{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lab 2: Frequency Domain Identification Techniques" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Interactive iPython tools will not work without IPython.display and ipywidgets installed.\n", "Interactive iPython tools will not work without IPython.display and ipywidgets installed.\n" ] } ], "source": [ "%load_ext autoreload\n", "%autoreload 2\n", "import vibration_toolbox as vtb\n", "from vibration_toolbox import sdof_cf\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import scipy.io as sio\n", "import math as math\n", "import scipy.linalg as la" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Beam Properties\n", "-----------------------" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "l=21.75*0.0254;# length in meters\n", "h=0.5*0.0254;# height in meters\n", "w=1*0.0254;# width in meters\n", "A=w*h;\n", "rho=2700;# density in kg/cubicmeter\n", "E=7.31e10;# youngs modulus in Pa\n", "I = (1/12)*w*h**3; # moment of inertia (m^4)\n", "k = (3*E*I)/l**3; # stiffness (N/m)\n", "V = l*w*h;# volume (m^3)\n", "m = rho*V;# mass (kg)\n", "wn = (np.sqrt(k/m))/(2*math.pi) # analytical natural frequency of massless beam with concentrated mass in Hz\n", "wnunibeam=((1.875)**(2)*np.sqrt((E*I)/(m*(l)**3)))/(2*math.pi) # natural freqency of a uniform section beam in Hz\n", "#c_cr = 2*sqrt(k*m); # critical damping coefficient" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "17.229977388638673" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wn" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "34.972495605920052" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wnunibeam" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Freq versus Magnitude plot\n", "-------------------------------" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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vl0AgQDCoPd88Hg/RaFSPhldaWkpZWZleRlFREV6vN6mM6upq/H6/HlDJ4/EQ\niUT0xRllZWVEIhFqa7U0gA6Hg6qqKurq6ojG1g74fD5aWlr0MioqKgiHwwQCAf07djqdNDU1AeB0\nOqmsrNTLBKipqaGpqYlQSJupUllZSSgUSiqjv3aqrq7my7e/xgdbW/Ry9xtezk1f2ocxlSW0tbWl\n3U6hUIja2lq8Xm/S78XtdmOz2bLeTjedOp3L5o3ljtc/42/LNVfPb59fz2+fX8/fz5jMYfuN6tFO\nJSUl+oBcJu0UiUQIhUJZb6fEvyfQepyD/XvKtJ3i7ZxpO2Xy9zTYdhrs31O8rIG2k9OZeqGiLdrP\nQiIhxDbgcuAD4D4p5YyEYyuklLP6LKD3Mt8BDgJcUso2IcRc4NJuPn7PihUrmt1u90CLB6C2tpaa\nmpqMrk1k3m9eZnNdgEP2qubtT+v51eLJnHXY+EGXmw2M0pxNIpEoD6/4PClEQbHDzrprF1CUQXC0\nfNJ87j3v6GkY49x6+ky+NN1Yv34+ac4VSnP6+P1+Zs2aVSGlbOl+LJ0e/i/RjPP5wFghxBpgLbAO\nGNbHdTpCiDOAUVLK3wohRgIjgHuAJcADsf+fTaesdDEiecDuliCb6wLYbDDeV87bn9bn9Swdn6//\naYxDyVWPfcR9b21J2nfL12aweMaYjMvMJ833nHswf3plAzc9K/V9331oJc+v2cElR+2D3WZjvxGD\nD4iVT5pzhdJsDOn48LcCN0gp50opa4Djgb8BrcCyNO/zODBXCPEa8BhwMfAL4OzYvmrg3oFWPhVv\nb6pj+jXP8/SH2wdVzr/f01ZUHjS+mvIS7dmYzz78+GtxvtEZifLjh1f1MPaPXnzYoIw95J/mi+fu\nzbLL5utB1wCeXL2dBTe/xnF/WMb9y7cM+jeUb5pzQX+aw50R+vNWFBrZaOd0evhfBq4VQowAPgZW\nobl3nibNQdvYq8VJvRw6Ns16DohLH1pJS7CTbz/4PptvXJhxOR99ofnepo+txGbT3A2dkSj+YJg/\nvbyBMw8dx+iq/FnynY9JIjojUaZc/VzS4rWDxnuZP3E4s8YN/i0s3zTbbDb29LlYe+0CXli7k2/e\n917S8Sv/9xFX/u8jLpwzgaa2EBfO3Zu9asoHdI9805wL+tK8vamNw254icoyJ6uuPi6Htcou2Wjn\nfg2+lPKbAEKInwNjgE3AfOBuoB4Ym/rqocFZNPgFxJ2RKG9s0AZXTpo+mmc/2gFoyVAOum4pbaFO\n/vTKRgCqGPASAAAgAElEQVSeuORIpo6tHPQ9zUY0GmXfXzxNYof2jcuPYkwePSSzybGTRvDm5Ufx\np1c28MDyz5KO3bVsEwD/fPdzNvzfCTgM+M1alftjb45NbSHuf2szM/bwqr/HFAzkV/ZVKeV3pJR/\nklKeD8wGXs9SvQaFs2jwmZFWbGmguT3MME8J08ZW6a/of33906TeKsBJf3w9L14nKyoqhroKOpFI\nlG8/+L5u7IvsNp79/mzDjX0+ae6N0VVlXHfyVDbfuJBbvjaj13O+968PuPfNzRz3h1ep9fe/2Dzf\nNWeDdDVf+dgaTvrj6zQFhjbekRFko50HYvCbhRD6jBwp5Qq0+fl5hxE9/OfWaD36U2ZqPub4QqCm\ntt5/SBc/8P6g7zlY4tOy8oF73tzMM7G3IgD5qwVMHGn8DzifNPfH4hlj2HzjQl74wRzmi675Dk+t\n3s7Vj69h/U4/B163lMseXtVnZq1C0mwUfWkucRT12Le9ua2XMwuLbLTzQCzj+cC9Qoh7hBCXCCHu\nAvLyMTrY1+NoNMoDy7XXxKP3HwGQNAgHsOqq45LGB55ds4OPdzQP6r6DJT7/d6hZvqmOXz25Vt9+\n62dHZc1lkS+aB8K+Izzc/Y0DUx5/eMVW9vnFM6zb3kx9L8lWClHzYOlL819e29Rj303PSiJ5PMEi\nHbLRzmn/FUop1wMHAM+gTatcB5xoeI0MYLAunTte3agnLj9gT215c0VZ12KGEoddz8L05KVH6vuf\n+yj7y+rzneufXsfX7l4OQI27mPevPJZRldbw2Q8EZ5Gdp787u89zTrjlNQ65fil/eW0T1z25lrP+\n+jYf72hma2N7n9dZibXbmmkJ9uwJv/TxLp5fq/4euzOg6DxSyg601bL/zk51jMGRwQKeROLzqIvs\nNr1nevT+w/Xj//jmofrnKWMq+fmJE7n+6Y/5w9L1fGf+3kM2AOdyufo/KYu8/1kDdy/r6m3df/4h\nVJcXZ/WeQ615MEwaXcGKK46hrrWDf77zOS+s28Hn9cmuiFBnlOueWqdvL7j5NQAqStcwvKKUG06Z\nykHjBz/bKd9J1c6NgdQzWXY2F/aDMRu/bVNODRiMD789YUD2iUu6eu8ljiJe+8l87jn3IGaN8yZd\nM190PQyeWN0zkmKu6GtJdTbY0dROnT9IW0cnT3+4nVP+9KZ+7NrFk9l/VPYHF3Ot2Wh87hL2G+Hh\nqpMm8fKP5vHgBYdw4dwJ/V7X3B5mwy4/p935FuMvf4ov/+kN3thQSzDcyW+e+5iNuwcT2Db/SNXO\njSnG1ABsg5+7MaRk47edcfxNIcQooD4fY9gPxuC/9PEuAMQID5NGJxusPapd7FHd86m797Cu8A8v\nrN3Jl2cOzUzVpqamrC8/j8957ou7zprF8ZPTD4A2GHKhOVc4iuwcsU8NR+xTw3lH7MUh17+Y9rUr\nP9OijvrKi6lr7eD2lzcOag1KvpGqneNjHKcfvCcXzZ3A3N+8oh8rcHufld/2YHr49wMfCyEGEjEz\nJzgG4cN/b7MWcGn2vul/0Xa7jWWXzQfg5Y93E+pjhkUh8/SH2/s19kDOjL2ZGVFRykfXHM9lxwue\n/f5sPr3hRJ77/hxGJeT4nblnz/C5dQmDvFsbtEG/9lAnO5ra2bDLz4ZdLfiDYX1R4VCyo6l90NOZ\n4wbf63IyzlfOuUeM7zpY6F38LJBOAhSBlvwkqWWklMcIIWzApGxVLlMc9syeY6HOCI+v0lwyRyX4\n7NNhT5+LCcPK2bS7lQ+/aOKAPb39X2Qw2XJv1PmDzLpuab/n/e606ZxywOBCJQyUQnfp9IW7xMF3\n5ndl/hIjPbz1s6PZWVvPcJ8Xm83Gpt1+fvCvD1i1tacBv/3ljRw1cXiP1b5xDt/bx4MXHKKvIu+L\nv7y2iSdWb+fBCw7BHQszEolEuX/5Fg6d4EOMHFiMoP+u3MoP/rWKi+buzeUnTOz3/FTtLHdo4QdG\nxdZ3+BLGjAY5lDfkDJVL5xFgnBBiPbAaLT3hauBDKeUuutIW5g3Fjsxa+hW5m1p/kAnDyjlswsAD\nFx2yl49Nu1t5a2PdkBj8ykrjVxfuaGrn0BuSXQtfmj6a339lOp/VB9jdEuSQDL4ro8iG5nxnRE3X\nIO2EYW4eu+RI1mxrYuGtyesgH3rnMx5657Pul+u8ubGOH/zrA27+2sx+7xkfOH50xVbOPnw8ABc9\nsEKfCTNQ99HNSz8B4M5XN6Zl8FO1c3xgVsSC0iXOCLMVuFMnG7/tfrvCUsqpaFExL0aLhzMB+Dmw\nWgixo69rh4pMe/hLYz/ek6aNTqvX0515scU097+1ZUhW3ibG2TaCaDTK4tuTjcj7Vx7LrafPxFFk\nZ8Iw95AaezBecyHQm+bJozMzDv/7YBuba1t7dUOu2NLAys8akmbC/PZ5STQapc4fHNS0x4H+eaRq\n5zXbtLUv8XUyibGtspmEJhdk47ed1qBtbGD2XSGEX0p5aXy/ECL33dg0yHTQ9t0tWuKGA8dnJuvY\n/UdQUepgR3M7W+oCjB9gUKx84sOtTSy58006YusRFk4dxe1nHDDEtVJkwrlHjGfa2EqufWItk0ZX\n0Brs5IPPG/Xj8377CgCHTqjm3c0NLJgyklu+OoMld2izro6e2OXebGkP88iKrVz2yOqke7S0h/CU\npueCCHVG+Kx+8IuK3tpYp4c5KYsZ/MRAdNc8sZZzj0gvN7JVGOgsne5+/IZUJw4lmSy82tHUzqbd\nrbhLHBnPa7bbbRwwzssrcjevb6jNa4O/YVcLH+9o6ZF0uz3UyTVPrE1yBVw4ZwI/O3H/XFdRMUDe\n/vnR/PY5yTlHjKfW38HZf9MS0v10wURKnUWcPGMMNpuNcGeER9/fmpSEBmD5Jq3D89Tq7TQnTHd8\nMTZzLU53Yw9w+aMfpt0h+PaDyWFIOsIRih12OsIR3ttSj6+8hPE1rl5DJiRy+p+X65/jPfyRlYNJ\ns21+0hm0vR14P/avIJxi9oTRmkgkmrSdimc/0mLnTxpdQamz7x9aXxw2wccrcjdvbazjzEPH9XpO\nNBrlpY93MWOPKnzukozv1Z3+pnAFOsJs2t3Kdx9ayaZaLZXbJf9YycKpo7h28WQcdjvTr30+6ZpL\nj9qH7x29r2F1NBqzTMkcCKk0j6go1ZOsR6NRfnHi/kwdW6n/nuNuSkeRna8etCfTxlZxwi2v9VrW\na58MzJ3w1Ifb+UldK+N8XZ2cFVsaeOidz7hy0SQqE1aqv9DNFbTfFc/wzi+O5s/LNvHn1z7V98fH\nBX72n9U89M7n/PvCwzh4L60ztq0xeYGa19X7Ar+mQEhfFV9oZOO3nY7vYxUwA7gZ8Agh1gohHhZC\nXCOE+KrhNTKARP/g5rrWtK7548sbANh72OB65cdM0mLvvP1pXUo//sMrtnL+ve8l9VCMIJ47MxWT\nr36ORbe9rhv7OE99uJ1Z1y3tYey/cuBYfnScyOvQvf1pNiPpaLbZbHxzzgQO7WOMZf9RFdx5Zvpu\nuttOn8nk0akX0x37h658SNsa21hyx5s8smIr0695nm2NbaxKcCN15+D/ezHJ2IMWqDAajfLQO1oi\noq/cpS0ye/2T2qRVtDXukqRO2vlHdrlxpl/7fJL7qpDIxm87nUHbu6WUlyZkvDoOLeNVAFhkeI0M\nINHQnnPPu/2eH+6MUOvXBqZOnTW4RVMTasqpLi+m1t/B1obeI/Y9tVp7m1i/088zH25nV4sxS8Dj\niZB746TbXh/QQNmvl0zlplOnG1Cr7NKXZrNipOYFU0alDNsM8JMFQv/sdRVz11mzmLPfMFzFRdx3\n3sGsu3aBfrwjrGWd+t3zksNvTF6vcfiNL7H49jf46+vJRr0vPq8P6DGtEvnxw6toae+Kn/P1g/dI\nOt7dJfvPPmYqpcOtL37CbS9+MqgyMiEbv+0Br7SVUm5FS3v4zECuE0KUAR8BvwJeRFu4VQRsB84y\ncsVuJMGypTM49HFsLu84n2vQWZhsNhsH7FnF0nW7WLpuZ6+DRokREC+O+TNvOGUqpx+8Z1r3iESi\nfLStiYfe+YyvHLgHM/uZAnrgdS/oDzSAZZfNZ2RlKcUOOzc8s46VWxo5cepIHlu1jeljq7hy0aSM\nEoorCpPFM8aweMYYdrcEsdngvre2cOuLn3DloknsmbCyvMrlZKzXxX3nHZyyrJflLm57aUPK44lR\nVAEWTRvFk6t7T0W66LbXee+KY3rs39HcnlROd5dtc3uyoRzM+qsHlm/h9y+sB+CSo/bJaPZePpFx\naIUMuAItQxbAtcDtUsqHhRDXA+cBdxh1o4EudH13c2x2jgEp9wDm7jeMpet28d6Whh4GPxqN8mEv\nqxx/9p8P6QhH9DnOqVi7rZkTb+3yu8Zfd//5rUOZPrrn4pdl63cnGfsPrjqWqgR/589O6BqMPacA\nZzRYcR5+tjQP82jjST88dj9+eKyW6iIxIUtVCl/4rafP5LsPrQS0wdt0eeZ7s5k40pPS4AMcmGLB\n3ye7UscKGu8zbrLEFf/7SP8cjkQNSa6ULkMyD98IhBAT0VbkPhXbNQ8tsTnAE0DPx/gg6O47789l\nohv8DKdjdife416+sa7HsV8k/ICApGiSVz++hs21qcccnly9LcnYJ/K1u5ez/y+Xctqdb9IUCBGJ\nRBl/+VN8IzZTA2DNNccnGXszoFw62aXGXcK5R4znhCkjGZ0izPWiqaP0z7takl/UX//p/JRl7z+q\nApvNxlhvcrkDCWsCsOSAZDfswXtVJ72ZZDrXpHs8/Xjy+aVrd7L4j6/zeRreg2Xrd/PlP73Bp338\nXXfn3+99zuybXmLTLuPza+RqNO53wA8TtssTXDi7gFE9L8mcSDeDHwyl7vJHIlHeihnmvga4BsKk\nURUUF9mpa+1Ieti0dXTyj7eT/YkrrjhG702BNifa30t875b2EJf8Y6W+fdqssfztnAMZ50sO5vbu\n5gamX/s8E37+dNL+Jy89kvKSXL7Q5QaVDCT7XH3SZO44c1bK2W52u419hrt77F922XzGel28d8Ux\n/OLE/Sl2dJmbRPfl6z89iomx0Azrrl3ALSlW/n5rTs8ooqMqS3sNaLhoWpdJebnbtNJ06e4Ofv8z\nbRb6Bfe9x6qtTVzzxNreLkvinHveYeVnjVz8wIq07/uTR1bzeX0bv3/B+HGDrFsAIcQ3gLeklJ9q\nYXl6kPLx29bWRnu7ZjBdLhcOh4PmZu2pV1xcjMfjoa5OM9Y2mw2fz0djYyNt7cm9jKbGBsoiAcrL\ny7Hb7bS0tOhlbGgI0xAIMaqimApbO1BOQ0MDnZ3agg6v15tUD7fbjc1m08soKSnB5XLR0KD9GOx2\nO9XV1Rw0roI3NjXy6PKNfOuoiQQCAV75uOfKxLq6Os47ZBRvbazlrdg86F8/+SHXnjKDhoYGIhHt\nYXXjy1v1a+bv6+W6L00kEonw6LlT2bA7wNfuTf0q/dgF0xlZos14aGlpoaNDc/FUVFQQDod1A+Jy\nuXA6nfrsAKfTSWVlZdKKv5qaGpqamvReZmVlJaFQKKmMdNspnsKtqqqKYDBIW5s2yN1bO7ndburr\n65O+44aGBsLhMLW1tRm3U319vf4de71eAoEAwaD2+/F4PESjUfx+zX1QWlpKWVmZXkZRURFerzep\njOrqavx+v/4dezweIpEIra1aD6+srIySkhIaG7WZIw6Hg6qqKurqumZ1+Xy+PtspEokQCoXyqp3u\nOk1w9O1dRm1sVQluWzvgoigU4MuTKvjSxAN5QjazfnsTP5w9ktraWr2dHjhTC8kVDgaodLl47ILp\nLP7LKr28fWvK+Pp0L3d3TQTSvt9iO8FgsEc7Jb7l74jN6BloO7W2J8fav+qxNTx41mR9OxjupLm5\nOWU7ddqL9ZzO63e20NTU1G87JeaxjUQiBAKBAbdTXzF4ctHlWwhMEEIsAsYCQcAvhCiTUrYBY4Be\ng8iXlZXhdif3HLrPTe2+XVVVRXFJ8tz2Gp+PmoQFGSUJxy+8TfMRHjd5FD6f1sP3epNdO263u0c9\nSrrfo1s9Fs/ckzc2NfLhrnaKiorweDws26wlB7lo7t5s2u1n2thK/bq/nH0Qk69+DoD7393GnP1H\nc2xsiue67c08suILAPYb4eae8w/X71NWVkZNDWy+cU+eWvkZ3/lXsuH/+YkTmb5P1ytv98TIxcXF\nPRIt9Pcdd/ctOp3OAZdRVZUc6dHhcFBenux77e87jhvo+L0zaafq6uRxG4/Hg8eTPBZSWpq8mKe/\nMnpLPl1Wluy26F5G/LeXqozEdgoEAjidzrxqpxrg418tYOKVzwIwR4zQv5fEv6cLhg+jN7q3k/ab\n7TL4vzttKuPH9LxWjK7Sr01qp14GV+P1CXSEOfOv77Bw2ijOOKRrrUxjoIOn1vuZs98wnlq1m1fX\n7066fsMuP6fe07XorMhu67OdLnt4VdKxeHv01U6JA87FxV3tNZB2ij/4eiPrBl9Kqc/VF0L8EtgM\nHA4sAR6I/f9stuvRG5FIlN0xn6PRyTr2HaEZnlek9qOJRqN67JHjJ49g5p7JAaPKSxw8ctFhnHrn\nWwB88773WHbZfNbtaObC+7t6Tn2lxTt28kg2/N9Y7nhlI6XOIuZPHD7odQX5jsNhPjdVf+Sr5sS5\n8Eb8PV27eLLWq77gECbGynv1snlJMe+vWtR7sN4zDtmTO17Z2GN/nT/I5f/5kDc31vHmxjrOOGQc\n4c4IO1uCHHFj/6G/EzOSFfUxY6elPcTDK7amPJ6Kzs6uN5PWDuPDrA/VL+dq4D4hxIXAFuBeIwvv\nPmjbmWICeiAhu5XRi4vig0aBjk7WbW9m424/TW0hqlzOlIGuDhxfzUVz9+bOV7Uf6pzfvJx0/PIT\nJvZZz+bmZmpqarg0j1fGGk1cs5XIZ80v/Wguy9bv5vSD9uj/5H74xmHjOevQcdhsNmpra6mpqUla\nyQtdM4u6M9bbe3rA429eljRrDeDIX7+su30GQl8zNNdtb0najkRhc20r/mCYKWNSz75JDGJXXWb8\nEGtODb6U8pcJm8dm6z7dzXuq7PV/f6NrEciCKcYm7UicffPnZZtYHZuK+aNj90savOrOT44XusHv\nzkVz9za0jgqF0UwY5mbCsJ4DuJli9Lz37sb+g88bMzL20DVrJ040GsVms/F5fYAtvazwjwepO3bS\nCK750uSkyJ7LN9VR5XImBaAb7jZ+Rl3+rpkfDN3se6oVpvE57ICe1MEobDYbd581C4D/rPyCDbv8\nVLmcfK2fxVV2u40N/3dCj/2PfeeIfu9ZXGyuKZfpoDRbg94079vLzKBETkijE3fy7W9kXKf3tjRw\ny9JPuPXFT/iisY2Dr3+Ru5dtZPZNL/caYC7OC2t38tW739K3a/1Bvnb3chbc/BqhhJXFnVHj5/zn\npzNwkETp36UTjUb5orH30AdGcfT+I5K2F00blVboZkeRnXXXLmBnczsdnRH2GeZOKwBc98FGK6A0\nW4NEzUsOGMuj72/lG4f1HpwwzjmHj+eZj7SUHa3BsJ6v2iha2sP8Yam2ClfuaGF3S5Drn/44rWsT\nxwJ2J6xdSHTpTB8/NMHTCo7u9r37vHyA1zd0TY06yKAFV90pstvwJqxOHIhLpqy4iPE15ew3wpOW\nsQf0qVpWQmm2Bomaf71kKs9+f3bKaLRxEsOD7G4JculDK/s4e3D0tno+XRLt0/qd2gybvYeVc+ho\n5dJJi+72/fqn1iX58etbO7j95a54HxfOyZ5v/LkfzOGGU6ay8foTUw4kKRSK9HEU2Zk4sqJf/35i\nRymcYhzPKDJJ6NLWoU0aiSRMxvnOP7TYWq7i7DhfzGnwu7l0Xvx4Fwdc94K+feZf3taTPQD4sjA4\nEme4p5TTD94zJ8HICj2wUyYozdYgE82J0ya7D7DmA+ffq0Xy7c3l7CiyZaWdzWnwe2nbxkDXgoa1\n25NjVFSUFWaChO50X7xjBZRma5CJ5kR72dFLmOWh5s2NdazZ1tTrw2jT7tastLM5DX6K/eMvf4rx\nlz/VY//ICnOkRYsv17cSSrM1yERzoh1tz9OE5gtvfb3XRElNbaGstLM5Df4A3t6euMQ8QcXisTSs\nhNJsDTLRnDgY2h5K3+BXlxfzzs+PHvD9MiWVuykb7WwOS9eD9C3+1LHWi6euUFiBxJ5zazB9g7/8\nZ7kz9gDtOXQ3WbqHf8XC/fs/qYDoHujKCijN1iATzYl2oLeQ471x/OQRFDvsOc349tjKL3rdn412\nNmUPP93+/d4GLgHPB4LBYN4G1soWSrM1yERzoqfkz8s29Xv+LV+bwVEThwOQywyf/0lh8LPRzqbs\n4adLPk7VGgzxOOVWQmm2BplonpAQKVbubOnjTI3FM8bosWzyYeprNtrZlAa/t1Hv3pg1LjsrbBUK\nxdBT4y7huEkj+j/RQpjyvTAdc7/mmuNNMzsnTvfEFFZAabYGmWrungK0ULhwzoSstLNJe/g99x2T\nEMjsx8ftZzpjD1raPquhNFuDTDVv3J1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rk/8ozdZAabYGmWruy27ms8H3z5kzx3qOO4VC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\nL0mNMPAlqRFfX9W1xGpdlLsAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Mag vs Freq\n", "\n", "%matplotlib inline\n", "mat_contents=sio.loadmat('Case2-2.mat')\n", "f = mat_contents['Freq_domain']\n", "Hf_chan_2 = mat_contents['Hf_chan_2']\n", "H= (20)*(np.log10(np.abs(Hf_chan_2)))\n", "plt.plot(f, H)\n", "plt.grid('on')\n", "plt.xlabel('$Freq,Hz$')\n", "plt.ylabel('$H,dB$')\n", "plt.title('$Magn$ versus $Freq$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Quadrature peak picking\n", "---------------------------" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "hpeak=85.23;# obtained from plot\n", "fd=34.06 #obtained from plot\n", "thredb=(hpeak)/np.sqrt(2);\n", "fda=33.65;#obtained from plot\n", "fdb=34.35;#obtained from plot\n", "zeta=(fdb-fda)/(2*fd)\n", "fn=fd/np.sqrt(1-zeta**2) # in hertz" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "34.06" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fd" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.010275983558426348" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zeta" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "34.061798439554778" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fn" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using Vibration Toolbox" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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pKH6waFmMiZalb+57eTNn8LQyYhVT4bCLBr5od7KuRUJbmVjh5Kz5k8hk4PZn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\nfMbSmjVrmDlzJgB77703K1eu5O233+azzz5j3jzlKicSibBhg1qil37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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "(0.00038369496345961473, 34.042986534080605, 16.813265077521343)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ " %matplotlib inline\n", " mat_contents=sio.loadmat('Case2-2.mat')\n", " f = mat_contents['Freq_domain']\n", " TF = mat_contents['Hf_chan_2']\n", " Fmin=70\n", " Fmax=125\n", " sdof_cf(f, TF, Fmin, Fmax)\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Closed form