{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Harmonic Linear Chain\n", "\n", "The equation of motion for nth mass in the chain is given by:\n", "\n", "\$$\n", " m_n \\ddot{q}_{n} = k_n(q_{n+1}-q_n)-k_{n-1}(q_n-q_{n-1})\n", "\$$\n", "\n", "Where $q_n$ is the nth mass' displacement from its equilibrium position. If we assume a normal mode solution we can form a matrix equation:\n", "\n", "\$$\n", "\\begin{bmatrix}\n", " \\ddots & \\vdots & \\vdots & \\vdots & \\\\\n", " & & & & \\\\\n", " \\dots & -k_{n-1}/m_n & (k_n+k_{n-1})/m_n & -k_n/m_n & \\dots \\\\\n", " & & & & \\\\\n", " & \\vdots & \\vdots & \\vdots & \\ddots\n", "\\end{bmatrix}\n", "\\begin{bmatrix}\n", " \\vdots \\\\\n", " q_{n-1} \\\\\n", " q_n \\\\\n", " q_{n+1} \\\\\n", " \\vdots\n", "\\end{bmatrix}\n", "=\n", "\\omega^2\n", "\\begin{bmatrix}\n", " \\vdots \\\\\n", " q_{n-1} \\\\\n", " q_n \\\\\n", " q_{n+1} \\\\\n", " \\vdots\n", "\\end{bmatrix}\n", "\$$\n", "\n", "Hence we find an eigenvalue problem which can be solved in the usual way. The eigenvectors obtained show the relative motion of the masses in the system. \n", "\n", "Below we will plot the eigenfrequencies, increasing from left to right, as a blue line. The eigenvectors will be represented as N red dots, representing the relative displacements of each of the masses." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#NAME: Harmonic Linear Chain\n", "#DESCRIPTION: Solving the eigenvalue problem for masses in a harmonic linear chain.\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline\n", "\n", "def tridiag(a,b,c,i = [-1,0,1]):\n", " return np.diag(a,i[0])+np.diag(b,i[1])+np.diag(c,i[2])\n", " \n", "\n", "def create_matrix(k,m):\n", " \n", " assert(k.shape[0] == m.shape[0]+1)\n", " \n", " N = m.shape[0]\n", " \n", " diagonal = -(k[:-1]+k[1:])/m\n", " upper_diag = k[1:-1]/m[:-1]\n", " lower_diag = k[1:-1]/m[1:]\n", " \n", " K = -1.0*tridiag(lower_diag,diagonal,upper_diag)\n", " \n", " return K\n", " \n", "def normalise(m,eig_vecs):\n", " norm = np.sum(m*np.linalg.norm(eig_vecs,axis = 0)**2)\n", " return