{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Mousai: An Open-Source General Purpose Harmonic Balance Solver\n", "\n", "ASME Dayton Engineering Sciences Symposium 2017 \n", "Joseph C. Slater, October 23, 2017" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2017-10-02T12:54:04.905714Z", "start_time": "2017-10-02T12:54:03.808563Z" }, "init_cell": true, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The autoreload extension is already loaded. To reload it, use:\n", " %reload_ext autoreload\n" ] }, { "data": { "text/plain": [ "{'theme': 'sky', 'transition': 'zoom'}" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2\n", "import scipy as sp\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "import mousai as ms\n", "from scipy import pi, sin\n", "matplotlib.rcParams['figure.figsize'] = (11, 5)\n", "from traitlets.config.manager import BaseJSONConfigManager\n", "path = \"/Users/jslater/anaconda3/etc/jupyter/nbconfig\"\n", "cm = BaseJSONConfigManager(config_dir=path)\n", "cm.update(\"livereveal\", {\n", " \"theme\": \"sky\",\n", " \"transition\": \"zoom\",\n", "})" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Overview\n", "A wide array of contemporary problems can be represented by nonlinear ordinary differential equations with solutions that can be represented by Fourier Series:\n", "\n", " * **Limit cycle oscillation of wings/blades**\n", " * Flapping motion of birds/insects/ornithopters\n", " * Flagellum (threadlike cellular structures that enable bacteria etc. to swim)\n", " * Shaft rotation, especially including rubbing or nonlinear bearing contacts\n", " * **Engines**\n", " * Radio/sonar/radar electronics\n", " * Wireless power transmission\n", " * Power converters\n", " * Boat/ship motions and interactions" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ " * **Cardio systems** (heart/arteries/veins)\n", " * Ultrasonic systems transversing nonlinear media\n", " * Responses of composite materials or materials with cracks\n", " * Near buckling behavior of vibrating columns\n", " * Nonlinearities in power systems\n", " * **Energy harvesting systems**\n", " * **Wind turbines**\n", " * Radio Frequency Integrated Circuits\n", " * **Any system with nonlinear coatings/friction damping, air damping, etc.**\n", " \n", "These can all be observed in a quick literature search on 'Harmonic Balance'. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Why (did I) write Mousai?\n", "\n", "* The ability to code harmonic balance seems to be publishable by itself\n", " * It's not research- it's just application of a known family of technique\n", "* A limited number of people have this knowledge and skill\n", " * Most cannot access this technique\n", " * \"Research effort\" is spent coding the technique, not doing research" ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true, "slideshow": { "slide_type": "slide" } }, "source": [ "### Why write Mousai? (continued)\n", "* Matlab command eig unleashed power to the masses\n", " * Very few papers are published on eigensolutions- they have to be better than ``eig``\n", " * ``eig`` only provides simple access to high-end eigensolvers written in ``C`` and ``Fortran``\n", " * Undergraduates with no practical understanding of the algorithms easily solve problems\n", " that were intractable a few decades ago.\n", " * *Access* and *ease of use* of such techniques enable *greater science* and *greater research*.\n", " * The real world is nonlinear, but **linear analysis dominates because the tools are easier to use**.\n", " * With ``Mousai``, an undergraduate can solve a nonlinear harmonic response problem easier then a PhD can today." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Theory: \n", "### Linear Solution\n", "\n", "- Most dynamics systems can be modeled as a first order differential equation\n", "\n", "\\begin{equation}\\ddot{\\mathbf{z}}(t)=\\mathbf{f}(\\mathbf{z}(t),\\mathbf{u}(t))\\end{equation}\n", "\n", " - Use finite differences\n", " - Use Galerkin methods (Finite Elements)\n", " - Of course- discrete objects\n", "- This is the common *State-Space* form:\n", " -solutions exceedingly well known if it is linear \n", "\n", "- Finding the oscillatory response, after dissipation of the transient response, requires **long** time marching. \n", " - Without damping, this may not even been feasible. \n", " - With damping, tens, hundreds, or thousands of cycles, therefore thousands of times steps at minimum. \n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "For a linear system in the frequency domain this is\n", "\n", "\\begin{equation}j\\omega\\mathbf{Z}(\\omega)=\\mathbf{f}(\\mathbf{Z}(\\omega),\\mathbf{U}(\\omega))\\end{equation}\n", "\n", "\\begin{equation}j\\omega\\mathbf{Z}(\\omega)=A\\mathbf{Z}(\\omega)+B\\mathbf{U}(\\omega)\\end{equation}\n", "\n", "where\n", "\n", "\\begin{equation}A = \\frac{\\partial \\mathbf{f}(\\mathbf{Z}(\\omega),\\mathbf{U}(\\omega))}{\\partial\\mathbf{Z}(\\omega)},\\qquad\n", "B = \\frac{\\partial \\mathbf{f}(\\mathbf{Z}(\\omega),\\mathbf{U}(\\omega))}{\\partial\\mathbf{U}(\\omega)}\\end{equation}\n", "\n", "are constant matrices. \n", "\n", "The solution is:\n", "\n", "\\begin{equation}\\mathbf{Z}(\\omega) = \\left(Ij\\omega-A\\right)^{-1}B\\mathbf{U}(\\omega)\\end{equation}\n", "\n", "where the magnitudes and phases of the elements of $\\mathbf{Z}$ provide the amplitudes and phases of the harmonic response of each state at the frequency $\\omega$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Nonlinear solution\n", "\n", "- For a nonlinear system in the frequency domain we assume a Fourier series solution\n", "\n", "\\begin{equation}\\mathbf{z}(t)=\\lim_{N\\to\\infty}\\sum_{n=-N}^{N}\\mathbf{Z}_n e^{j n \\omega t}\\end{equation}\n", "\n", "- $N=1$ for a single harmonic. $n=0$ is the constant term.\n", "- This can be substituted into the governing equation to find $\\dot{\\mathbf{z}}(t)$:\n", "\n", "\\begin{equation}\\dot{\\mathbf{z}}(t)=\\mathbf{f}(\\mathbf{z}(t),\\mathbf{u}(t))\\end{equation}\n", "\n", "- This is actually a function call to a Finite Element Package, CFD, Matlab function, - whatever your solver uses to get derivatives \n", "\n", "- We can also find $\\dot{\\mathbf{z}}(t)$ from the derivative of the Fourier Series:\n", "\n", "\\begin{equation}\\dot{\\mathbf{z}}(t)=\\lim_{N\\to\\infty}\\sum_{n=-N}^{N}j n \\omega\\mathbf{Z}_n e^{j n \\omega t}\\end{equation}\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "- The difference between these methods is zero when $\\mathbf{Z}_n$ are correct.\n", "\n", "\\begin{equation}\\mathbf{0} \\approx\\sum_{n=-N}^{N}j n\\omega \\mathbf{Z}_n e^{j n \\omega t}-\\mathbf{f}\\left(\\sum_{n=-N}^{N}\\mathbf{Z}_n e^{j n \\omega t},\\mathbf{u}(t)\\right)\\end{equation}\n", "\n", "- These operations are wrapped inside a function that returns this error\n", "- This function is used by a Newton-Krylov nonlinear algebraic solver. \n", "- Calls any solver in the SciPy family of solvers with the ability to easily pass through parameters to the solver *and* to the external derivative evaluator.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Examples:\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Duffing Oscillator\n", "\n", "\\begin{equation}\\ddot{x}+0.1\\dot{x}+x+0.1 x^3=\\sin(\\omega t)\\end{equation}\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "code_folding": [], "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "# Define our function (Python)\n", "def duff_osc_ss(x, params):\n", " omega = params['omega']\n", " t = params['cur_time']\n", " xd = np.array([[x[1]],\n", " [-x[0] - 0.1 * x[0]**3 - 0.1 * x[1] + 1 * sin(omega * t)]])\n", " return xd" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "code_folding": [], "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Displacement amplitude is 0.9469563546008394\n", "Velocity amplitude is 0.09469563544416415\n" ] } ], "source": [ "# Arguments are name of derivative function, number of states, driving frequency,\n", "# form of the equation, and number