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@selimb
Created October 13, 2014 04:53
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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Theoretical Results\n",
"===================\n",
"\n",
"First three natural frequencies\n",
"-------------------------------"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from numpy import cos,sin,sinh,cosh\n",
"from scipy.optimize import fsolve"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Apparatus specifications\n",
"m = 0.051; l = 0.32; w = 0.015; \n",
"h = 0.004; rho = 2.7*10**3;\n",
"E = 6.9*10**10\n",
"I = (w*h**3)/12\n",
"A0 = w*h\n",
"#Set a to 20cm\n",
"a = 0.2"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculated constants\n",
"alpha = m/(rho*A0*l)\n",
"xi = a/l"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Must solve equation below iteratively for $\\lambda$\n",
"\n",
"$$f(\\lambda) = 2\\sin(\\lambda)\\sinh(\\lambda)-\\alpha\\lambda \\Big[\n",
"\\sin(\\lambda\\xi)\\sin(\\lambda\\cdot(1-\\xi))\\sinh(\\lambda) -\n",
"\\sinh(\\lambda\\xi)\\sinh(\\lambda\\cdot(1-\\xi))\\sin(\\lambda)\n",
"\\Big]$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#f(lambda)\n",
"def f(x):\n",
" f1 = 2*sin(x)*sinh(x)\n",
" f2 = sin(x*xi)*sin(x*(1-xi))*sinh(x)\n",
" f3 = sinh(x*xi)*sinh(x*(1-xi))*sin(x)\n",
" return f1-alpha*x*(f2-f3)\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's get a feel for what the function looks like. \n",
"\n",
"This also allows us to guess roots!"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"lamb = np.arange(0,20,0.01) \n",
"plt.plot(lamb,f(lamb))\n",
"plt.axis([0,20,-100,100])\n",
"plt.plot([0,20],[0,0],'--k')\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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g9ddjV3K0lLqApNQZAJG0tcEpp5RvHMAAkNJhAERUxoHgVMYAJBkAUc2eDS++GLuKox0+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\nkiRJkiRJkiRJkiRJkqrk/wEcHTTQTUOkIgAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x38496d0>"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Guess 3,6,9 from plot above.\n",
"lambdas = fsolve(f,[3,6,9])\n",
"print \"First three roots are:\"\n",
"print lambdas"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"First three roots are:\n",
"[ 2.44448096 5.80840068 9.20869831]\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's do a sanity check as well to make sure that $f(root) = 0$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"for root in lambdas:\n",
" print \"\"\"f(%.4f) = %f\n",
" \"\"\" % (root,np.abs(f(root)))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"f(2.4445) = 0.000000\n",
" \n",
"f(5.8084) = 0.000000\n",
" \n",
"f(9.2087) = 0.000000\n",
" \n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"------------"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def get_frequency(lamb):\n",
" lamb = np.array(lamb)\n",
" omega = lamb**2 * \\\n",
" np.sqrt(E*I/(rho*A0*l**4))\n",
" return omega/(2*np.pi)\n",
"\n",
"frequencies = get_frequency(lambdas)\n",
"print \"The first three natural frequencies are :\"\n",
"print frequencies"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The first three natural frequencies are :\n",
"[ 54.21326006 306.0873221 769.35839485]\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First three mode shapes\n",
"-----------------------"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def get_mode_shapes(lamb,quiet = False):\n",
" step = 0.005\n",
" x1 = np.arange(0,a,step)\n",
" x2 = np.arange(a,l+step,step)\n",
" x = np.hstack((x1,x2))\n",
" C = 1.0\n",
" lamb = np.array(lamb)\n",
" s = (sinh(lamb)*sin(lamb*(1-xi))) / \\\n",
" (sin(lamb)*sinh(lamb*(1-xi)))\n",
" s1= (sinh(lamb)*sin(lamb*xi)) / \\\n",
" (sin(lamb)*sinh(lamb*xi))\n",
" D = (C*sinh(lamb*xi)) / \\\n",
" (sinh(lamb*(1-xi)))\n",
" y1 = C * (sinh(lamb*x1/l)- \\\n",
" s*sin(lamb*x1/l))\n",
" y2 = D * (sinh(lamb*(1-x2/l)) - \\\n",
" s1*(sin(lamb*(1-x2/l))))\n",
" y = np.hstack((y1,y2))\n",
" y_max = y[np.argmax(np.abs(y))]\n",
" y_normed = y/y_max\n",
" if not quiet:\n",
" print \"For lambda = %f\" % lamb\n",
" print \"sigma = \",s\n",
" print \"sigma_1 = \",s1\n",
" print \"D = \",D\n",
" print \"\\n\"\n",
" return (x,y_normed)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 26
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"shapes = [get_mode_shapes(a_lamb) for a_lamb in lambdas]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"For lambda = 2.444481\n",
"sigma = 6.72890540093\n",
"sigma_1 = 4.05355894771\n",
"D = 2.08983649546\n",
"\n",
"\n",
"For lambda = 5.808401\n",
"sigma = -68.6392486333\n",
"sigma_1 = 9.07372104712\n",
"D = 4.32454043011\n",
"\n",
"\n",
"For lambda = 9.208698\n",
"sigma = -452.272563332\n",
"sigma_1 = -74.230910857\n",
"D = 10.0058136711\n",
"\n",
"\n"
]
}
],
"prompt_number": 27
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure()\n",
"ax = plt.axes()\n",
"def plot_th(an_ax,ls='-'):\n",
" lines = []\n",
" for a_shape in shapes:\n",
" lines.append(an_ax.plot(a_shape[0],a_shape[1],'-'))\n",
" return lines\n",
"plot_th(ax)\n",
"ax.legend(('n = 1','n = 2','n = 3'),loc='best', fancybox=True, framealpha=0.5)\n",
"ax.plot([0,l],[0,0],'--k')\n",
"ax.set_title('Theoretical normalized mode shapes')\n",
"ax.grid()\n",
"plt.show()\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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HPHWqWtW5aZOaDu0qrDiPumyusnR4rgNfbfoq3mOtqD8xmKL/t9/URfXMM04X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\nH6+PmNS5XSJmAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x11ad91b0>"
]
}
],
"prompt_number": 191
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig.savefig('latex/pics/plot_three_theo')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 108
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Fourth mode shape\n",
"-----------------"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fourth_lambda = fsolve(f,12)\n",
"print \"The fourth root is: %.2f\" % fourth_lambda"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The fourth root is: 11.33\n"
]
}
],
"prompt_number": 38
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fourth_shape = get_mode_shapes(fourth_lambda,quiet=True)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 39
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig_fourth = plt.figure()\n",
"ax_fourth = plt.axes()\n",
"ax_fourth.plot(*fourth_shape)\n",
"ax_fourth.legend(('n = 4',),loc='best', fancybox=True, framealpha=0.5)\n",
"ax_fourth.plot([0,l],[0,0],'--k')\n",
"ax_fourth.set_title('Fourth mode shape')\n",
"ax_fourth.grid()\n",
"plt.show()\n",
"fig_fourth.savefig('latex/pics/plot_four_theo')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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7sDLimI7AvaF/NgX+A0QbxKZ9BC566CFpBAYMMJ0kPezZI9s+zp8P9eqZTiOG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\nlFJKKaWUUkoppZRSSimllPKb/wesjPTMKvPVWgAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0xe2a4530>"
]
}
],
"prompt_number": 48
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"-----\n",
"\n",
"Experimental Results\n",
"===================="
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import pandas as pd"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 50
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#We read from a file containing the theoretical data for \n",
"#testing purposes.\n",
"data = pd.read_csv('results.csv',)\n",
"data.dropna(how=\"all\", inplace=True)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 105
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig_exp = plt.figure()\n",
"ax_exp = plt.axes()\n",
"def plot_ex(an_ax,ls = '-'):\n",
" lines = []\n",
" for col in data.columns[1:]:\n",
" lines.append(an_ax.plot(data['x'],data[col],ls))\n",
" return lines\n",
"plot_ex(ax_exp)\n",
"ax_exp.legend(('n = 1','n = 2','n = 3'),loc='best', fancybox=True, framealpha=0.5)\n",
"ax_exp.plot([0,l],[0,0],'--k')\n",
"ax_exp.set_title('Experimental normalized mode shapes')\n",
"ax_exp.grid()\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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ILuW76C3Hc+nSBV55Bfr1c6iaKVNULpitW/ULb24TPXtC6tQqzLaHYO4jcCKh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\nw9+0ov137RIAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x11761d10>"
]
}
],
"prompt_number": 190
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Plot both\n",
"fig_both = plt.figure()\n",
"ax_both = plt.axes()\n",
"lines_ex = plot_ex(ax_both,'.')\n",
"lines_th = plot_th(ax_both,ls = '-')\n",
"plt.setp(lines_th[0],'color','b')\n",
"plt.setp(lines_th[1],'color','g')\n",
"plt.setp(lines_th[2],'color','r')\n",
"ax_both.legend(('n=1','n=2','n=3'),loc='best', fancybox=True, framealpha=0.5)\n",
"ax_both.set_title('Experimental (solid) and Theoretical (dashed) mode shapes')\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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xQZX5sow6HnPcdFthfv118u6GIIFm3sTuc7tVwQ8LqmYTmqmuU7uaqm5zBQMG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\nMFoSz/DAA/D33/DTTzlOBV4ysCR/9P2DN1a8wco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1Gx39Cfx+799PSq8F/u2grNvo6E/g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\ngiAIgiAIgiAIgiAIgiAIgrDU+T++vb1t8Hb6hAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x11ae2850>"
]
}
],
"prompt_number": 213
}
],
"metadata": {}
}
]
}
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