eig_vecs/norm\n", "\n", "def sort_by_freq(eig_freq,eig_vecs):\n", " sort_indices = np.argsort(eig_freq)\n", " return eig_freq[sort_indices],eig_vecs[:,sort_indices]\n", "\n", "def eigenanalysis(k,m):\n", " K = create_matrix(k,m)\n", "\n", " eig_freq,eig_vec = np.linalg.eig(K)\n", " eig_vec = normalise(m,eig_vec)\n", "\n", " eig_freq,eig_vec = sort_by_freq(eig_freq,eig_vec)\n", " \n", " return eig_freq,eig_vec\n", "\n", "def plotter(eig_freq,eig_vec):\n", " fig = plt.figure(figsize = (12,24));\n", " ax1 = plt.subplot(212);\n", " ax1.set_xticks([])\n", " ax1.set_ylabel('Squared frequency')\n", " ax1.plot(eig_freq,'b');\n", " ax1.set_xlim((-0.5,len(eig_freq)-0.5));\n", " \n", " ax1_2 = plt.subplot(211);\n", " ax1_2.set_xticks([])\n", " ax1_2.set_ylabel('Squared frequency')\n", " ax1_2.plot(eig_freq,'b');\n", " ax2_2 = ax1.twinx();\n", " ax2_2.set_ylabel('Eigenvector components')\n", " ax2_2.plot(eig_vec.T,'ro');\n", " ax2_2.set_xlim((-0.5,len(eig_freq)-0.5));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First a system of 3 unit masses connected by unit springs\n", "\n", "Analytic solution ($x = \\omega^2$):\n", "\n", "$$\\det \\begin{bmatrix}\n", " 2 - x & -1 & 0 \\\\\n", " -1 & 2 - x & -1 \\\\\n", " 0 & -1 & 2 - x\n", "\\end{bmatrix} = 0$$\n", "\n", "$$-x^3+6 x^2-10 x+4 = 0 \\to x = 2,2\\pm\\sqrt{2}$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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y1qzj0i0APdvfZVyAbmjWAWBqBH2ge5p1AJgiqztA1zTrADBVgj7QrY1mnQsv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\naGzC3W67squRJNXU9sAL+e3+2MnADpn5bESMGmBroy9JY2Q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JA9Vlou8affU8Q7EkSVId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\nQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k = np.ones(4)\n", "m = np.ones(3)\n", "\n", "eig_freq,eig_vec = eigenanalysis(k,m)\n", "\n", "plotter(eig_freq,eig_vec)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next a set of 99 masses, every other mass having m = 1.5 while the others have m = 1. All the springs have a spring constant