{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# From multiple degree-of-freedom to distributed systems: linear strings and sound synthesis \n", "\n", "![](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/w.png)\n", "\n", "### Alberto Torin\n", "\n", "A.Torin@ed.ac.uk\n", "\n", "----\n", "\n", "![](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/AAG_Logo.jpg)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "% Test sound\n", "DT = 2; % sound duration (in s)\n", "t = (0:DT*44100)/44100;\n", "y = sin(2*pi*t*440);\n", "soundsc(y , 44100 )" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "%plot -s 1000,400" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Outline\n", "\n", "---\n", "#### Multiple degree-of-freedom systems\n", "- Equations of motion\n", "- Simple example\n", "- Normal modes and frequencies\n", "---\n", "#### Sound synthesis applications\n", "- Modal approach\n", "- Finite difference approach" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Multiple degree-of-freedom systems" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Mass-spring system with N DOFs\n", "\n", "![](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/w.png)\n", "Consider an array of $N$ masses connected by $N+1$ springs, as in the following figure.\n", "\n", "![](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/masses.png)\n", "\n", "We wish to calculate the equation of motion of the system and do some experiments with it." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Deriving the equations of motion\n", "\n", "![](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/w.png)\n", "Elegant approach by __Prof. Gilbert Strang__, available online at this link:\n", "\n", "http://www.courses.com/massachusetts-institute-of-technology/computational-science-and-engineering-i/2" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Start from the individual __positions of the masses__, link those to the __elongations of the springs__, which in turn give rise to __forces__ determined by Hooke's law. Then, relate these to the __total force__ acting on each mass and eventually to their __acceleration__. \n", "\n", "Here's a diagram:\n", "\n", "
$$\\vec{u} \\rightarrow \\vec{e} \\rightarrow \\vec{f} \\rightarrow \\vec{F} \\rightarrow \\ddot{\\vec{u}}$$
\n", "\n", "Four steps, where each arrow is actually a matrix..." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "To start, consider 4 masses and 5 springs, but the argument can easily be generalised.\n", "\n", "![Array of 4 masses and 5 springs](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/4masses.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$${\\vec{u} \\rightarrow \\vec{e}} \\rightarrow \\vec{f} \\rightarrow \\vec{F} \\rightarrow \\ddot{\\vec{u}}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### 1. Elongations of the springs, $\\vec{u} \\rightarrow \\vec{e}$\n", "\n", "![](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/masses_eu.png)\n", "\n", "- $e_1 = u_1$\n", "- $e_2 = u_2 - u_1$\n", "- $\\dots$\n", "- $e_5 = -u_4$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### 1. Elongations of the springs, $\\vec{u} \\rightarrow \\vec{e}$\n", "\n", "Putting everything in matrix form, one can write:\n", "\n", "$$ \\left[\\begin{array}{c} e_1\\\\ \n", "e_2 \\\\ \n", "e_3 \\\\\n", "e_4 \\\\\n", "e_5 \\end{array} \\right] =\n", "\\left[\\begin{array}{cccc} 1 & 0 & 0 & 0\\\\ \n", "-1 & 1 & 0 & 0 \\\\ \n", "0 & -1 & 1 & 0 \\\\\n", "0 & 0 & -1 & 1\\\\\n", "0 & 0 & 0 & -1\\end{array} \\right] \\left[\\begin{array}{c} u_1\\\\ \n", "u_2 \\\\ \n", "u_3 \\\\\n", "u_4 \\end{array} \\right] \\quad \\Longrightarrow \\quad \\vec{e} = A \\vec{u}, $$\n", "\n", "where the matrix $A$ is rectangular (5x4). " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### 2. Hooke's law, $\\vec{e} \\rightarrow \\vec{f}$\n", "\n", "Relate the elongations to the forces acting on the masses using Hooke's law: for each elongation $e_j$, a recall force $f_j$ proportional to $e_j$ is generated. Mathematically, \n", "\n", "$$f_j = - k_j e_j, $$\n", "\n", "where $k_j$ is the stiffness constant of the $j$-th spring. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### 2. Hooke's law, $\\vec{e} \\rightarrow \\vec{f}$\n", "\n", "In matrix form, this becomes\n", "\n", "$$\\left[\\begin{array}{c} f_1\\\\ \n", "f_2 \\\\ \n", "f_3 \\\\\n", "f_4 \\\\\n", "f_5 \\end{array} \\right] = - \\left[\\begin{array}{ccccc}\n", "k_1 & 0 & 0 & 0 & 0 \\\\ \n", "0 & k_2 & 1 & 0 & 0 \\\\\n", "0 & 0 & k_3 & 0 & 0 \\\\\n", "0 & 0 & 0 & k_4 & 0 \\\\\n", "0 & 0 & 0 & 0 & k_5 \\\\\n", "\\end{array} \\right] \\left[\\begin{array}{c} e_1\\\\ \n", "e_2 \\\\ \n", "e_3 \\\\\n", "e_4 \\\\\n", "e_5 \\end{array} \\right] \\quad \\Longrightarrow \\quad \\vec{f} = -C\\, \\vec{e}\n", "$$\n", "\n", "where $C$ is the diagonal square matrix (5x5) of the stiffness coefficients. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### 3. Resultant force, $\\,\\vec{f} \\rightarrow \\vec{F}$\n", "\n", "![](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/masses_fF.png)\n", "\n", "Calculate the total forces by summing the vectors of the individual spring forces acting on each mass. \n", "\n", "- $F_1 = f_1 - f_2 $\n", "- $F_2 = f_2 - f_3 $\n", "- $\\dots$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### 3. Resultant force, $\\,\\vec{f} \\rightarrow \\vec{F}$\n", "\n", "You can easily see where this is going once we move to matrix notation:\n", "\n", "$$\\left[\\begin{array}{c} F_1\\\\ \n", "F_2 \\\\ \n", "F_3 \\\\\n", "F_4 \\end{array} \\right] = \\left[\\begin{array}{ccccc} 1 & -1 & 0 & 0 & 0\\\\ \n", "0 & 1 & -1 & 0 & 0 \\\\ \n", "0 & 0 & 1 & -1 & 0 \\\\\n", "0 & 0 & 0 & 1 & -1 \\end{array} \\right] \\, \\left[\\begin{array}{c} f_1\\\\ \n", "f_2 \\\\ \n", "f_3 \\\\\n", "f_4 \\\\\n", "f_5 \\end{array} \\right] \\quad \\Longrightarrow \\quad \\vec{F}= A^T \\vec{f} .$$\n", "\n", "The interesting fact here is that the matrix we obtain is exactly the transpose of the elongation matrix $A$!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### 4. Newton's law, $\\,\\vec{F} \\rightarrow \\ddot{\\vec{u}}$\n", "\n", "Each resultant force $F_j$ can be related to the acceleration $\\ddot{u}_j$ of the $j$-th mass via Newton's second law,\n", "\n", "$$F_j = m_j \\ddot{u}_j. $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### 4. Newton's law, $\\,\\vec{F} \\rightarrow \\ddot{\\vec{u}}$\n", "\n", "In matrix form\n", "\n", "$$ \\left[\\begin{array}{c} F_1\\\\ \n", "F_2 \\\\ \n", "F_3 \\\\\n", "F_4 \\end{array} \\right] = \\left[\\begin{array}{cccc}\n", "m_1 & 0 & 0 & 0 \\\\ \n", "0 & m_2 & 1 & 0 \\\\\n", "0 & 0 & m_3 & 0 \\\\\n", "0 & 0 & 0 & m_4\n", "\\end{array} \\right] \\left[\\begin{array}{c} \\ddot{u}_1\\\\ \n", "\\ddot{u}_2 \\\\ \n", "\\ddot{u}_3 \\\\\n", "\\ddot{u}_4 \\end{array} \\right] \\quad \\Longrightarrow \\quad \\vec{F} = M \\ddot{\\vec{u}}. $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Putting it all together, ${\\vec{u} \\rightarrow \\vec{e}} \\rightarrow \\vec{f} \\rightarrow \\vec{F} \\rightarrow \\ddot{\\vec{u}}$\n", "\n", "Combine all the previous steps backwards to get the equations of motion: \n", "\n", "$$M \\ddot{\\vec{u}} = \\vec{F} = A^T \\vec{f} = -A^T C \\, \\vec{e} = -A^T C\\, A\\, \\vec{u} .$$\n", "\n", "We can rewrite this in a more familiar form as\n", "\n", "
$$ M \\ddot{\\vec{u}} = -K \\vec{u}, \\qquad K \\equiv A^T C A .$$
" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## A simple example\n", "\n", "![](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/w.png)\n", "Suppose now that all the masses are equal as well as all springs. The above equation simplifies to\n", "\n", "$$ \\ddot{\\vec{u}} = -\\omega^2 A^T A \\vec{u}, \\qquad \\omega^2 = k/m .$$\n", "\n", "So, accelerations and positions are related by the symmetric matrix $A^T A$... but how does this matrix look like?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### $A$ and $A^T$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "\n", "$$ A = \\left[\\begin{array}{cccc} 1 & 0 & 0 & 0\\\\ \n", "-1 & 1 & 0 & 0 \\\\ \n", "0 & -1 & 1 & 0 \\\\\n", "0 & 0 & -1 & 1\\\\\n", "0 & 0 & 0 & -1\\end{array} \\right], \\quad\n", "A^T = \\left[\\begin{array}{ccccc} 1 & -1 & 0 & 0 & 0\\\\ \n", "0 & 1 & -1 & 0 & 0 \\\\ \n", "0 & 0 & 1 & -1 & 0 \\\\\n", "0 & 0 & 0 & 1 & -1 \\end{array} \\right] $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Let's do the math in Matlab" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "A =\n", "\n", " 1 0 0 0\n", " -1 1 0 0\n", " 0 -1 1 0\n", " 0 0 -1 1\n", " 0 0 0 -1" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = [1 0 0 0; -1 1 0 0; 0 -1 1 0; 0 0 -1 1; 0 0 0 -1]" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/plain": [ "AT =\n", "\n", " 1 -1 0 0 0\n", " 0 1 -1 0 0\n", " 0 0 1 -1 0\n", " 0 0 0 1 -1" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "AT = A'" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "D =\n", "\n", " 2 -1 0 0\n", " -1 2 -1 0\n", " 0 -1 2 -1\n", " 0 0 -1 2" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "D = AT * A" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The product of the two matrices $A^T A$ is:\n", "\n", "$$ D = \\left[\\begin{array}{cccc} 2 & -1 & 0 & 0\\\\ \n", "-1 & 2 & -1 & 0 \\\\ \n", "0 & -1 & 2 & -1 \\\\\n", "0 & 0 & -1 & 2 \\end{array} \\right]$$\n", "\n", "The matrix $D$, or better its negative version, is particularly important in finite difference applications, as we will see shortly. For the moment, let's investigate the eigenvalues and eigenvectors." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Eigenvalues and eigenvectors\n", "\n", "![](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/w.png)\n", "Suppose we know that a solution of $\\ddot{\\vec{u}} = -\\omega^2 D \\vec{u}$ can be written in this form:\n", "\n", "$$ \\vec{u}(t) = \\vec{U} \\sin(\\Omega t + \\phi),$$\n", "\n", "where $\\vec{U}$ is some constant vector, $\\Omega$ a non-negative frequency and $\\phi$ the phase. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Then, the differential equation becomes an eigenvector problem, \n", "\n", "
$$\\Omega^2 \\vec{U} = \\omega^2 D \\vec{U}.$$
" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Do the calculations in Matlab" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "V =\n", "\n", " 0.3717 -0.6015 -0.6015 -0.3717\n", " 0.6015 -0.3717 0.3717 0.6015\n", " 0.6015 0.3717 0.3717 -0.6015\n", " 0.3717 0.6015 -0.6015 0.3717\n", "\n", "\n", "E =\n", "\n", " 0.3820 0 0 0\n", " 0 1.3820 0 0\n", " 0 0 2.6180 0\n", " 0 0 0 3.6180" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[V,E] = eig(D)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Add extra immobile masses at the ends\n", "\n", "Imagine that we have two extra masses, $m_0$ and $m_5$, at the two ends of the system, held fixed by some invisible agent. \n", "\n", "These correspond to the boundary conditions that we are implicitly applying to the array of masses.\n", "\n", "![](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/fixed_masses.png)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "V =\n", "\n", " 0 0 0 0\n", " 0.3717 -0.6015 -0.6015 -0.3717\n", " 0.6015 -0.3717 0.3717 0.6015\n", " 0.6015 0.3717 0.3717 -0.6015\n", " 0.3717 0.6015 -0.6015 0.3717\n", " 0 0 0 0" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "V = [zeros(1,4); V; zeros(1,4)]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Plot the modal shapes" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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y8vKioqJTp05ZLJbIyMgHHnjA+V0KvslqtX7xxRcnT548e/ZseHh4VFTU/Pnz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\nTO/evR02O3v2rPXHW6b0er3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for II=1:4\n", "subplot(2,2,II)\n", "plot(0:5, V(:,II), '.k', 'markersize', 22)\n", "title(['Mode n. ', num2str(II, '%d')])\n", "xlim([0, 5])\n", "end" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The modes of this system look suspiciously similar to those of a linear string... Let's see what happens when we increase the number of masses.\n", "\n", "First, however, we need a way to generalise the creation of the matrix $D$ to $N$ masses..." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Matlab function that creates $D$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "createTridiag = \n", "\n", " @(N)(full(spdiags([-ones(N,1),2*ones(N,1),-ones(N,1)],-1:1,N,N)))" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "createTridiag = @(N)(full(spdiags(...\n", " [-ones(N,1), 2*ones(N,1), -ones(N,1)], -1:1, N, N)))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Test with N=10" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "D10 =\n", "\n", " 2 -1 0 0 0 0 0 0 0 0\n", " -1 2 -1 0 0 0 0 0 0 0\n", " 0 -1 2 -1 0 0 0 0 0 0\n", " 0 0 -1 2 -1 0 0 0 0 0\n", " 0 0 0 -1 2 -1 0 0 0 0\n", " 0 0 0 0 -1 2 -1 0 0 0\n", " 0 0 0 0 0 -1 2 -1 0 0\n", " 0 0 0 0 0 0 -1 2 -1 0\n", " 0 0 0 0 0 0 0 -1 2 -1\n", " 0 0 0 0 0 0 0 0 -1 2" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N = 10;\n", "D10 = createTridiag(N)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Array with 10 DOFs\n", "\n", "Create the eigenvectors and add the fixed masses." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "[V10,E10] = eig(D10);\n", "V10 = [zeros(1,N); V10; zeros(1,N)];" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "... then plot the modes!" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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gzLj9AO1iNm6gOwjc0QWKolit1piYGIvFIitfRVEsFouMn6iOEVLcfoCm8ZUb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\nq6tbs2aN0+lcv359Zmbm6dO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SpI7W9w6Ds2fPHjp06MyZMykpKSkpKSrmBBpFPQmh93oS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\nte+7KRuWTCYTLTRawaX0jcIeME6dRlEnoKso7D4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for II=1:4\n", "subplot(2,2,II)\n", "plot(0:N+1, V10(:,II), '.k', 'markersize', 22)\n", "title(['Mode n. ', num2str(II, '%d')])\n", "xlim([0, N+1])\n", "end" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Array with 50 DOFs\n", "\n", "Again, create the matrix $D$, calculate the eigenvectors and add the fixed masses." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "N = 50;\n", "D50 = createTridiag(N);\n", "[V50,E50] = eig(D50);\n", "V50 = [zeros(1,N); V50; zeros(1,N)];" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "... then plot the modes!" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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0pgA65fF4RD2+1HnEqvBkj7Cnn37aYrGsWbOGT2lubrbZbCNGjDh69GiQL2LT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\n8mdn41Hp9ARTwsE+bWy6qbJd9igejxf0TZPJZF1dnamRCldOcemZgoM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for II=1:4\n", "subplot(2,2,II)\n", "plot(0:N+1, V50(:,II), '.k', 'markersize', 20)\n", "title(['Mode n. ', num2str(II, '%d')])\n", "xlim([0, N+1])\n", "end" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Results\n", "\n", "![](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/w.png)\n", "The modal shapes are sinusoids with a period that is an integer multiple of $L/2$, where $L$ is the string length.\n", "\n", "\n", "![](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/w.png)\n", "### These are the modes of a linear string!\n", "----\n", "\n", "_Confirm this by math calculation..._\n", "\n", "See http://www.physics.usu.edu/riffe/3750/lecture_notes.htm, Lecture 5, for some help!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Important comment\n", "\n", "\n", "For a string, the vibration is transverse to the length of the string. In the case of the mass-spring system, the vibrations are along the chain of oscillators, as the next videos show." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "scrolled": true, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Frequencies of vibration\n", "\n", "![](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/w.png)\n", "From the eigenvalue equation $\\, \\Omega^2 \\vec{U} = \\omega^2 D \\vec{U}, \\,$ the frequencies are given by\n", "\n", "
$$\\frac{\\Omega}{2\\pi} = \\frac{\\omega}{2\\pi} \\sqrt{\\text{eig}(D)}.$$
\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "#### Frequencies of a string\n", "\n", "They are integer multiples of the frequency of the first mode... think of a guitar string!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Find eigenvalues for N=30 and N=50" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "[V30, E30] = eig(createTridiag(30));\n", "[V50, E50] = eig(createTridiag(50));" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "#### ... then normalise and sqrt" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "ev30 = diag(E30); ev50 = diag(E50);\n", "y30 = sqrt(ev30/ev30(1)); y50 = sqrt(ev50/ev50(1));" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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WNJw5rr0Ghm0JDcw81XAuh4g0rWYYZHQA0LCdDrlgWXCbOkN98MEHn3zySWho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\neHIXEQBAE6Fw56VHt64zLwLOF3QyEuzxsiQi4ZMbnAYFAKCO/ObMvW0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "subplot(1,2,1), plot(y30,'.','markersize',20), hold on\n", "plot(y50,'.','markersize',20), plot(1:50, 'k'), xlim([0, 50]), hold off\n", "ylabel('\\Omega/\\Omega_1'), xlabel('Mode')\n", "legend('N=30', 'N=50', 'String', 'location', 'best')\n", "subplot(1,2,2), plot(y30,'.','markersize',20), hold on\n", "plot(y50,'.','markersize',20), plot(1:50, 'k'), xlim([0, 15]), hold off\n", "xlabel('Mode'), legend('N=30', 'N=50', 'String', 'location', 'best')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\Omega = \\omega \\sqrt{\\text{eig}(D)}, \\qquad \\Omega_1 = \\text{ fundamental}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Key points\n", "\n", "- Modal shapes are the same as those of a string (sinusoidal shapes)\n", "\n", "- Frequencies of the oscillator system are \"detuned\" w.r.t. those of a string (difference dispersion relation)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Sound synthesis applications" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Sound synthesis\n", "- Diverse range of techniques (especially digital) to create sounds\n", " - Additive synthesis, Wavetable synthesis, AM and FM synthesis, etc.\n", " - Physical modelling" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Physical modelling\n", "- Physical description of the instrument underlying the numerical algorithm\n", " - Lumped mass-spring networks (CORDIS-ANIMA by Cadoz et al.)\n", " - Modal synthesis (MOSAIC-Modalys at IRCAM, Paris)\n", " - Digital waveguides (J. Smith III, Stanford)\n", " - Time stepping methods" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Modal approach" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Back to the mass-spring system" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "The global solution to the equations of motion can be written as a linear combination of the solutions to the $N$ eigenvalue problems for the system. \n", "\n", "$$ \\vec{u}(t) = \\sum_1^N A_j \\, \\vec{U_j} \\, sin(\\Omega_j t + \\phi_j) $$ \n", "\n", "It requires, therefore, $N$ amplitudes and $N$ phases to be specified, one for each of the $N$ eigenmodes for the system. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Create the eigenmodes" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": true }, "outputs": [], "source": [ "[V50, E50] = eig(createTridiag(50));\n", "V50 = [zeros(1,50); V50; zeros(1,50) ];" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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Lnd3Y2Nja2kpvOoCezh5VsCmler3ecDhst9utVqsgL/laZvDS0tJrr7326quv\nFuTXR8Zp+/P8etPoFhZCdLtd9jAyjsAdmZNYLXR0dEQVP9ISBEGtVtMGi1wwbZalFvlqIFOCIFhd\nXWV/Iq9IlUHmJFYLJbaRBxajIPWmM5pMJrR/R5axP5FjBO4AcIGC1JsCeZVYRw7YiMAdmWPWt0kp\n6eeCRRqPx4PBIGy2Imh4/lmO45h5wJSlYgHCu3I8Hp/zM9Vq1dyfhb1bkT8E7sgcKeWDBw+ivy4t\nLT18+DDF+aBoOp3O8vLy5ubm5uZmlMwdL26TUha8RcuDBw9KpVL015WVlSJfDSyAUsp13fCuXF5e\nNuug4rQaUw6KQZ5QnIrMMYtTpZR7e3sUp2IBzO0XL2sLguDw8LDRaBTkzMezmC1jKf7DXJn10Be+\neeZuRS4RuCNzEtvIb21tkS2DBTDjAyHE8+fPHcdJYzpZNJlMKpWKNiilHI1GqcwHube9vX3//n1t\nkPeKKCZSZQAAAAALELgjcxKriJrN5uJnggIyT5+QUvJxe5zjOGapLqd2YH4Sj3Wi3hTFROCOzDEL\niTY2NkhwxzyETdHjfdG73a4WlXJeikm7JktLS48ePTIz3IDz+b7vvnTO/qlWq1pWjJSSelMUEznu\nyKKz2sunNiHk0VnbLGyBHg6acTxCSqnXX399f38/Pljww3ZwKWYh+Pn7x/f9sD1fq9Vim6GwCNyR\nOYPBYHNzUxskIMDNGo/Hy8vL2iDlbpdiFvJSoorZsX+AKyBVBnYIP2gBbsrBwUHaU7DbdDo1j99R\nSk2n0zSmgzxg/wAXInAHAFxauVw2k4iklOVyOY3pIA/YP8CFSJVBFmlfodbr9b29PVKNcR1ROnu7\n3Q73kvlN/Wg0YpvNzsxRfvDgwX//93+3Wq3oIqOYlFLD4TD881lZjuc3OwOQ7AWQPXt7e/GG6o7j\njEajtCcFi8VDByllv99/8eLFaDSKxqNBXIrneWGAXq/X4/dsmKyc9uyQjn6/H3/b5nnehT8ZnhKz\nyEkCluITd2QRDdVxg8wP9qSUe3t74Rmjk8lECMFJ7VcWXsA333zzgw8+iI9zzxaW+V3W+acLcA8C\nsyPHHVkUfcca8X0/fLgDl2VWNiulouJUx3GIGK4jvIBmsS/3bDFtb2+bVcvnny7APQjMjsAdAAAA\nsACBO7KItvO4pvihcmZrdClls9lc7Ixy7px7lgP+cmk6nSaubKPRMOuSzXsQwNUQuCOLtHaVS0tL\nDx8+TG86sEnYRP3WrVuu64ap7Z7nafm13W43THDHTdHu2bANbXwtzmloD7sopTqdzq1bt27dutXp\ndLTEmGq12u124yPmDQjgyihORUZtbm4OBoP4CEf14UJKKdd14yNRiWTUL10L6HtemQAAGLlJREFU\nMXGDwoscHgc5HA4v1dAettBqT8M3ado9FR4HGW4GFh24QQTuyKIgCGq1mjbIIRW4kHkekRDi+Pi4\nWq2mMZ1Co6F9Lg0Gg83NTW2Qt2TAwpAqgyw6PDw0B82jZgBN4iZJ3E5YPBra59X5h8YAuEEE7sii\nRqNhDprVb4AmcZMkbicsHg3t84raU2BhCNyRRdVq1fziVSt4AsTL5kpRhoyZv+55HnkyqTBv2Ggk\nrG5MzGtCpkT3V5T1tLGxoT2cpZR8qgIsTsqdW4Gzra2txfcqDbGh0QKIcIeETdRD7Jl0xRva9/v9\naJD7OvvMwwCiFRyNRp7nRbfYaDRKc6JAwVCciowaj8fLy8vaICVQiLBDbDGdTqMMmSAIVldXtaJV\nVi2DzO9DpJSPHz/m+ysgXaTKIKPMDuqCEijEsENsEc9rPzw81KJ2waplklnnrZSizhtIHYE7AAD4\nDOq8gWwicEdGNZtN+mbDNJlMJpOJYIfYqdFoXLhqk5cWNy28FF1881aSUpInA6SOwB0ZVa/Xtb70\nX/7CF1KcD1LzMrPC933XdSuVSqVScV339PRUO0OGVOnsq1ar2qp5nhetWnjaTLjEd+7cOfPMGSPZ\nBjfC9/3/+9Wvhtd/d3d3Y2Mj+qewPWqKcwMQojgVmfaNb3xja2urLcQbQnhCDIVYevBg7R/+IeVp\nYTGGQ/GjHwnfF+325NVXK2+/Hf9HKeXe3p54mezebDbjb/OQZePxOHHVzIJI/c1YbEuIN94QvE+7\nOdt//dfB3/2dJ8RQiB8J4Qvhed7f/u3fcn8BmULgjuyaHh5+/6tfTTi8XUrheeKNN4TxnTvyQCnx\nox+Jd97Rh1/GE+rlyNbWVvxDQVgtCIJaraYNep7X7/fP2hI8Cm7Aubfbw08+cb7+9RRmBeAMBO7I\nsFdeOe9fpRQ7O7xg59C5666EWH8ZuxO458n29vb9+/e1QSnlaDTiUTBHXFvAKuS4I6subKkYflCE\nnLlo3aUQ3gKmgYVLPLGk3W7zKJgjri1gGz5xR1a57sUlaFKK0WgRk8HCzLDuSgg3SqJAjmg57mFB\npFxf51EwLzxmAdvwiTsyyfdnOjhCKWF0CYHFZlt3KcTHf/VXRO350+/3+/2+lFJK6Xnezs6OHA55\nFMwLj1nAQnzijkxaX5/1paLdFhxSlhusOzRsifnh2gIWInDH9fR6c/kw5lL/zaQOf7AS6w4NW2J+\nuLZFwDuu3FlKewKwXKsl5tSrcvaPgroJJ0bCVqw7NGyJ+eHa5hvHAeURn7gjk4ZDsb4+00/u7PBR\nUH6w7tBcfksEQXB4eNhoNKrV6lynZj1uN8BCFKcik6Sc9XWCl5O8UEq9/YMfDGf8ada9IC7zKFBK\nua5bq9Xu379fq9U6nc5852Y7HrOAhQjckUlSijfeuPjHOFckR3q93v8bDGY6Mpp1L47LPArW19dV\n7JgU3/f9C88pLzIes4CFSJVBViklXPeCnxmNyOHLh8lkUqlUhBBSiIuPjGbdC2W2R0Hw+c/XajVt\n+DeNV3GWGa7t9Je/LCf1xgKQCj5xR1aFXT/eeccM0ZQQPSFcKYne8kcJ4QrRE0KZ/yaleOcd8eIF\n614sZz8K2BLXddFj9hUhTuv1FCYG4AwE7sgwKUW3K3Z2Tt5//+DznxdCKCE6QrhCvBP2QkdeOI4j\nX4YOSoh3hFgX4odra79JrpVS9PtiNOJoi4J6+SgQ/f45W0Ia0SdPiYvFru3/r1bFZx+zUkrHcVKe\nIYAYUmVgB9/346VmS0tLr7322rvvvmu+VMMuvu/3ej0hRL1e39/fj8Z/0+6e9cXMtKdE4hbyfX93\nd3c4HAohut2u53kLnWK2KaW0OoGwPzFXDMgOAndYw/f973znO0+ePIlGSGC1XafTiZcP1uv1ZrNZ\nKpWEEN1ul6gdlxXG5eGfzS2kRfZCiH6/TyQap5QK30gLIbrd7nA45IoBmULgDmsMBoPNzU1tkFcR\newVBYFYTep7X5xQLzIf2RlHw5v8iruvGP4AXXDEgbeS4w27Rp2uwzuHhoTk4vFQbduAyzN2llJpM\nJmnMxQLT6dQcVEoljgNYDAJ32K3VaqU9BVxRI+mMOaoJgYwol8vmoJQycRzAYhC4wxrNZlPLWK1U\nKr/7u7+b0nRwLePxeH9/3wzTeSeG+ekapxJ5nmeemjIejweDwWAwGI/Hi5paRplXTLtnBy9xrYAF\neQHYYzQamQWL/X4/7XnhcuJlCWEpqhBCSslSYt76/X70DPE8z/wBrWaGPel53llXLH6twtz3lOYI\nFAjFqbCMUso1Wv1RomoR82SP5eXln/70p1/5ylfSmhIKJUpqNz9rNzenlHJvb69e7CZEiVeMSl8g\nFaTKwDKJxYuUqFrEXKyjo6N/+7d/S2UyKCDnJfOfzM2plDo4OFjIvLIr8YpR6QukgsAdAAAAsACB\nOyyTeOoIFY0WSVysZrO5+JkAmtk3J0cimo9iKWXi9xiCywXcHAJ3WEZKaaaz93o9LdsS2dTpdKK+\njJF+v1/wHGJkhOd5ZnGqtjl933dd99atW67ragnxhaI1ppVSmkfQiM9eLp7SwPVRnAor+b7/ne98\n58mTJ/HBxDNnkB1mNdva2to//uM/smrIFN/3w2R3LTYVQiil1tfX481EC97rN7xWrVar3W6bN7J5\ny3OQAHBNBO6wUhAEtVpNGyz4K2jGTSaTSqWiDbJksIsZiQohjo+Pq9VqGtPJtMlkcufOnfibHMHJ\nM8C1kSoDKx0eHpqDiQfOIMtYMuRA4uMIQggtagdwfQTusFKj0TAHE+tWkWUsGXIg8XEEIQRZcMCN\nI3CHlarVqpkoefv2bT7gySzHcdbW1rRBjgOCXcysd8/ztDyZsItTYlJNoTiOY74zTyxgDSmluG7A\nxVLu3Apcg+d52oEPUkpalGfQaDTS3mg5jsNKwUb9fj+M3cMTrrR/1fa5+QNFE79c59zyWq0L1w04\nC8WpsBttt63AMiFnptNpuVzWBsPP2rVBTrsSZ1yuyHg8Xl5e1gY5fwZIRKoM7EbbbSskLlMQBGnM\nBbgBiWFoeIikhgpsccblihwcHJiDiRcTAIE7AAAAYAECd9jNLH5aXl4+q+020mJWpEkpOfoaOZNY\nbK09oyaTCV8JaprNpplNdGHlOlcSxUTgDruZeZBHR0f01s6adrtdKpWiv9br9Z2dnRTnA8yD2VAs\nKs0UQiilXNetVCqVSsV1XY7AitTrde24Hs/zzklw932fK4nCojgVeTAYDL75zW8+f/48PkhNWEaY\nXeLr9fre3h6rg1waj8dh0naz2YyOvTLvAinlzs4Od0Ek8bqZuJIoOD5xR05oUbsQotfrpTITaIbD\nofaR2Hg8pmIPeVWv1zc2NjY2NuLRp3kXKKW4C+ISr5uJK4mCI3AHMF+Jp0NwZAQKhbvgpnDRUHAE\n7siDZrOZ9hRwpsQiM3qmolC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AAgTuAAAAgAUI3AEAAAALELgDAAAAFiBwBwAAACxA4A4A\nAABYgMAdAAAAsACBOwAAAGABAncAAADAAgTuAAAAgAUI3AEAAAALELgDAAAAFiBwBwAAACzwP9tM\nWLO+D2KBAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(V50(:,1), 0:N+1, 'k.', 'markersize', 20), \n", "hold on, plot(V50(20,1), 19, 'r.', 'markersize', 25)\n", "plot(V50(:,2)+0.5, 0:N+1, 'k.', 'markersize', 20), plot(V50(20,2)+0.5, 19, 'r.', 'markersize', 25)\n", "plot(V50(:,3)+1, 0:N+1, 'k.', 'markersize', 20), plot(V50(20,3)+1, 19, 'r.', 'markersize', 25)\n", "plot(V50(:,4)+1.5, 0:N+1, 'k.', 'markersize', 20), plot(V50(20,4)+1.5, 19, 'r.', 'markersize', 25)\n", "plot([-0.3, 1.8], [19, 19], 'r')\n", "axis off" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Sound in Matlab" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "DT = 2; % sound duration (in s)\n", "t = (0:DT*44100)/44100;\n", "y = sin(2*pi*t*440) + sin(2*pi*t*660);\n", "soundsc(y , 44100 )" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### How does the mass-spring system sound like?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Create system matrix $D$ and find the e.values" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [], "source": [ "[V50,E50] = eig(createTridiag(50));\n", "ev50 = sqrt(diag(E50));" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Define $\\omega$, amplitudes and phases" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "omega = 2*pi*440;\n", "A = rand(50,1);\n", "%A = (50:-1:1)'/50;\n", "%A = (((1:50)-25).^2/25^2)';\n", "phi = zeros(50,1);" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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ioqKiwiZ3z8nJEUJMmDDB4VHS0pry8vLm5mbrdqnCTHCwRt5jAAB4iKT4sLQ5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\nCsTUuYKDg8V/t8RpEkOsuiGWcp3Q0NDly5cnJCT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(A, '.', 'markersize', 20)\n", "title('Amplitudes for the various modes')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Select a point and create the oscillators" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": true }, "outputs": [], "source": [ "pt = 23;" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "#### Create amplitudes for each point and individual sounds" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": true, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "% Create the argument of sine function\n", "T = kron(omega*ev50, t) + kron(phi, ones(numel(t),1)');\n", " \n", "Amps = V50(pt, :)'.*A;\n", "snd = sparse(diag(Amps)) * sin(T); " ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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3v6vQzo6Q4oGm4Mw7g0jxQHPBK8saEr1tFJxOYRCJ4XYCTqcgLNDe3n7mzJkv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(snd(1,1:2000))\n", "hold on, plot(snd(2,1:2000))\n", "plot(snd(3,1:2000)), plot(snd(4,1:2000))\n", "legend('1','2','3','4')\n", "title('Oscillation of the first four modes')\n", "hold off" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Plot the final signal" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false, "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "image/png": 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QbgjcGcBc+xT6U9NJxuADSXdgGluBWgJQBh0XJrZeCoWH22JC4M4A5tqnMKkq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\nAAAAYoeM+xSuXr3a3d2dl5eXn58v91oAAAAAQFwI3AEAAAA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(snd(1,1:2000) + snd(2,1:2000) + snd(3,1:2000) + snd(4,1:2000))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Let's play!" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "soundsc(sum(snd,1), 44100)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "## Try the code yourself!\n", "\n", "``MDoF_Modal.m`` $\\,$ available at: https://github.com/atorin/Dynamics3-Lecture" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Finite difference approach" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Discretise time\n", "\n", "$$u(t) \\quad \\longrightarrow \\quad u(nk) = u^n,$$ \n", "\n", "with $n$ integer and $k$ the time step." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Recursions\n", "\n", "Time differentiation becomes recursions: knowing $u^n$ you can calculate $u^{n+1}$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Second difference\n", "$$ \\ddot{u} \\quad \\longrightarrow \\quad \\frac{u^{n+1} - 2 u^n + u^{n-1}}{k^2}$$\n", "\n", "Notice the pattern (1, -2, 1)..." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "### Equation for the mass-spring system" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "
\n", "\n", "$$ M \\frac{\\vec{u}^{ n+1} - 2\\vec{u}^{ n} + \\vec{u}^{ n-1}}{k^2} = - \\omega^2 D \\vec{u}^n$$
" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Try the code yourself!\n", "\n", "``MDoF_FD.m`` $\\,$ available at: https://github.com/atorin/Dynamics3-Lecture" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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33HCD/c9jjjnmxhtvPHjw4Gc/+9kf/ehHGzdufOyxx66++up9+/ZdccUVs2fP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%for II=1:5\n", "MDoF_FD \n", "%pause(rand)\n", "%end" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Conclusions\n", "\n", "- We discussed a general method to find the equations of motion of a mass-spring system" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- We looked at the normal modes and frequencies in the case of large $N$, and compared them with those of a string" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- We had some fun with basic sound synthesis techniques" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Thank you for your attention!\n", "---\n", "![](https://github.com/atorin/Dynamics3-Lecture/raw/master/files/w.png)\n", "\n", "### Alberto Torin\n", "\n", "A.Torin@ed.ac.uk\n", "\n", "Slides and Codes on Github:\n", "http://github.com/atorin/Dynamics3-Lecture" ] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Matlab", "language": "matlab", "name": "matlab_kernel" }, "language_info": { "codemirror_mode": "Octave", "file_extension": ".m", "help_links": [ { "text": "MetaKernel Magics", "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" } ], "mimetype": "text/x-matlab", "name": "octave" } }, "nbformat": 4, "nbformat_minor": 0 }