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Last active May 24, 2018 04:24
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Notebook showing how to calculate the modal vibration of a structure
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Natural Frequency Mode of Vibration for Planar Truss Structures"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Nodes strictly contain x, y coordinates; associated with a unique identifier. Strictly speaking, nodes is a hashmap mapping the unique identifier, to a (x, y) coordinate."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"nodes = {\n",
" 1: (0, 0),\n",
" 2: (1, 0),\n",
" 3: (0, 1),\n",
" 4: (1, 1)\n",
"}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Edges contain a little more information. They include a unique identifier, the two node IDs they connect to."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"edges = {1: (1, 3),\n",
" 2: (2, 4),\n",
" 3: (3, 4),\n",
" 4: (1, 4),\n",
" 5: (2, 3)}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Material properties\n",
"\n",
"For our case, we can assume the material being steel; which has a density of 7.85 g/cm<sup>3</sup> We need to do the unit conversion to kg/m<sup>3</sup> which is 7,850 kg/m<sup>3</sup>"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"E = 400_000_000 # 400 MPa -> 400 MN / m^2\n",
"𝜌 = 7850 # 7.85 g / cm^3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Geometry Properties\n",
"\n",
"While this annalysis would allow us to specify different cross sectional area of beams, we can assume the same beam geometry, or more specifically, cross-sectional area. I came up with the value below by looking up the thickest beam in an old textbook reference of mine"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"A = 0.04361282"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We also need a function to get the lenght of a truss member"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"def calc_length(truss, nodes):\n",
" x1, y1 = nodes[truss[0]]\n",
" x2, y2 = nodes[truss[1]]\n",
" return (x2-x1) ** 2 + (y2-y1) ** 2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that we've defined everything we need to know about the basic geometry and the material properties, we need to construct two matrices, a mass matrix (M) and a stiffmess matrix (K). We initialize these as empty matrices, the size of n_nodes * n_dims x n_nodes * n_dims"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"size = len(nodes) * len(nodes[1]) # figure out how many dimensions we're actually storing in the coordinate system\n",
"\n",
"M = np.zeros((size, size))\n",
"K = np.zeros((size, size))"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"for edge in edges.values():\n",
" L = calc_length(edge, nodes)\n",
" k_constant = E * A / L\n",
" index_x1 = (edge[0] * 2) - 2 \n",
" index_x2 = (edge[1] * 2) - 2\n",
" index_y1 = (edge[0] * 2) - 1\n",
" index_y2 = (edge[1] * 2) - 1\n",
" \n",
" K[index_x1, index_x1] += k_constant\n",
" K[index_x1, index_x2] += -k_constant\n",
" \n",
" K[index_x2, index_x1] += -k_constant\n",
" K[index_x2, index_x2] += k_constant\n",
" \n",
" m_constant = 𝜌 * A * L / 6\n",
" M[index_x1, index_x1] += 2 * m_constant\n",
" M[index_x1, index_x2] += m_constant\n",
" \n",
" M[index_y1, index_y1] += 2 * m_constant\n",
" M[index_y1, index_y2] += m_constant\n",
" \n",
" M[index_x2, index_x1] += m_constant\n",
" M[index_x2, index_x2] += 2*m_constant\n",
" \n",
" M[index_y2, index_y1] += m_constant\n",
" M[index_y2, index_y2] += 2*m_constant"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we apply boundary conditions, or in other words, we say which nodes are fixed to the ground and cannot move, and get rid of those corresponding rows and columns\n",
"\n",
"A standard approximation method is to assume one of two truss's is completely fixed to the ground, and the other has a \"roller\" constrant, meaning it can move side to side, but not up and down"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"# this forces y dislacement of node 2 to be 0\n",