of 1. This approximates a diatomic chain, although the periodic boundary conditions are not respected" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SSrPddnDBBfCVrxSdRJKqT0SQUnJT6RZKWtMAjAV+kVL6Y4vX74qIHUv4+uuB\nl9sqDM3uBU4C7oiIbYDJrmeQpHxNmZKd5ixJUilKKQ0bL25KUUqpzS1UF4qI7YEjgRcjYgKQgB8B\na2Vfnq5OKY2IiIER8SYwg2xEQ5KUI0uDJKkjSpmeNJRsLcLk5uv/AC5KKQ2uQL6WOZyeJEllsuKK\n8O67FgdJaovTk1or5XC3jRcWBoCU0sfAZvlFkiTlacECmDkzKw6SJJWilNLQo3l0AYCI+AylTWuS\nJFWhqVNhhRWgRym/ASRJorQ//i8CnoiI3wIBHAT8JNdUkqTcuJ5BktRRpZzTcFNEPAPs3PzSAR09\nGVqSVD0sDZKkjip1mtGrwMcL74+INVNKf88tlSQpN5YGSVJHLbE0RMTJwNnAh8ACsilKCdg432iS\npDxYGiRJHVXKSMOpwBdSSv/KO4wkKX+WBklSR5Wyd8Y7wJS8g0iSKsPSIEnqqFJGGt4CGiPifmDO\nwhdTSr/MLZUkKTeWBklSR5VSGv7e/Fi6+SFJqmFTpkCfPkWnkCTVklK2XD0HICKWSynNzD+SJClP\nU6bAWmsVnUKSVEuWuKYhIraNiJfJtl0lIjaJiCtyTyZJyoXTkyRJHVXKQuhLgAHAvwBSSs8DO+YZ\nSpKUH0uDJKmjSikNpJTeWeSlBTlkkSRVgKVBktRRpSyEficitgNSRPQiO7fhlXxjSZLyYmmQJHVU\nKSMNJwAnAWsA7wGbNl9LkmqQpUGS1FGRUio6Q0kiItVKVkmqZiutBH//u9uuStLiRAQppSg6RzVZ\nYmmIiBuAVjellAbnFWoxOSwNktRFCxbA0kvD3LnQs2fRaSSpOlkaWitlTcMfWjzvDewPTMwnjiQp\nT9OmwfLLWxgkSR1TyuFud7e8jojbgMdySyRJyo3rGSRJnVHSlquLWB9YtdxBJEn5szRIkjpjiSMN\nETGNbE1DNH/8ADgz51ySpBxYGiRJnVHK9KQVKxFEkpQ/S4MkqTNKGWnYvL3Pp5SeLV8cSVKeLA2S\npM4oZfekK4DNgRfIpihtDDwNzCabrrRLbukkSWVlaZAkdUYpC6EnAluklL6cUtoC2Ax4L6W0c0rJ\nwiBJNcTSIEnqjFJKwxdSSi8uvEgpvQRsmF8kSVJeLA2SpM4oZXrSCxFxLTCs+fpIsqlKkqQaM2UK\n/Nd/FZ1CklRrSikNxwLfBk5tvh4HXJlbIklSbhxpkCR1Rilbrs6OiKuAESml1yqQSZKUE0uDJKkz\nlrimISLoV19zAAAgAElEQVT2A54DHmi+3jQi7s07mCSp/CwNkqTOKGUh9NnAVsBkgJTSc8A6eYaS\nJOXD0iBJ6oxSSsO8lNKURV5LeYSRJOXL0iBJ6oxSFkL/OSKOAHpGxPrAKcAf840lScqDpUGS1Bml\njDScDHwRmAPcCkwBvpNnKElS+TU1wfTpsNJKRSeRJNWaSGnxM40ioidwfkrp9MpFWmyW1F5WSVL7\npkyB/v1h2rSik0hSdYsIUkpRdI5q0u5IQ0ppAfCVCmWRJOXIqUmSpM4qZU3DhOYtVn8LzFj4Ykrp\nd7mlkiSVnaVBktRZpZSG3sC/gF1avJYAS4Mk1ZCpUy0NkqTOWWxpiIjzU0pnkp0E/dsKZpIk5cCR\nBklSZ7W3pmFgRATww0qFkSTlx9IgSeqs9qYnPQB8DKwQEVNbvB5ASim5aZ8k1RBLgySpsxY70pBS\nOiOl1Ae4P6W0UovHihYGSao9lgZJUmct8XC3lNKgSgSRJOXL0iBJ6qxSToSWJNUBS4MkqbMsDZLU\nTVgaJEmdZWmQpG7C0iBJ6qz2zml4kewQtzallDbOJZEkKReWBklSZ7W35eo+zR9Pav54c/PHI/OL\nI0nKi6VBktRZkdJiBxOyGyImpJQ2W+S1Z1NKm+earHWOtKSskqTFW3ttGDsW1lmn6CSSVN0igpRS\nFJ2jmpSypiEiYvsWF9uV+HWSpCriSIMkqbPam5600DeA6yNi4a+aycDg/CJJksotJZg2DVbyaE5J\nUicscXrSJzc2l4aU0pRcEy3++zs9SZI6ado0WG01mD696CSSVP2cntTaEqcZRUS/iLgOuD2lNCUi\nNoqIb1QgmySpTJyaJEnqilLWJtwIPAis3nz9OvCdvAJJksrP0iBJ6opSSsMqKaU7gSaAlNJ8YEGu\nqSRJZWVpkCR1RSmlYUZE9KX5oLeI2AYoZF2DJKlzLA2SpK4oZfek04B7gXUj4nHgP4GDck0lSSor\nS4MkqSvaLQ0R0QPoDewEfAEI4LWU0rwKZJMklYmlQZLUFe2WhpRSU0Rc3nwi9J8rlEmSVGaWBklS\nV5SypmF0RBwYEe5VK0k1ytIgSeqKUkrD8cBvgTkRMTUipkXE1JxzSZLKyNIgSeqKJS6ETimtWIkg\nkqT8WBokSV1Ryu5JRMR/AOuTLYoGIKU0Lq9QkqTysjRIkrpiiaUhIo4DTgX6A88B2wBPALvkG02S\nVC6WBklSV5SypuFUYEvgbymlnYHNgMm5ppIklZWlQZLUFaWUhtkppdkAEbFMSulVsjMbJEk1wtIg\nSeqKUtY0vBsRfYDfAw9HxMfA3/KNJUkqJ0uDJKkrIqVU+s0ROwErAw+klObmlqrt7506klWSlEkJ\nevWCWbOyj5Kk9kUEKSXPKGuhlIXQa7a4fLv542eBv+eSSJJUVjNmwDLLWBgkSZ1XyvSk+4EEBNmW\nq+sArwFfzDGXJKlMnJokSeqqUg53+++W1xGxOXBibokkSWVlaZAkdVUpuyf9m5TSs8DWOWSRJOXA\n0iBJ6qpS1jSc1uKyB7A5MDG3RJKksrI0SJK6qpQ1DSu2eD6fbI3D3fnEkSSVm6VBktRVpaxpOKcS\nQSRJ+bA0SJK6qpTpSfeR7Z7UppTSfmVNJEkqK0uDJKmrSpme9BbZuQzDmq8PBz4kOyFaklTlLA2S\npK4qpTRsn1L6covr+yLi6ZTSd5f0hRFxHbAP8GFKaeM2Pr8TMJysmAD8LqX0fyVkkiSVaMoUWH/9\nolNIkmpZKVuuLh8Rn1t4ERHrAMuX+P43AAOWcM+4lNLmzQ8LgySVmSMNkqSuKmWk4btAY0S8RXYq\n9FrAt0p585TSYxGx1hJui1LeS5LUOZYGSVJXlbJ70gMRsT6wQfNLr6aU5pQxw7YR8RzwHnBGSunl\nMr63JHV7lgZJUlcttjRExJbAOymlD1JKcyJiE+BA4G8RMSSlNKkM3/8ZYM2U0syI2ItscfXnF3fz\nkCFDPnne0NBAQ0NDGSJIUn2zNEhS+xobG2lsbCw6RlWLlNreTTUingV2SylNiogdgduBk4FNgQ1T\nSgeV9A2y6Un3tbUQuo173wa2aKuQRERaXFZJ0uJ97nPw8MOw7rpFJ5Gk2hARpJScQt9Ce9OTerb4\n4/1Q4OqU0t3A3c3TiUoVLGbdQkT0Syl92Px8K7ISU44RDElSM0caJEld1W5piIilUkrzgV3598XP\npSygJiJuBRqAvhHxd+BsYGkgpZSuBg6KiG8D84BZZOVEklQmKcHUqZYGSVLXtDc96X+BgcA/gTWB\nzVNKKSLWA4amlLavXEynJ0lSZ8yYAf/5nzBzZtFJJKl2OD2ptcWOGKSUfhIRo4HVgIda/MXeg2xt\ngySpyjk1SZJUDu1OM0op/amN117PL44kqZwsDZKkcijlRGhJUo2yNEiSysHSIEl1zNIgSSoHS4Mk\n1TFLgySpHCwNklTHLA2SpHKwNEhSHbM0SJLKwdIgSXXM0iBJKgdLgyTVMUuDJKkcLA2SVMcsDZKk\ncrA0SFIdszRIksrB0iBJdczSIEkqB0uDJNUxS4MkqRwsDZJUxywNkqRysDRIUh2zNEiSysHSIEl1\nKiVLgySpPCwNklSnZs2CpZaCpZcuOokkqdZZGiSpTjnKIEkqF0uDJNUpS4MkqVwsDZJUpywNkqRy\nsTRIUp2yNEiSysXSIEl1ytIgSSoXS4Mk1SlLgySpXCwNklSnLA2SpHJZqugAkqTOWbAAnn4annoK\nJk7MHu+//+nHqVPh0kuLTilJqgeRUio6Q0kiItVKVknKy+TJ8OCDcP/98MADsOqqsMMO0L8/rLYa\nrL76px/79oUejidLUodFBCmlKDpHNbE0SFKV+/BDuOkm+MMfYMKErCTsvTcMHAhrr110OkmqP5aG\n1iwNklSl3noLLrwQbr8dDjgA9t8fdt4Zlluu6GSSVN8sDa25pkGSqsyECXD++TBqFBx/PLzyCvTr\nV3QqSVJ35mxXSaoSjY0wYADsuy9suSW8/Tb85CcWBklS8RxpkKSCvfMOnHoqvPAC/OhHcOSRsMwy\nRaeSJOlTjjRIUkHmzcvWLGy2GWyyCbz0EgwebGGQJFUfRxokqQCPPw4nnJBtjfrEE7D++kUnkiRp\n8SwNklRB//wnnHlmdtbCL38JBx8M4f4ckqQq5/QkSaqQkSPhv/8bVlwRXn4ZDjnEwiBJqg2ONEhS\nzubOzRY433FH9thxx6ITSZLUMZYGScrRm2/C4YfDaqvBc89B375FJ5IkqeOcniRJObntNth2W/ja\n12D4cAuDJKl2OdIgSWU2YwacfDI89hg89FC2paokSbXMkQZJKqO33oKtt4b58+GZZywMkqT6YGmQ\npDJ55BHYbrvs/IWhQ7NdkiRJqgdOT5KkMrjmGjjrLLjlFthtt6LTSJJUXpYGSeqC+fPhe9/LDmt7\n9FH4/OeLTiRJUvlZGiSpkz7+GA49NDug7U9/gj59ik4kSVI+XNMgSZ3wxhuwzTaw0UZw//0WBklS\nfbM0SFIHjR+fner8ve/BJZfAUo7ZSpLqnL/qJKkDRo6EY46B66+HffYpOo0kSZXhSIMklWjoUDj2\n2Ox0ZwuDJKk7caRBkpYgJbjgArjySmhshA02KDqRJEmVZWmQpHY0NcF3vwtjx8If/wirr150IkmS\nKs/SIEmLMWdOtn7h/fdh3Dh3SJIkdV+uaZCkNsycCYMGwbx52cFtFgZJUndmaZCkRUybBnvtBauu\nCnfcAb17F51IkqRiWRokqYWPP4bddssObbvxRs9gkCQJLA2S9ImPPoKdd4avfAWuuAJ6+BNSkiTA\n0iBJALz3XnbK86BBcOGFEFF0IkmSqoelQVK39/bbsMMOMHgwnHOOhUGSpEU5W1dSt/bGG7DrrnDm\nmXDSSUWnkSSpOlkaJHVbr78Ou+ySjS584xtFp5EkqXo5PUlSt/Taa1lhOPdcC4MkSUviSIOkbue1\n17IpSeedB8ceW3QaSZKqn6VBUrfy6qtZYfjJT+DrXy86jSRJtcHSIKnbWFgYfvpTOOaYotNIklQ7\nXNMgqVt45RULgyRJneVIg6S69+qrsNtu8LOfwdFHF51GkqTa40iDpLr2xhtZYfjpTy0MkiR1lqVB\nUt16++1sStLZZzslSZKkrrA0SKpLf/97dg7DD34A3/xm0WkkSaptlgZJdee997LCcOqpcOKJRaeR\nJKn2WRok1ZX3388Kw/HHw3e+U3QaSZLqg6VBUt346KNs0fPRR8MZZxSdRpKk+mFpkFQXJk2C3XeH\nAw+E//3fotNIklRfIqVUdIaSRESqlaySKmvq1GyXpIYGuOACiCg6kSSplkUEKSV/m7RgaZBU02bM\ngD33hI03hssuszBIkrrO0tCapUFSzZo9G/bdF/r3h+uugx5OuJQklYGloTVLg6SaNG9etn5h2WXh\n1luhZ8+iE0mS6oWloTX/XU5SzVmwAI46Kns+bJiFQZKkvC1VdABJ6oimJjjuOPj4Y7j3XujVq+hE\nkiTVv1xHGiLiuoj4MCJeaOeeSyPijYh4LiI2zTOPpNqWEpxyCrz5JtxzD/TuXXQiSZK6h7ynJ90A\nDFjcJyNiL2DdlNL6wPHAVTnnkVTDfvQjGD8e7r8fll++6DSSJHUfuZaGlNJjwMft3DIIuKn53vHA\nyhHRL89MkmrTz34G990HDzwAK61UdBpJkrqXohdCrwG80+L6vebXJOkTl12Wban68MPQt2/RaSRJ\n6n5qaiH0kCFDPnne0NBAQ0NDYVkkVcbQodkpz+PGwWqrFZ1GklSPGhsbaWxsLDpGVcv9nIaIWAu4\nL6W0cRufuwoYm1K6o/n6VWCnlNKHbdzrOQ1SN3PXXdnC5zFjYIMNik4jSeouPKehtUpMT4rmR1vu\nBY4GiIhtgMltFQZJ3c/IkXDSSTBihIVBkqSi5To9KSJuBRqAvhHxd+BsYGkgpZSuTimNiIiBEfEm\nMAM4Ns88kmrDuHFw9NHZOQybuhGzJEmFy316Urk4PUnqHp5+GgYOhNtug113LTqNJKk7cnpSa0Xv\nniRJn3j5ZdhnH7jmGguDJEnVxNIgqSq8/TYMGAAXXgiDBhWdRpIktWRpkFS4iRNht93ghz+Eo44q\nOo0kSVqUpUFSof71L9hjDzjuODjxxKLTSJKktrgQWlJhpk7N1i7suiv8/OdFp5EkKeNC6NYsDZIK\nMWsW7LUXbLghXHEFhD+aJUlVwtLQmqVBUsXNmwf77w8rrQTDhkEPJ0pKkqqIpaE1f1VLqqgFC7KD\n23r0gKFDLQySJNWCXE+ElqSWUsoWO3/4IYwYAb16FZ1IkiSVwtIgqSJSgjPPhAkTYPRo6N276ESS\nJKlUlgZJFfHzn2ejC488AiuuWHQaSZLUEZYGSbm7/HK49lp49FHo27foNJIkqaMsDZJyNWxYNsow\nbhysvnrRaSRJUmdYGiTlZvhwOP10GDMG1lmn6DSSJKmzLA2ScjF6NHzzm9k6ho02KjqNJEnqCkuD\npLJ74gk47DC4+2748peLTiNJkrrKY5UkldULL8BXv5od3LbjjkWnkSRJ5WBpkFQ2b7wBe+4Jl14K\nAwcWnUaSJJWLpUFSWbzzDuy+O5x7Lhx6aNFpJElSOVkaJHXZRx/BbrvBKafAcccVnUaSJJWbpUFS\nl0yeDAMGZKMLp51WdBpJkpSHSCkVnaEkEZFqJavUXUyfDnvsAVtuCZdcAhFFJ5IkqesigpSSv9Va\nsDRI6pTZs2GffWCtteCaa6CH45aSpDphaWjN0iCpw+bNg4MPhqWXhttug549i04kSVL5WBpa83A3\nSR3S1ARf/3pWHO6808IgSVJ3YGmQVLKU4MQT4b33YOTIbKRBkiTVP0uDpJKkBN//PkyYAKNGwbLL\nFp1IkiRViqVBUkn+7//ggQfgkUdgxRWLTiNJkirJ0iBpiS6+GG6+GcaNg898pug0kiSp0iwNktp1\n9dXwq19lheGzny06jSRJKoKlQdJi3XILnHsuNDbCmmsWnUaSJBXF0iCpTffcA9/7HoweDeutV3Qa\nSZJUJEuDpFYeeACOPz77+MUvFp1GkiQVzdIg6d888gh87WswfDhsvnnRaSRJUjXoUXQASdVj/Hg4\n6CC4/XbYbrui00iSpGphaZAEZIe27bcf3HAD7Lpr0WkkSVI1sTRI4s9/hoED4YorYJ99ik4jSZKq\njaVB6uZefx322AMuuggOPLDoNJIkqRpZGqRu7O23Ybfd4Lzz4Igjik4jSZKqlaVB6qbefTdbu3Dm\nmTB4cNFpJElSNbM0SN3QBx9kheHEE+Gkk4pOI0mSqp2lQepm/vnPbErSUUfB6acXnUaSJNUCS4PU\njUyaBLvvnm2tetZZRaeRJEm1IlJKRWcoSUSkWskqVaPJk7MRhp13hgsugIiiE0mSVJ0igpSSvylb\nsDRI3cDUqdm2qltvDZdcYmGQJKk9lobWLA1SnZs+HfbcEzbeGC6/3MIgSdKSWBpaszRIdWzGDNh7\nb1h/ffjNb6CHq5gkSVoiS0NrlgapTs2aBfvuC/37w/XXWxgkSSqVpaE1S4NUh+bMgUGDoG9fuOkm\n6Nmz6ESSJNUOS0Nr/tujVGfmzIEDDoCVVoKhQy0MkiSp6ywNUh2ZMwcOPBCWXRZuuQWWWqroRJIk\nqR5YGqQ6MWcOHHwwLL003HYb9OpVdCJJklQvLA1SHZg7Fw45JJuKdPvtFgZJklRelgapxi0sDBFw\nxx3ZSIMkSVI5OeNZqmHz5sFhh0FTE9x1l4VBkiTlw9Ig1aiFhWHePAuDJEnKl6VBqkFz52aFYe5c\nuPtuWGaZohNJkqR6ZmmQaszCNQxNTRYGSZJUGS6ElmrInDlw0EHZoue77rIwSJKkyrA0SDVi9uzs\n4LZeveDOO13DIEmSKsfSINWA2bNh//1hueU8h0GSJFWepUGqcrNmwaBBsPLKcOutFgZJklR5lgap\nis2cCfvtB6usAsOGwVJuXSBJkgpgaZCq1PTpMHAgrLYa3HSThUGSJBXH0iBVoSlTYI89YP314cYb\noWfPohNJkqTuzNIgVZlJk2C33WCLLeA3v4Ee/l8qSZIK5p8jUhX5xz9gl11gp53g0kstDJIkqTr4\nJ4lUJd5/HxoaYN994Re/yA5wkyRJqgaWBqkKvPtuNrpw+OFw3nkWBkmSVF0sDVLB3noLdtwRvvUt\nOOusotNIkiS1ZmmQCvTKK9kIwxlnwOmnF51GkiSpbe78LhVkwoTsHIYLLoCvfa3oNJIkSYtnaZAK\n8PjjsP/+cNVVcMABRaeRJElqn6VBqrBRo7IFz8OGwYABRaeRJElaMtc0SBU0fDgccQT87ncWBkmS\nVDssDVKF3HorHH88jBgBO+xQdBpJkqTSOT1JqoDLL4ef/SybmvSlLxWdRpIkqWMsDVKOUsoOa7vp\nJnj0UVhnnaITSZIkdVzu05MiYs+IeDUiXo+IM9v4/E4RMTkinm1+eLyV6kJTE3znO9n6hcceszBI\nkqTaletIQ0T0AC4DdgUmAk9FxPCU0quL3DoupbRfnlmkSpo3DwYPhr/+FRoboU+fohNJkiR1Xt7T\nk7YC3kgp/Q0gIm4HBgGLlobIOYdUMbNmwSGHZFOTHnwQlluu6ESSJEldk/f0pDWAd1pcv9v82qK2\njYjnIuL+iNgo50xSbqZMybZS7dMH7rnHwiBJkupDNSyEfgZYM6U0MyL2An4PfL6tG4cMGfLJ84aG\nBhoaGiqRTyrJxImw117Q0AAXXww93NBYkqSa0NjYSGNjY9ExqlqklPJ784htgCEppT2br38ApJTS\n+e18zdvAFimlSYu8nvLMKnXFa6/BnnvCt74FP/gBhBPuJEmqWRFBSsnf5i3k/W+hTwHrRcRaEbE0\ncBhwb8sbIqJfi+dbkRWZSUg1Yvz4bHTh7LPhhz+0MEiSpPqT6/SklNKCiPgf4CGygnJdSv+fvXsP\nk6Oq8z/+qZkkEzIhmUCYTEgWhwVUNrKS4OY2WUwyBJKQO4EQQhJxuUpkkeizXoKAsrrrqr+IF1BR\nAdFwXV1uust1ICjoykVdQC5JQAQENQQJJITk/P6onmSmp86p7tNV1dUz79fzzJPMdFfV6eruqvM9\n53vOMY8HQXBG+LD5lqTFQRCcJWmHpDclLUmzTECSbr1VOuUU6YorpNmzq10aAACAdKSanpQk0pOQ\nN9/7nvTJT0o//rE0YUK1SwMAAJJCelJPeRgIDdQUY6TPf1769rfDNRje9a5qlwgAACBdBA1AGd5+\nW/rnfw5XeL7/fmn//atdIgAAgPQRNAAl2rpVOvFEaft26b77pCFDql0iAACAbDCTPFCCl14KZ0ja\nb79w8DMBAwAA6EsIGoAYjz8uTZokzZsnfec7Uv/+1S4RAABAtkhPAhw6OqQTTpC+8AVp5cpqlwYA\nAKA6CBoAix/+UDr3XGndOqm9vdqlAQAAqB6CBqCIMdLnPid985vSnXdKhx1W7RIBAABUF0ED0MX2\n7dJpp4XjGB58UBo5stolAgAAqD4GQgM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SsY9sCgsAAIA+K2L4wB8kHdDl99GFvxU/528i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H3nTrn7yBE5e+bMk79nlVGhe/bOxcXg3Xbn4qK5XhYfoLnLXpG5JIVo4j6Fzi80GnKTktb8pvFx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fT9Zd/w4RnyTiHcpzaUobpDYJajGwtjRkEQyQdtZzVLpWPxZPEPFbiPhNRPyC9esZsDQ82eRe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\n2c2bveP7lk99it7/6KP07Fe/SmuuvZbe8lM/Rdc/5zl0/XOe43y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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k = np.ones(100)\n", "m = np.ones(99)\n", "m[::2] = 1.5\n", "\n", "eig_freq,eig_vec = eigenanalysis(k,m)\n", "\n", "plotter(eig_freq,eig_vec)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Evolution of the eigenfrequencies from broken symmetry\n", "\n", "In this section we investigate the effect of a systems eigenfrequencies when the spring constants of some of the springs are varied. Starting with a diatomic system of 20 masses with unit springs, we start to increase the spring constants from the selected springs in k_i.\n", "\n", "The resulting plot is reminiscent of band structure, with avoided crossings and band gaps." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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8KCws1ERyU1NTQkTX9va2ZqcPl8uFw8NDGcnqASs5OTlRHefp6Sn6+vrQ3d0t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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def freq_evolution(k,m,k_i,k_val):\n", " assert(len(k_i) == len(k_val))\n", " \n", " N_k = k_val[0].shape[0]\n", " eig_freqs = []\n", " \n", " for i in range(N_k):\n", " for j in range(len(k_i)):\n", " k[k_i[j]] = k_val[j][i]\n", " eig_freq,eig_vec = eigenanalysis(k,m)\n", " eig_freqs.append(eig_freq)\n", " \n", " fig = plt.figure(figsize = (12,12));\n", " ax1 = plt.subplot(111);\n", " ax1.set_xlim((k_val[0].min(),k_val[0].max()))\n", " ax1.set_xlabel('First variable spring constant')\n", " ax1.set_ylabel('Squared frequency')\n", " ax1.plot(k_val[0],eig_freqs,'k'); \n", " \n", "\n", "k = np.ones(21)\n", "m = np.ones(20)\n", "m[::2] = 1.5\n", "\n", "k_i = [2,6,9,13]\n", "k_vals = np.linspace(1.,1.75,50)\n", "k_val = [k_vals,]*len(k_i)\n", "\n", "freq_evolution(k,m,k_i,k_val)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }