6FWgTS9gujrWAVEiUt9L317ANM/X04Denq8VqCoiIUAkkA4cO7vTM8YEgvjEZKYt+B+T0v5GXTkKwCkN57N2r1ti8BE3ySEG+DlPOclT56ZNSX3rqeo+AM/naE/9POAksA/YA/xLVY8UDEpEholIgogkHDx40MVpGGP81ZLl/2Nq0FPUluMAHNdIBqY/wRMbavg4ssrLTXKQIurUZRs3fQtqB2QBDYCmwEgRaVZoJ6pvqmqcqsbVrVvXyy6NMX5r9xe8lDaOGnIKgKNahfvTx5Cgl7I3JdXHwVVebpJDEpB3cvSGwF6XbUrqu99z6wnP5wOe+nuBFaqaoaoHgLVAnIs4jTGBZudHMLMPF4iTBA7rBQxI/xvf6sUANIiK9GFwlZub5LAeiBWRpiISBvQHFhdosxgY6Bm1dA1w1HOrqKS+i4FBnq8HAYs8X+8BOnr2VRW4Bvj+LM/PGOOvtn8A79wNGc4Vw0GNon/6k2zRJgBEhgYzqmtzHwZYuYV4a6CqmSIyAlgJBANvq+pmEXnIs30ysAzoAewATgGDS+rr2fUEYI6IDMVJCP089a8BU4DvcG5LTVHVjWVxssYYP7H1fzB3MGRnOOXqMXzT9i1OrU1DUlJpEBXJqK7N6d264ONNU15E1dsjAP8XFxenCQkJvg7DGOPGpnmwYBhollOOushZwa1mE5+GVRmJyAZVLfK2vdcrB2OMKTMbpsL/HiFnXErti2HgYqhhVwj+xqbPMMaUj89egv/9mZzEUPcy+O0ySwx+yq4cjDHnlyp88Hf4/JXcugZtnNlVq9b2XVymRJYcjDHnT3aWc7WQOCO3rulN0P9dCL/Ad3EZryw5GGPOj8w0mP8gbM0z8v3S2+Gu/0JohO/iMq5YcjDGlL20E/Defc5LbmdcdR/0fAWC7ddOILB/JWNM2Tp1BN7pB8l5hpdf8zB0+QcE2RiYQGHJwRhTdo7thRl94ODW3LqOf4MbHwcpaqo1468sORhjysbBbTDzLjh6ZiJmgR4Tod3vfBqWOTuWHIwx527POnj3Hjid4pSDQqD3ZLiiX8n9jN+y5GCMOTdbl8D8oZB52imHVoW7p0NsJ9/GZc6JJQdjzNlb/x9YNgo02ylXrQv3zYUGrX0blzlnlhyMMaWnCmuegU9fyK2r1Qzun+98NgHPkoMxpnSyMpy3nr95J7euQRu4dw5Us1UZKwpLDsYY99JOwNxBsGNVbl1sF+g3FcKq+iwsU/YsORhjShSfmMzEldvITNnLtMgXuFR35m5sfT/cPsneeq6A7F/UGFOs+MRkxizYxEWZu3g7/Hka6JHcjTf9BW75q73cVkHZu+zGmGJNXLmN9lkbmBc2jgbiJIZMDeKfIb+Hjv/PEkMFZsnBGFOsjscX89/QiVQT5x2GYxrJ4Iy/MPnEjT6OzJxvrpKDiHQTkW0iskNERhexXUTkFc/2jSLSxltfEaklIh+IyHbP55p5tl0hIl+IyGYR2SQiNr+vMeUpOwtW/JVnQqcQLM7KbUlah77p4/g0+woaREX6OEBzvnlNDiISDLwGdAdaAANEpEWBZt2BWM/HMOANF31HA6tVNRZY7SkjIiHATOAhVW0JdAAyzv4UjTGlkn4S3rsf1r2WU/VNdjPuTHuaH7QRkaHBjOra3IcBmvLg5sqhHbBDVXeqajowG+hVoE0vYLo61gFRIlLfS99ewDTP19OA3p6vuwAbVfVbAFU9rKpZZ3l+xpjSOLYPpnSHbctyqvbW78xjkc9yiChioiJ5rk8rere2dZ8rOjejlWKAn/OUk4D2LtrEeOlbT1X3AajqPhGJ9tRfAqiIrATqArNV9fmCQYnIMJyrFBo3buziNIwxJdqbCLPuheN7c+uu+xMNOj3FGluHodJxkxyKGo6gLtu46VtUTDcAbYFTwGoR2aCqq/PtRPVN4E2AuLg4b/s0xpTku/kQ/zBkpjplCYbbXoC4wb6Ny/iMmz8HkoBGecoNgb0u25TUd7/n1hOezwfy