of harmonics\n", "\n", "t, x, e, amps, phases = ms.hb_time(duff_osc_ss, num_variables=2, omega=.1,\n", " eqform='first_order', num_harmonics=5)\n", "print('Displacement amplitude is ', amps[0])\n", "print('Velocity amplitude is ', amps[1])" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Mousai can easily recreate the near-continuous response\n", "\n", "````python\n", "time, xc = ms.time_history(t, x)\n", "````" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "def pltcont():\n", " time, xc = ms.time_history(t, x)\n", " disp_plot, _ = plt.plot(time, xc.T[:, 0], t,\n", " x.T[:, 0], '*b', label='Displacement')\n", " vel_plot, _ = plt.plot(time, xc.T[:, 1], 'r',\n", " t, x.T[:, 1], '*r', label='Velocity')\n", " plt.legend(handles=[disp_plot, vel_plot])\n", " plt.xlabel('Time (sec)')\n", " plt.title('Response of Duffing Oscillator at 0.0159 rad/sec')\n", " plt.ylabel('Response')\n", " plt.legend\n", " plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig=plt.figure()\n", "ax=fig.add_subplot(111)\n", "time, xc = ms.time_history(t, x)\n", "disp_plot, _ = ax.plot(time, xc.T[:, 0], t,\n", " x.T[:, 0], '*b', label='Displacement')\n", "vel_plot, _ = ax.plot(time, xc.T[:, 1], 'r',\n", " t, x.T[:, 1], '*r', label='Velocity')\n", "ax.legend(handles=[disp_plot, vel_plot])\n", "ax.set_xlabel('Time (sec)')\n", "ax.set_title('Response of Duffing Oscillator at 0.0159 rad/sec')\n", "ax.set_ylabel('Response')\n", "ax.legend\n", "ax.grid(True)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "scrolled": true, "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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DB7+ezts+UZ+LjgzEW3fGorC0Gr96dyOqahuMDomIiHoJk1KyyvGKGtz+1gY0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\niYmM4GfXDeemUX2J0LmjYUuhVERE5Ch9usXzwh2jeHfrPh5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DB7+ezts+UZ+LjgzEW3fGorC0Gr96dyOqahuMDomIiHoJk1KyyvGKGtz+1gY0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\niYmM4GfXDeemUX2J0LmjYUuhVERE5Ch9usXzwh2jeHfrPh5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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "time, xc = ms.time_history(t, x)\n", "disp_plot, _ = plt.plot(time, xc.T[:, 0], t,\n", " x.T[:, 0], '*b', label='Displacement')\n", "vel_plot, _ = plt.plot(time, xc.T[:, 1], 'r',\n", " t, x.T[:, 1], '*r', label='Velocity')\n", "plt.legend(handles=[disp_plot, vel_plot])\n", "plt.xlabel('Time (sec)')\n", "plt.title('Response of Duffing Oscillator at 0.0159 rad/sec')\n", "plt.ylabel('Response')\n", "plt.legend\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "omega = np.arange(0, 3, 1 / 200) + 1 / 200\n", "amp = sp.zeros_like(omega)\n", "amp[:] = np.nan\n", "t, x, e, amps, phases = ms.hb_time(duff_osc_ss, num_variables=2,\n", " omega=1 / 200, eqform='first_order', num_harmonics=1)\n", "for i, freq in enumerate(omega):\n", " # Here we try to obtain solutions, but if they don't work,\n", " # we ignore them by inserting `np.nan` values.\n", " x = x - sp.average(x)\n", " try:\n", " t, x, e, amps, phases =\n", " ms.hb_time(duff_osc_ss, x0=x,\n", " omega=freq, eqform='first_order', num_harmonics=1)\n", " amp[i] = amps[0]\n", " except:\n", " amp[i] = np.nan\n", " if np.isnan(amp[i]):\n", " break\n", "plt.plot(omega, amp)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Let's sweep through driving frequencies to find a frequency response function" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "hide_input": false, "scrolled": true, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "omegal = np.arange(3, .03, -1 / 200) + 1 / 200\n", "ampl = sp.zeros_like(omegal)\n", "ampl[:] = np.nan\n", "t, x, e, amps, phases = ms.hb_time(duff_osc_ss, num_variables=2,\n", " omega=3, eqform='first_order', num_harmonics=1)\n", "for i, freq in enumerate(omegal):\n", " # Here we try to obtain solutions, but if they don't work,\n", " # we ignore them by inserting `np.nan` values.