"M = np.delete(M, 3, 0)\n",
"M = np.delete(M, 3, 1)\n",
"\n",
"K = np.delete(K, 3, 0)\n",
"K = np.delete(K, 3, 1)\n",
"\n",
"# this forces y displacement of node 1 to be 0\n",
"M = np.delete(M, 1, 0)\n",
"M = np.delete(M, 1, 1)\n",
"\n",
"K = np.delete(K, 1, 0)\n",
"K = np.delete(K, 1, 1)\n",
"\n",
"# this forces x displacement of node 1 to be 0\n",
"M = np.delete(M, 0, 0)\n",
"M = np.delete(M, 0, 1)\n",
"\n",
"K = np.delete(K, 0, 0)\n",
"K = np.delete(K, 0, 1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we get the eigenvalues and eigenvectors"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"def non_normalized_eigh(A, B):\n",
" B_evalues, B_evectors = np.linalg.eigh(B)\n",
" phi_B_prime = B_evectors @ np.diag(1 / np.sqrt(B_evalues))\n",
" A_prime = phi_B_prime.T @ A @ phi_B_prime\n",
" \n",
" A_prime_evalues, A_prime_evectors = np.linalg.eigh(A_prime)\n",
" \n",
" V = B_evectors @ np.diag(1 / np.sqrt(B_evalues)) @ A_prime_evectors\n",
" L = V.T @ A @ V\n",
" L = np.sort(np.diag(L))\n",
" return L, V"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"L, V = non_normalized_eigh(K, M)\n",
"fn = np.sqrt(L / (2 * np.pi))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's look at our natural frequencies!"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.00000000e+00, 5.30172469e-15, 4.61969640e+01, 1.55978903e+02,\n",
" 1.55978903e+02])"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fn"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that we've got our modes of vibration back, we need to insert the columns of 0s we took out earlier for the constraints"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"V = np.insert(V, 1, 0, axis=0)\n",
"V = np.insert(V, 0, 0, axis=0)\n",
"V = np.insert(V, 0, 0, axis=0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We ignore ~0 Hz natural frequencies"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.00000000e+00, 5.30172469e-15, 4.61969640e+01, 1.55978903e+02,\n",
" 1.55978903e+02])"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fn"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We grab the 3rd natural frequency, which is at 46.2 Hz"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"mode_order = 2\n",
"mode = V[:, mode_order]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we start some basic plotting"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"%matplotlib notebook"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"nodes_x, nodes_y = zip(*nodes.values())\n",
"plt.plot(nodes_x, nodes_y, 'ro')\n",
"\n",
"\n",
"for edge in edges.values():\n",
" x1, y1 = nodes[edge[0]]\n",
" x2, y2 = nodes[edge[1]]\n",
" plt.plot([x1, x2], [y1, y2], 'k-')\n",
"\n",
"nodes_x_nf = V[:, mode_order][::2] + nodes_x\n",
"nodes_y_nf = V[:, mode_order][1::2] + nodes_y\n",
"\n",
"plt.plot(nodes_x_nf, nodes_y_nf, 'bo')\n",
"\n",
"for edge in edges.values():\n",
" x1 = mode[edge[0] * 2 - 2] + nodes[edge[0]][0]\n",
" x2 = mode[edge[1] * 2 - 2] + nodes[edge[1]][0]\n",
" \n",
" y1 = mode[edge[0] * 2 - 1] + nodes[edge[0]][1]\n",
" y2 = mode[edge[1] * 2 - 1] + nodes[edge[1]][1]\n",
" \n",
" plt.plot([x1, x2], [y1, y2], color='gray', linestyle='dashed')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But we want to animate!"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"from matplotlib import animation\n",
"from IPython.display import HTML"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"offset = np.sin(np.linspace(0, 2 * np.pi, num=100, endpoint=False))\n",
"mode_t = np.outer(mode, offset)\n",
"for node_id, (x, y) in nodes.items():\n",
" mode_t[node_id * 2 - 2, :] += x\n",
" mode_t[node_id * 2 - 1, :] += y"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"def animate(i):\n",
" x1, y1, x2, y2, x3, y3, x4, y4 = mode_t[:, i] \n",
" \n",
" edge1.set_data([x1, x3], [y1, y3])\n",
" edge2.set_data([x2, x4], [y2, y4])\n",
" edge3.set_data([x3, x4], [y3, y4])\n",
" edge4.set_data([x1, x4], [y1, y4])\n",
" edge5.set_data([x2, x3], [y2, y3])"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"fig, ax = plt.subplots()\n",
"ax.set_xlim((-0.1, 1.1))\n",
"ax.set_ylim((-0.1, 1.1))\n",
"plt.close()"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"<link rel=\"stylesheet\"\n",
"href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
"css/font-awesome.min.css\">\n",
"<script language=\"javascript\">\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" document.getElementById(this.slider_id).max = this.frames.length - 1;\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src =\n",
" this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" }\n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_forward();\n",
" }, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_reverse();\n",
" }, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<div class=\"animation\" align=\"center\">\n",
" <img id=\"_anim_imgfa6863428f7e42838781d5a9333dd116\">\n",
" <br>\n",
" <input id=\"_anim_sliderfa6863428f7e42838781d5a9333dd116\" type=\"range\" style=\"width:350px\"\n",
" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
" onchange=\"animfa6863428f7e42838781d5a9333dd116.set_frame(parseInt(this.value));\"></input>\n",
" <br>\n",
" <button onclick=\"animfa6863428f7e42838781d5a9333dd116.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
" <button onclick=\"animfa6863428f7e42838781d5a9333dd116.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
" </i></button>\n",
" <button onclick=\"animfa6863428f7e42838781d5a9333dd116.previous_frame()\">\n",
" <i class=\"fa fa-step-backward\"></i></button>\n",
" <button onclick=\"animfa6863428f7e42838781d5a9333dd116.reverse_animation()\">\n",
" <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
" <button onclick=\"animfa6863428f7e42838781d5a9333dd116.pause_animation()\"><i class=\"fa fa-pause\">\n",
" </i></button>\n",
" <button onclick=\"animfa6863428f7e42838781d5a9333dd116.play_animation()\"><i class=\"fa fa-play\"></i>\n",
" </button>\n",
" <button onclick=\"animfa6863428f7e42838781d5a9333dd116.next_frame()\"><i class=\"fa fa-step-forward\">\n",
" </i></button>\n",
" <button onclick=\"animfa6863428f7e42838781d5a9333dd116.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
" </i></button>\n",
" <button onclick=\"animfa6863428f7e42838781d5a9333dd116.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
" <form action=\"#n\" name=\"_anim_loop_selectfa6863428f7e42838781d5a9333dd116\" class=\"anim_control\">\n",
" <input type=\"radio\" name=\"state\"\n",
" value=\"once\" > Once </input>\n",
" <input type=\"radio\" name=\"state\"\n",
" value=\"loop\" checked> Loop </input>\n",
" <input type=\"radio\" name=\"state\"\n",
" value=\"reflect\" > Reflect </input>\n",
" </form>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
" /* Instantiate the Animation class. */\n",
" /* The IDs given should match those used in the template above. */\n",
" (function() {\n",
" var img_id = \"_anim_imgfa6863428f7e42838781d5a9333dd116\";\n",
" var slider_id = \"_anim_sliderfa6863428f7e42838781d5a9333dd116\";\n",
" var loop_select_id = \"_anim_loop_selectfa6863428f7e42838781d5a9333dd116\";\n",
" var frames = new Array(0);\n",
" \n",
" frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbAAAAEgCAYAAADVKCZpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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"IKjgwqKC3c35v/BPjwRFwKZPn+b7eddzznR/T2ifXz/nPOd3ZIIgCCAiIpIYK7EDEBERDQULGBER\\\n",
"SRILGBERSRILGBERSRILGBERSRILGBERSRILGBERSRILGBERSRILGBERSRILGBERSRILGBERSRIL\\\n",
"GBERSRILGBERSRILGBERSRILGBERSRILGBERSRILGBERSRILGBERSRILGBERSRILGBERSRILGBER\\\n",
"SRILGBERSRILGBERSRILGBERSRILGBERSRILGBERSRILGBERSRILGBERSRILGBERSRILGBERSRIL\\\n",
"GBERSRILGBERSRILGBERSRILGBERSZJc7ADDxd7eHm5ubmLHICKSlLq6OrS0tIgdY0AstoC5ubmh\\\n",
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