7OtjVT2kqqeAZUAbjHASUeEAABX0SURBVDFlLzsbVj8D84bkJobwGs7keZYYKjU3yWE9ECsiTUUkDOgPLC7QZjEw0DNq6RrgqOeWUUl9FwODPF8PAhZ5vl4JXCEiVTwPp28Gtpzl+RljipN23Hnw/Om/cutqx8Lv1sDFt/ouLuMXvN5WUtVMERmB80s7GHhbVTeLyEOe7ZNx/rrvAezAuRU0uKS+nl1PAOaIyFBgD9DP0+dXEXkRJ7EosExVl5bVCRtjgF9/glkD4ECev7su7gR3/Rcio3wWlvEfohr4t+vj4uI0ISHBe0NjDPz0Gbz3AKTmmQrj2hHQ+WkICvZdXKbceZ7nxhW1zeZWMqYySXjbWZwnO9MpB4fB7S9D6/t8G5fxO5YcjKkMMk7D8lHw9fTcuqrRcM9MaFxwZLoxlhyMqfiOJjm3kfZ+nVtX/0ro/y7UaOi7uIxfs+RgTEW282OYNxhOHc6ta3U39JwEYVV8F5fxe5YcjKmIVOHzV2HVWNBspy4oBLo+C+2G2VTbxitLDsZUNGnHYdEI2BKfW1etHvSbBhdd67u4TECx5GBMRXJou/Ni28Hvc+satXcSQ/X6vovLBBxLDsZUFFsWw6KHIe1Ybl3b3zm3kkLCfBeXCUiWHIwJYPGJyby84jsGnfwvg0NW5m4IiXAeOl/Z33fBmYBmycGYABWfmMy/F6xmkrzElSE7c+pPVmlI1QfedYarGnOWbJJ2YwLUl8umsSDoCa4Myk0MK7La0idrgiUGc87sysGYQJOZDqvG8lzG6zkrpqRrMM9l3suUrG7IURumas6dJQdjAsmvu52X2pI35FQlaR0eTv8T3+rFADSIivRVdKYCseRgTKDYshgW/xFOp+RUrdY4HksbxlGqARAZGsyors19FaGpQCw5GOPv0k/CijHw9bTcuqAQ6PQUxyN6U+39HziWkkqDqEhGdW1O79YxvovVVBiWHIzxZ/u+hXlD4fD23LoajaDv29CoHb2B3m1s8jxT9iw5GOOPsrPhyzdg1TjISs+tb3mns/6CrdZmzjNLDsb4m+P7If738OPq3LrQqtDjebjqPps0z5QLSw7G+JPtHziJ4eTB3LoGrZ21nWv/xndxmUrH1UtwItJNRLaJyA4RGV3EdhGRVzzbN4pIG299RaSWiHwgIts9n2sW2GdjETkhIo+fywkaExDSTsCSR+GdvnkSg8D1j8CQ9y0xmHLnNTmISDDwGtAdaAEMEJEWBZp1B2I9H8OAN1z0HQ2sVtVYYLWnnNdLwPKzOCdjAsuedTD5Bmd95zOqXQgD46HzUzZpnvEJN7eV2gE7VHUngIjMBnoBW/K06QVMV1UF1olIlIjUB5qU0LcX0MHTfxrwEfCEp11vYCdw8hzOzRj/lpkGH46Hta8Amlt/6e3Q8xWoWttnoRnjJjnEAD/nKScBBVckL6pNjJe+9VR1H4Cq7hORaAARqYqTJDoDxd5SEpFhOFcpNG7c2MVpGONH9m2EhcPhQJ6/scJrQI+JcMXd9tDZ+Jyb5FDUT6m6bOOmb0FPAS+p6gkp4T+Iqr4JvAkQFxfnbZ/G+IesTFj7Enw0AbIzc+ubdYBer0ENe2fB+Ac3ySEJaJSn3BDY67JNWAl994tIfc9VQ33ggKe+PdBXRJ4HooBsETmtqv92c0LG+K0D3zuL8SQn5NaFREKXZyBuKATZJMnGf7hJDuuBWBFpCiQD/YF7C7RZDIzwPFNoDxz1/NI/WELfxcAgYILn8yIAVb3xzE5FZBxwwhKDCUTxiclMXLmNAynH+Uu15QzJnkdwdkZug4ZtofdkqHOx74I0phhek4OqZorICGAlEAy8raqbReQhz/bJwDKgB7ADOAUMLqmvZ9cTgDkiMhTYA/Qr0zMzxofiE5MZs2ATv8nczn/C3uSyzD25G4NCocNoZ5hqsL1qZPyTOAOMAltcXJwmJCR4b2hMObnlueXcffIdfhe8lBDJzqnfLLG0fGg61Cs4GtyY8iciG1Q1rqht9meLMWVt9+f8N/VRmoXsy6lK1TBeyOzHlKzu/GiJwQQASw7GlJXTR2H1M7D+LZrlebb8RVYLRmc+yG69kBhbiMcECEsOxpwrVdi8wFlz4cT+nOoTGsmzmfcyK+sWlCBbiMcEFEsOxpyLIzth6eP5Z1AFiO3C2qZP8PEnxyAllRhbiMcEGEsOxpyNzDRn2otP/wWZp3Prq9WDbhOg5Z10FaHrdb4L0ZhzYcnBmNLa9QkseSz/6mwItBsGHf8fRNTwWWjGlBVLDsa4dWwfrBoLG9/LX1//Smd1tpg2RfczJgBZcjDGm8w0WPc6fPIvSD+RWx92Adz6JLR9EIKCfRefMeeBJQdjiqMKP6yElWOcB895tejtPFuoXt83sRlznllyMKYoh7Y7Q1N3fJC/vu5l0H2CM4uqMRWYJQdj8jp9FD6ZCOveyD+ldkQN6PBXaDsUgkN9F58x5cSSgzEAWRmQMAU+ngCnDufZIHD1IOj4JFSt47PwjClvlhxM5aYK3y+BD8bCkR/zb2t0DXT/JzS4yjexGeNDlhxMpXNmnYXooxsZFzGLK/X7/A1qNIJO4+Dyu2y5TlNpWXIwlUp8YjKvLVjFGN7l9vB1+RetDa8BN42EdsMhNMJnMRrjDyw5mMrj2D6ylzzG0qAPCJOsnOp0DWZhSA/u+fMrUKWWDwM0xn9YcjAV38nD8NmLsP4/9Mk6DXnuFC3Jas/zmf35Oa0e91hiMCaHJQdTcZ0+Cp//23m7Oe+bzcCX2ZcyIWMAiRoLYOssGFOAJQdT8aSfhC//D9ZOgtMp+Tb9WqMlo47cwaqMyzlzCWHrLBhTWJD3JiAi3URkm4jsEJHRRWwXEXnFs32jiLTx1ldEaonIByKy3fO5pqe+s4hsEJFNns8dy+JETSVw+hh8+gK83ApWP5U/MdS9DO6ZSc1H1nJ7nweIiaqC4FwxPNenla2zYEwBoqolNxAJBn4AOgNJwHpggKpuydOmB/BHoAfQHpikqu1L6isizwNHVHWCJ2nUVNUnRKQ1sF9V94rI5cBKVS3xf25cXJwmJCSc1TfAVACpv8K6yfDlG86tpLxqNoFb/p8zLNUmxzMmHxHZoKpxRW1zc1upHbBDVXd6djYb6AVsydOmFzBdnUyzTkSiRKQ+0KSEvr2ADp7+04CPgCdUNTHPfjcDESISrqppLmI1lcnJQ/DFa/DVW5B+PP+2Go3gxpHQ+n6b7sKYs+AmOcQAP+cpJ+FcHXhrE+Olbz1V3QegqvtEJLqIY98FJBaVGERkGDAMoHHjxi5Ow1QYR5Odh8wJb0PGqfzbajZ1ksIV90BImG/iM6YCcJMcinpFtOC9qOLauOlb9EFFWgL/BLoUtV1V3wTeBOe2kpt9mgD3y3fw+avw3bz8k+IB1GkONz0OLftAsI2zMOZcuflflAQ0ylNuCOx12SashL77RaS+56qhPnDgTCMRaQgsBAaqaoEJb0ylogo7P3SSwo9rCm+v18pJCpfdAUGuxlcYY1xwkxzWA7Ei0hRIBvoD9xZosxgY4Xmm0B446vmlf7CEvouBQcAEz+dFACISBSwFxqjq2nM5ORN4zsx7dCDlOPdfsIFHIldQ49i2wg0bXwfX/wku6WbzHxlzHnhNDqqaKSIjgJVAMPC2qm4WkYc82ycDy3BGKu0ATgGDS+rr2fUEYI6IDAX2AP089SOAi4EnReRJT10XVc25sjAVU3xiMv9a8Cl3Zq/ivvDV1M84Ahl5GkiQc4Vw3R+hYZEDLIwxZcTrUNZAYENZA5wqJCWwcsrT3JK1Nt+8RwCphBPZbhBc83uo1cxHQRpT8ZzrUFZjzo+MVPhuAXz1Juz7hq6QbwjDQa3BtMwuvJPVicQe/X0VpTGVkiUHU/4OboOvp8M370LqkUKbN2THMi2zC8uz25NBiM17ZIwPWHIw5SP9JGxe6CSFn78svD04nN0xPXhsVzs2ZFyUU23zHhnjG5YczPmjCslfQ+J02DS/8FvMADUaQ9uh0GYgF1WpxQOJyfyycht7U1JpEBXJqK7Nbd4jY3zAkoMpeyk/w6a5sHEOHNxaeHtQCDTvDm0GwW865pvzqHfrGEsGxvgBSw6mbKSmwJZFTkLY/VnRbWrHQpuBcGV/qFbUbCnGGH9hycGcvYxU2P4BbJoDP6yErPTCbUIioeWdTlJofI29sGZMgLDkYFyLT0zm1RXfcunxL+gTsYGb5WtCslILN5QgaNbBmfzu0tsg/ILyDtUYc44sORjvTh8j4YNZVEmYxxK+ITIsHbKLaFf/KichXH4XXFCv3MM0xpQdSw6maL/udm4VbV8Juz4hLiu9yDl290gDGt9wL1xxN9S1IafGVBSWHIwjKxOS1sMPK5ykUNQoI49t2Q1Znt2OZVnt2a4N2XXr7eUYqDGmPFhyqMx+3Q27PoadHznTYaf+WmzT7dKEReltWZ7djh/zrNpqby8bUzFZcqhMTh2BXZ84yWDnR/DrruLbBodD05vgkq4Q24XNP4Xw3wWbSM3KnRTP3l42puKy5FABnFkDodBbxcf2wc/rYM862P05/LKJEhfiq3ahkwwu6QbNboawqjmbetd0Phd5HGNMhWPJIcDFJyYzZsEm0jIyuFj2End8G7LwRU5+sIuqp5JK7hwSCRdd5ww7bXYzXHhFie8h2NvLxlQelhwCUXa2c0tobyKpSxYxVX6gZfhPVJPTuW1OFdFPgiDmak8y6AAN20JIeHlEbIwJMJYc/F3acWeK6wNb4MD3sH8T7P0W0o4CMACguKWTQyKcBNCoPTS+Fhq1hYga5RW5MSaAWXLwB6pw8hAc2el8HNoGB7Y6CSFlj+vdHNQaJGZfzFfZl7K76hW89ZchEBJ2HgM3xlRUlhzOs/jEZCau+J7jRw9zRfWT/KFNJNfVPQ2//pSbDI78VPR01iWpUhsatGZb0MW8srUaCRlN2E9NQIgMDea57q0sMRhjzpqr5CAi3YBJQDDwH1WdUGC7eLb3wLnb/VtV/bqkviJSC3gPaAL8BNytqr96to0BhgJZwJ9UdeU5nWUxnlozg/m73iI7+FeCsmpyV9PfMbbjA+46Z2VC2jE4dbjoj5OHOJC8iysO7uF9DlM1Ig3SgXWlDDIoBGpfDNGXQXQL53P9q6BGQxChOdA5MZlvVm5DbBSRMaaMiGoJQxsBEQkGfgA6A0nAemCAqm7J06YH8Eec5NAemKSq7UvqKyLPA0dUdYKIjAZqquoTItICmAW0AxoAq4BLVDX/qvN5xMXFaUJCQqlO/Kk1M4jfPZHMoNzzD80WHsmOYWD1epCd6SSAzFRnFbP0k5B+wvmcdgKy0kp1PK/CLoDazaBmU6j9G08iaOEkBrsCMMacByKyQVXjitrm5sqhHbBDVXd6djYb6AVsydOmFzBdnUyzTkSiRKQ+zlVBcX17AR08/acBHwFPeOpnq2oasEtEdnhi+MLtCbsxf9dbaEj+xJgRpMzM+omBmz8vy0MBcErD2ae1+EVrsZ+a9Ol4PdRqlvtRpbZNZ22M8RtukkMM8HOechLO1YG3NjFe+tZT1X0AqrpPRM6s/hJD/psvZ/aVj4gMA4YBNG7c2MVp5Jcd/GtR88jxS0hwEbVFEQivDlVqOb/Ycz5yyyNXHOC7E9XYp7U4RlXOzFwXExVJn1s6ljpmY4wpL26SQ1G/QwveiyqujZu+Z3M8VPVN4E1wbit52WchQVk10ZDCcwlFZFWBvlOce/1BwRAaCWHVnLeFw6pC6JnPkV7/0r8xKJllCzaRmmFTThhjAoub5JAENMpTbgjsddkmrIS++0WkvueqoT5woBTHO2d3Nf0dc3e/hARl5NRpdii3Nf0jXN6nTI5x5qGwTTlhjAk0bpLDeiBWRJoCyUB/4N4CbRYDIzzPFNoDRz2/9A+W0HcxMAiY4Pm8KE/9uyLyIs4D6Vjgq7M8v2KN7fgArCHfaKW+pRmt5JJNOWGMCURek4OqZorICGAlznDUt1V1s4g85Nk+GViGM1JpB85