\n", " x = x - np.average(x)\n", " try:\n", " t, x, e, amps, phases = ms.hb_time(duff_osc_ss, x0=x,\n", " omega=freq, eqform='first_order', num_harmonics=1)\n", " ampl[i] = amps[0]\n", " except:\n", " ampl[i] = np.nan\n", " if np.isnan(ampl[i]):\n", " break" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide_input": true, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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hBpOb9ikpkYinxEREJMTsO1nLXY9v5XVXBVdlpPLQp2YzIXUwGzfuD3ZoIn7X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\nwUcuvIAf584mbVhCsMMSETk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(omega,amp, label='Up sweep')\n", "plt.plot(omegal,ampl, label='Down sweep')\n", "plt.legend()\n", "plt.title('Amplitude versus frequency for Duffing Oscillator')\n", "plt.xlabel('Driving frequency $\\\\omega$')\n", "plt.ylabel('Amplitude')\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Two degree of freedom system\n", "\n", "$$\\begin{bmatrix}1&0\\\\0&1\\end{bmatrix}\\begin{bmatrix}\\ddot{x}_1\\\\ \\ddot{x}_2\\end{bmatrix}+\\begin{bmatrix}2&-1 \\\\-1&2\\end{bmatrix}\\begin{bmatrix}{x}_1\\\\{x}_2\\end{bmatrix}+\\begin{bmatrix}\\alpha x_{1}^{3}\\\\0\\end{bmatrix}=\\begin{bmatrix}0 \\\\A \\sin(\\omega t)\\end{bmatrix}$$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "code_folding": [], "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "def two_dof_demo(x, params):\n", " omega = params['omega']\n", " t = params['cur_time']\n", " force_amplitude = params['force_amplitude']\n", " alpha = params['alpha']\n", " # The following could call an external code to obtain the state derivatives\n", " xd = np.array([[x[1]],\n", " [-2 * x[0] - alpha * x[0]**3 + x[2]],\n", " [x[3]],\n", " [-2 * x[2] + x[0]]] + force_amplitude * np.sin(omega * t))\n", " return xd" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Let's find a response. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "scrolled": false, "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "array([0.86696762, 0.89484597, 0.99030411, 1.04097851])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parameters = {'force_amplitude': 0.2}\n", "parameters['alpha'] = 0.4\n", "t, x, e, amps, phases = ms.hb_time(two_dof_demo, num_variables=4,\n", " omega=1.2, eqform='first_order', params=parameters)\n", "amps" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Or a parametric study of response amplitude versus nonlinearity." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "alpha = np.linspace(-1, .45, 2000)\n", "amp = np.zeros_like(alpha)\n", "for i, alphai in enumerate(alpha):\n", " parameters['alpha'] = alphai\n", " t, x, e, amps, phases = ms.hb_time(two_dof_demo, num_variables=4, omega=1.2,\n", " eqform='first_order', params=parameters)\n", " amp[i] = amps[0]" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "hide_input": true, "scrolled": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(alpha,amp)\n", "plt.title('Amplitude of $x_1$ versus $\\\\alpha$')\n", "plt.ylabel('Amplitude of $x_1$')\n", "plt.xlabel('$\\\\alpha$')\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true, "slideshow": { "slide_type": "slide" } }, "source": [ "### Two degree of freedom system with Coulomb Damping\n", "\n", "$$\\begin{bmatrix}1&0\\\\0&1\\end{bmatrix}\\begin{bmatrix}\\ddot{x}_1\\\\ \\ddot{x}_2\\end{bmatrix}+\\begin{bmatrix}2&-1 \\\\-1&2\\end{bmatrix}\\begin{bmatrix}{x}_1\\\\{x}_2\\end{bmatrix}+\\begin{bmatrix}\\mu |\\dot{x}|_{1}\\\\0\\end{bmatrix}=\\begin{bmatrix}0 \\\\A \\sin(\\omega t)\\end{bmatrix}$$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "hidden": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "def two_dof_coulomb(x, params):\n", " omega = params['omega']\n", " t = params['cur_time']\n", " force_amplitude = params['force_amplitude']\n", " mu = params['mu']\n", " # The following could call an external code to obtain the state derivatives\n", " xd = np.array([[x[1]],\n", " [-2 * x[0] - mu * np.abs(x[1]) + x[2]],\n", " [x[3]],\n", " [-2 * x[2] + x[0]]] + force_amplitude * np.sin(omega * t))\n", " return