solution\n", "--------------------------" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "Beta1= 1.87510407/l\n", "Beta2= 4.69409133/l\n", "\n", "w1=Beta1**2*np.sqrt((E*I)/(rho*A))\n", "f1=((Beta1**2)/(2*math.pi))*np.sqrt((E*I)/(rho*A))\n", "w2=Beta2**2*np.sqrt((E*I)/(rho*A))\n", "f2=((Beta2**2)/(2*math.pi))*np.sqrt((E*I)/(rho*A))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.3941606842248166" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Beta1" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8.496861851751289" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Beta2" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "219.76306397380711" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "w1" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "34.976377940451826" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f1" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1377.23172666088" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "w2" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "219.19323708106515" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Beam Deflection at center due to an excitation on the tip with specified frequency (using vibration toolbox)\n", "-----------------------------------------------------------------------------------------------------------------------------------" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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09dBnLmOv3c3ThS72Zw0GRsdJjeaddWacdL7IoXSeQ2nY3ped1XyfxyAW7CAe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\nLPxhYWxsbFHntyKqaVZNL2j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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "[fout,H]=vtb.euler_beam_frf(xin=l, xout=l/2, fmin=0.0, fmax=100.0, zeta=0.01,\n", " bctype=2, npoints=2001,\n", " beamparams=np.array([E, I,\n", "rho, A, l]));\n", "\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "y=np.where(fout==100)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1.39445290e-07, 7.13702202e-08])" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "admittance = np.abs(H[2000])\n", "excitationforce=100\n", "displacement = admittance*excitationforce\n", "displacement" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "hide_input": false, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": 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