Q1sEl9fXsegIwR0SGAnuAfp4+m0VkDs5D60zg4ZJGKp2LsR0fYCxlmwyMMaYi8DqUNRCczVBWY4yp7EoaylrcrDzGGGMqMUsOxhhjCrHkYIwxphBLDsYYYwqpEA+kPUNmd5/DLuoAh8oonPIWyLFDYMcfyLFDYMcfyLGD/8R/karWLWpDhUgO50pEEop7Yu/vAjl2COz4Azl2COz4Azl2CIz47baSMcaYQiw5GGOMKcSSg+NNXwdwDgI5dgjs+AM5dgjs+AM5dgiA+O2ZgzHGmELsysEYY0whlhyMMcYUUmmSg4h0E5FtIrLDs2Z1we0iIq94tm8UkTa+iLM4LuK/VES+EJE0EXncFzEWx0Xs93m+5xtF5HMRudIXcRbHRfy9PLF/IyIJInKDL+IsirfY87RrKyJZItK3POPzxsX3voOIHPV8778Rkb/7Is7iuPn+e87hGxHZLCIfl3eMxVLVCv+BM134j0AznAWIvgVaFGjTA1iOsxLdNcCXvo67lPFHA22B8cDjvo65lLFfB9T0fN09AL/31ch9fncF8L2v43Ybe552a3Cm3u/r67hL+b3vACzxdaznEH8UzvIEjT3laF/Hfeajslw5tAN2qOpOVU0HZgO9CrTpBUxXxzogyrNCnT/wGr+qHlDV9UBGUTvwITexf66qZ9ZsXYez+p+/cBP/CfX8zwaq4n0p3PLi5uce4I/AfHJXY/QXbuP3V27ivxdYoKp7wPl/XM4xFquyJIcY4Oc85SRPXWnb+Io/x+ZNaWMfinMF5y9cxS8id4rI98BSYEg5xeaN19hFJAa4E5hcjnG55fZn51oR+VZElotIy/IJzRU38V8C1BSRj0Rkg4gMLLfovHCzTGhFIEXUFfzrzk0bX/Hn2LxxHbuI3IKTHPzmnj0u41fVhcBCEbkJeAbodL4Dc8FN7C8DT6hqlkhRzX3KTfxf48wPdEJEegDxOEsL+wM38YcAVwO3ApHAFyKyTlV/ON/BeVNZkkMS0ChPuSGw9yza+Io/x+aNq9hF5ArgP0B3VT1cTrG5Uarvvap+IiK/EZE6qurridXcxB4HzPYkhjpADxHJVNX48gmxRF7jV9Vjeb5eJiKv+8n3Htz/3jmkqieBkyLyCXAl4PPk4POHHuXxgZMEdwJNyX0w1LJAm9vI/0D6K1/HXZr487Qdh389kHbzvW+Ms/74db6O9yzjv5jcB9JtgOQzZX+PvUD7qfjXA2k33/sL83zv2+GsR+/z730p4r8MWO1pWwX4Drjc17GrauW4clDVTBEZAazEGUHwtqpuFpGHPNsn44zU6IHzS+oUMNhX8RbkJn4RuRBIAKoD2SLyCM7IiGPF7rgcuPze/x2oDbzu+Qs2U/1kxkqX8d8FDBSRDCAVuEc9//N9yWXsfstl/H2B34tIJs73vr8/fO/BXfyqulVEVgAbgWzgP6r6ne+izmXTZxhjjCmksoxWMsYYUwqWHIwxxhRiycEYY0whlhyMMcYUYsnBGGNMIZYcjDHGFGLJwRhjTCH/H7Gbh15EwN3cAAAAAElFTkSuQmCC\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('Deflection at end of guitar neck:',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": 284,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Deflection at end of guitar neck: 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('Deflection at end of guitar neck:',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. \n",
"\n",
"**Answer** In order to converge to the mode shape, there needs to be about 30 nodes"
]
},
{
"cell_type": "code",
"execution_count": null,
"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": 145,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 6-element string (Hz)\n",
"[194.43708661 379.1242858 544.80061022]\n",
"\n",
"Longest time period =5.143 ms\n",
"shortest time period =1.174 ms\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=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",
"print('Natural frequencies of {}-element string (Hz)'.format(N))\n",
"print(e.real[0:3]**0.5/2/np.pi)\n",
"f1=np.sqrt(e.real[0])/2/np.pi\n",
"fn=np.sqrt(e.real[-1])/2/np.pi\n",
"print('\\nLongest time period ={:1.3f} ms\\nshortest time period ={:1.3f} ms'.format(1/f1*1000,1/fn*1000))\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});"
]
},
{
"cell_type": "code",
"execution_count": 151,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 30-element string (Hz)\n",
"[195.99464595 391.48617646 585.97276757]\n",
"\n",
"Longest time period =5.102 ms\n",
"shortest time period =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('Natural frequencies of {}-element string (Hz)'.format(N))\n",
"print(e.real[0:3]**0.5/2/np.pi)\n",
"print('\\nLongest time period ={:1.3f} ms\\nshortest time period ={:1.3f} ms'.format(1/f1*1000,1/fn*1000))"
]
},
{
"cell_type": "code",
"execution_count": 150,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 45-element string (Hz)\n",
"[196.04043699 391.85229959 587.20727994]\n",
"\n",
"Longest time period =5.101 ms\n",
"shortest time period =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('Natural frequencies of {}-element string (Hz)'.format(N))\n",
"print(e.real[0:3]**0.5/2/np.pi)\n",
"print('\\nLongest time period ={:1.3f} ms\\nshortest time period ={:1.3f} ms'.format(1/f1*1000,1/fn*1000))"
]
},
{
"cell_type": "code",
"execution_count": 152,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 60-element string (Hz)\n",
"[196.05687232 391.9837462 587.65070938]\n",
"\n",
"Longest time period =5.101 ms\n",
"shortest time period =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('Natural frequencies of {}-element string (Hz)'.format(N))\n",
"print(e.real[0:3]**0.5/2/np.pi)\n",
"print('\\nLongest time period ={:1.3f} ms\\nshortest time period ={: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": 241,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Natural frequencies of 71.34 N string (Hz)\n",
" 195.403\n",
" 390.579\n",
" 585.299\n",
"\n",
"Natural frequencies of 70.76 N string (Hz)\n",
" 194.596\n",
" 388.966\n",
" 582.882\n",
"\n",
"Natural frequencies of 71.74 N string (Hz)\n",
" 195.939\n",
" 391.65\n",
" 586.905\n",
"\n",
"Natural frequencies of 82.42 N string (Hz)\n",
" 210.022\n",
" 419.799\n",
" 629.086\n",
"\n",
"Natural frequencies of 88.49 N string (Hz)\n",
" 217.626\n",
" 434.998\n",
" 651.862\n",
"\n",
"Natural frequencies of 75.56 N string (Hz)\n",
" 201.091\n",
" 401.948\n",
" 602.337\n",
"\n",
"[195.40331448 390.57879743 585.29888297 194.59641503 388.96593934\n",
" 582.88194677 195.93940139 391.65034621 586.90464424 210.02173133\n",
" 419.79858671 629.08597572 217.62566517 434.99758855 651.86232421\n",
" 201.09136654 401.94826954 602.33651883]\n"
]
}
],
"source": [
"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('Natural frequencies of {:.4} N string (Hz)'.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",
"'''\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",
"\n",
"#f1=np.sqrt(e.real[0])/2/np.pi\n",
"#fn=np.sqrt(e.real[-1])/2/np.pi\n",
"#print('Natural frequencies of {}-element string (Hz)'.format(N))\n",
"#print(e.real[0:3]**0.5/2/np.pi)\n",
"#print('\\nLongest time period ={:1.3f} ms\\nshortest time period ={:1.3f} ms'.format(1/f1*1000,1/fn*1000))"
]
},
{
"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": 247,
"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": 247,
"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)"
]
},
{
"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
}