xd" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "hidden": true, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "text/plain": [ "array([0.68916938, 0.68228248, 0.67299991, 0.66065019])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parameters = {'force_amplitude': 0.2}\n", "parameters['mu'] = 0.1\n", "t, x, e, amps, phases = ms.hb_time(two_dof_coulomb, num_variables=4,\n", " omega=1.2, eqform='first_order', params=parameters)\n", "amps" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "hidden": true, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "mu = np.linspace(0, 1.0, 200)\n", "amp = np.zeros_like(mu)\n", "for i, mui in enumerate(mu):\n", " parameters['mu'] = mui\n", " t, x, e, amps, phases = ms.hb_time(two_dof_coulomb, num_variables=4, omega=1.2,\n", " eqform='first_order', num_harmonics=3, params=parameters)\n", " amp[i] = amps[0]" ] }, { "cell_type": "markdown", "metadata": { "hidden": true, "slideshow": { "slide_type": "slide" } }, "source": [ "#### Too much Coulomb friction can increase the response. \n", "* Did you know that? \n", "* This damping shifted resonance. " ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "hidden": true, "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(mu,amp)\n", "plt.title('Amplitude of $x_1$ versus $\\\\mu$')\n", "plt.ylabel('Amplitude of $x_1$')\n", "plt.xlabel('$\\\\mu$')\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### But can I solve an equation in one line? Yes!!!\n", "\n", "Damped Duffing oscillator in one command." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "1.4779630014433971" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "out = ms.hb_time(lambda x, v,\n", " params: np.array([[-x - .1 * x**3 - .1 * v + 1 *\n", " sin(params['omega'] * params['cur_time'])]]),\n", " num_variables=1, omega=.7, num_harmonics=1)\n", "out[3][0]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "OK - that's a bit obtuse. I wouldn't do that normally, but Mousai can. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## How to get this?\n", "\n", "* Install Scientific Python from [SciPy.org](https://www.scipy.org/install.html)\n", " * AFRL: See your tech support to get the Enthought distribution installed\n", "* See the Mousai [documents for](https://josephcslater.github.io/mousai/index.html) installation instructions\n", " * `pip install mousai`\n", " * AFRL: Talk to me- install is easy if I send you the files.\n", "* See [Mousai on GitHub](https://github.com/josephcslater/mousai) (https://github.com/josephcslater/mousai)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Conclusions\n", "\n", "* Nonlinear frequency solutions are within reach of undergraduates\n", "* Installation is trivial\n", "* Already in use (GitHub logs indicate dozens of users)\n", "* Custom special case and proprietary solvers such as BDamper can be replaced for free\n", "* Research potential is about to be unleashed" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Future\n", "\n", "* Add time-averaging method\n", " * currently requires high number of harmonics for non-smooth systems\n", "* Add masking of known harmonics (average is often fixed and known)\n", "* Automated sweep control\n", "* Branch following\n", "* Condense the one-line method\n", "* Evaluate on large scale problems\n", " * Currently attempting to hook to ANSYS\n", "* Parallelize \n", "* Leverage CUDA" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Slideshow", "hide_input": false, "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": "3.7.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "livereveal": { "theme": "sky", "transition": "zoom" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": { "height": "646px", "left": "0px", "right": "1145px", "top": "90px", "width": "165px" }, "toc_section_display": "block", "toc_window_display": false }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "position": { "height": "444px", "left": "890px", "right": "20px", "top": "120px", "width": "388px" }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }