{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Universidade Federal do Rio Grande do Sul (UFRGS) \n", "Programa de Pós-Graduação em Engenharia Civil (PPGEC) \n", "\n", "# PEC00025: Introduction to Vibration Theory\n", "\n", "\n", "### Class 08 - Vibration analysis in frequency domain\n", "\n", "[1. Frequency preservation theorem](#section_1) \n", "[2. Reological models](#section_2) \n", "[2.1. General linear model](#section_21) \n", "[2.2. The Kevin-Voigt model](#section_22) \n", "[2.3. The Maxwell model](#section_23) \n", "[2.4. The standard model](#section_24) \n", "[3. Equilibrium in frequency domain](#section_3) \n", "[4. Assignment](#section_4) \n", "\n", "---\n", "_Prof. Marcelo M. Rocha, Dr.techn._ [(ORCID)](https://orcid.org/0000-0001-5640-1020) \n", "_Porto Alegre, RS, Brazil_ " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Importing Python modules required for this notebook\n", "# (this cell must be executed with \"shift+enter\" before any other Python cell)\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from MRPy import MRPy\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Frequency preservation theorem <a name=\"section_1\"></a> \n", "\n", "Let us assume now that our idealized single degree of freedom system is subjected to a harmonic\n", "(sinusoidal) loading with frequency $f_0$:\n", "\n", "$$ F(t) = F_{\\rm max} \\sin(2\\pi f_0 t + \\theta_F) $$\n", "\n", "with $F_{\\rm max}$ being the force function amplitude and $\\theta$ some phase angle.\n", "\n", "<img src=\"images/singleDOF.png\" alt=\"SDOF system\" width=\"240px\"/>\n", "\n", "Recalling the convolution theorem for Fourier Transform presented in last class we anticipate that, \n", "in the same way as with Laplace Transform, the system response can calculated as:\n", "\n", "$$ u(t) = f(t) * h(t) = \\int_{-\\infty}^{\\infty} {f(t - \\tau}) h(\\tau) \\, \\; d\\tau $$\n", "\n", "with $f(t) = F(t)/m$. Deriving now the displacement twice we got the acceleration:\n", "\n", "$$ \\ddot{u}(t) = \\int_{-\\infty}^{\\infty} {\\ddot{f}(t - \\tau}) h(\\tau) \\, \\; d\\tau $$\n", "\n", "but replacing the sinusoidal function we get:\n", "\n", "$$ \\ddot{u}(t) = -(2\\pi f_0)^2 \\int_{-\\infty}^{\\infty} {f(t - \\tau}) h(\\tau) \\, \\; d\\tau $$\n", "\n", "Replacing now the integral in the expression above by $u(t)$ we arrive at:\n", "\n", "$$ \\ddot{u}(t) + (2\\pi f_0)^2 u(t) = 0 $$\n", "\n", "what is a homogeneous differential equation with solution:\n", "\n", "$$ u(t) = u_{\\rm max} \\sin(2\\pi f_0 t + \\theta_u) $$\n", "\n", "This solution states that _a linear system responds to a harmonic excitation preserving\n", "the same excitation frequency_. On the other hand, whenever a system is subjected\n", "to a harmonic excitation and the excitation frequency is not exclusivelly preserved\n", "in the system response, this will be a strong indication that _the system is not linear_.\n", "\n", "This theorem is demonstrated below with a excitation frequency $f_0 = 1$Hz applied to a linear\n", "system with natural frequency $f_{\\rm n} = 2$Hz. The system equation is solved with\n", "the ```MRPy``` method ```sdof_Fourier()``` which assumes that the loading is periodic and\n", "hence no initial conditions are required. How this method works will be explained in\n", "the following sections.\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x144 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x144 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x144 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f0 = 1.0 # excitation frequency (kg)\n", "F0 = 1.0 # excitation amplitude (N)\n", "\n", "m = 1.0 # system mass (kg)\n", "fn = 2.0 # system natural frequency (Hz)\n", "zt = 0.01 # system damping ratio (nondim)\n", "\n", "F = F0*MRPy.harmonic(NX=1, N=1024, Td=8, f0=1, phi=0) # MRPy harmonic function\n", "F = (F + 2*F0)**1.05 - 2*F0\n", "\n", "u = F.sdof_Fourier(fn, 0.01)/m # frequency domain solution\n", "\n", "f0 = F.plot_time(0, figsize=(8,2), axis_t=(0, 8, -1.50, 1.50 ))\n", "f1 = u.plot_time(1, figsize=(8,2), axis_t=(0, 8, -0.02, 0.02 ))\n", "f2 = u.plot_freq(2, figsize=(8,2), axis_f=(0, 8, 0.00, 0.0004))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Reological models <a name=\"section_2\"></a> \n", "\n", "### 2.1. The general linear model <a name=\"section_21\"></a> \n", "\n", "The damped spring-mass system depicted at the beginning of this notebook, with a single spring in parallel\n", "with a single damper, is one amongst many possible models for the reological behavior of linear systems.\n", "In general, the equilibrium equation may be written as:\n", "\n", "$$ m \\ddot{u} + r(u, t) = F(t) $$\n", "\n", "where $r(u, t)$ is a time function abridging both _restitutive_ and _reactive_ forces, which obviously \n", "depend on the system response itself, $u(t)$. In general, it can be stated that a linear reological model\n", "is the solution of the equation:\n", "\n", "$$ \\left(a_0 + a_1\\frac{\\partial}{\\partial t} + a_2\\frac{\\partial^2}{\\partial t^2} + \\dots \\right) r(t) =\n", " \\left(b_0 + b_1\\frac{\\partial}{\\partial t} + b_2\\frac{\\partial^2}{\\partial t^2} + \\dots \\right) u(t) $$\n", "\n", "If we apply a Fourier Transform to this equation, with $\\mathscr{F} \\left\\{ r(t) \\right\\} = R(\\omega)$\n", "and $\\mathscr{F} \\left\\{ u(t) \\right\\} = U(\\omega)$, after some algebraic manipulation we arrive \n", "at the following general relation:\n", "\n", "$$ R(\\omega) = K(\\omega) \\left[ 1 + i\\mu(\\omega) \\right] U(\\omega)$$\n", "\n", "what in short means that there will be an _in phase_ and an _out of phase_ force to displacement response. \n", "Each reological models will have its own $K(\\omega)$ and $\\mu(\\omega)$ functions. \n", "It is important to observe the importance of the Fourier Transform approach here, \n", "which makes possible the solution of equilibrium equation in frequency domain without\n", "the need of solving an integral-differential equation in time domain.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2. The Kevin-Voigt model <a name=\"section_22\"></a> \n", "\n", "The parallel spring-damper system, commonly used for elastic structures in\n", "Civil Engineering, is known as _Kelvin-Voigt_ model.\n", "\n", "<img src=\"images/Kelvin_Voigt_diagram.svg\" alt=\"Kelvin-Voigt\" width=\"160px\"/>\n", "\n", "In time domain the model is formulated as:\n", "\n", "$$ r(t) = c\\dot{u}(t) + ku(t) $$\n", "\n", "while its properties are:\n", "\n", "\\begin{align*}\n", " K(\\omega) &= k \\\\\n", "\\mu(\\omega) &= -\\frac{c\\omega}{k} \n", "\\end{align*}\n", "\n", "We will be always using this model, unless otherwise explicitly stated.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.3. The Maxwell model <a name=\"section_23\"></a> \n", "\n", "The series spring-damper system, the most basic representation of a viscous\n", "material, is known as _Maxwell_ model.\n", "\n", "<img src=\"images/Maxwell_diagram.svg\" alt=\"Maxwell\" width=\"240px\"/>\n", "\n", "In time domain the model is stated as:\n", "\n", "$$ r(t) + \\frac{c}{k} \\; \\dot{r}(t) = c\\dot{u}(t)$$\n", "\n", "while its properties are:\n", "\n", "\\begin{align*}\n", " K(\\omega) &= \\frac{c^2 k}{c^2 \\omega^2 + k^2} \\omega^2 \\\\\n", "\\mu(\\omega) &= -\\frac{k}{c\\omega}\n", "\\end{align*}\n", "\n", "Observe that this model implies the possibility (almost a certainty) \n", "of a system non-zero final response. Furthermore, for zero excitation frequency\n", "(what means a static load) the displacement will become infinity.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.3. The Zener (standard) model <a name=\"section_24\"></a> \n", "\n", "A more complex reological model is known as the Zener (or standard) model. \n", "There are two versions for these model, as illustrated below.\n", "\n", "<table align=\"center\">\n", " <tr>\n", " <td align=\"center\"><img src=\"images/Zener_Maxwell_diagram.svg\" alt=\"Zener-Maxwell\" width=\"200px\"/></td>\n", " <td align=\"center\"><img src=\"images/Zener_Kelvin_diagram.svg\" alt=\"Zener-Kelvin\" width=\"180px\"/></td>\n", " </tr>\n", " <tr>\n", " <td align=\"center\"> The Zener model (Maxwell version) </td>\n", " <td align=\"center\"> The Zener model (Kelvin version) </td>\n", " </tr>\n", "</table> <br>\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "The time domain equation for the Maxwell version of Zener model is:\n", "\n", "$$ r(t) + \\frac{c}{k_2} \\; \\dot{r}(t) = k_1 u(t) + \\frac{c(k_1 + k_2)}{k_2} \\; \\dot{u}(t) $$\n", "\n", "while the equation for the Kelvin version is:\n", "\n", "$$ r(t) + \\frac{c}{k_1 + k_2} \\; \\dot{r}(t) = \\frac{k_1 k_2}{k_1 + k_2} \\; u(t) + \\frac{c k_1}{k_1 + k_2} \\; \\dot{u}(t) $$\n", "\n", "As an exercise, it is suggested the derivation of frequency domain functions, $K(\\omega)$ and $\\mu(\\omega)$\n", "for these two Zener model versions.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Equilibrium in frequency domain <a name=\"section_3\"></a> \n", "\n", "After choosing a suitable reological model, we may now go back to the linear dynamic equilibrium equation:\n", "\n", "$$ m \\ddot{u} + r(u, t) = F(t) $$\n", "\n", "and apply a Fourier transform to both sides of equation:\n", "\n", "$$ -\\omega^2 U(\\omega) + \\frac{1}{m} \\; R(\\omega) = F(\\omega) $$\n", "\n", "where $\\mathscr{F} \\left\\{ F(t)/m \\right\\} = F(\\omega)$.\n", "\n", "After replacing the expression for the choosen $R(\\omega)$, the system response $U(\\omega)$ can be \n", "calculated as a function of excitation $F(\\omega)$, and transformed back to time domain (if required).\n", "One must be aware that this is complex algebra and the solution will have both an _in phase_ and \n", "an _out of phase_ components. \n", "\n", "In the following we will do the math for the most used Kevin-Voigt model. The equilibrium in \n", "frequency domain is:\n", "\n", "$$ -\\omega^2 U(\\omega) + \\frac{k}{m} \\; \\left( 1 - i\\frac{c\\omega}{k} \\right) U(\\omega) = F(\\omega) $$\n", "\n", "Now we isolate $U(\\omega)$ and recall that $\\omega_{\\rm n}^2 = k/m$ and that $\\zeta = c/(2m\\omega_{\\rm n}) $, what gives:\n", "\n", "$$ U(\\omega) = H(\\omega) F(\\omega) $$\n", "\n", "where:\n", "\n", "$$ H(\\omega) = \\frac{1}{\\omega_{\\rm n}^2} \\; \\left[ \\frac{1}{(1 - \\beta^2) - i(2\\zeta\\beta)} \\right]$$\n", "\n", "is called the _system mechanical admittance_, with $\\beta = \\omega / \\omega_{\\rm n}$ being \n", "a nondimensional frequency. \n", "\n", "These expressions allow a straightforward solution of the equilibrium equation in time domain \n", "(although its complex algebra). The mechanical admittance can be understood as a frequency \n", "dependent flexibility, for as the excitation frequency goes to zero (static condition) the \n", "admittance goes to $1/\\omega_{\\rm n}^2$, which is the flexibility coefficient \n", "(inverse of the stiffness coefficient, $\\omega_{\\rm n}^2$) with unity mass.\n", "\n", "In the expression above it can also be observed that for undamped systems, $\\zeta = 0$, the \n", "admittance, and consequently the system response, will rise to infinity when the excitation\n", "frequency equals the system natural frequency, $\\omega = \\omega_{\\rm n}$. This condition is\n", "called _resonance_, and must be always avoided in structural systems design.\n", "\n", "The class ``MRPy`` has a method ``sdof_Fourier()`` that is an implementation of this\n", "solution in frequency domain (for Kevin-Voigt model). It requires no inicial condition,\n", "for in Fourier analysis the numerical approach (where signals must have a finite duration)\n", "assumes the signal is always periodic.\n", "\n", "The example below compares the solutions with ``sdof_Fourier()`` and ``sdof_Duhamel()``\n", "for a linear system subject to a harmonic load. Observe the difference due to \n", "the initial conditions in time domain approach. The two responses become the same\n", "after some acceleration time in the solution with Duhamel. This difference between\n", "the two solution methods is exactly the system response to some initial conditions.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x144 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x144 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x144 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x144 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "m = 1.0 # system mass (kg)\n", "fn = 1.0 # system natural frequency (Hz)\n", "zt = 0.01 # system damping ratio (nondim)\n", "\n", "F = MRPy.white_noise(1, 2048, Td=32) # 32 seconds white noise\n", "F = (F - F.mean())/F.std() # unit variance\n", "\n", "# Uncomment the following line for padding zeros to force same result\n", "# F = F.double().double()\n", "\n", "uF = F.sdof_Fourier(1, 0.01)/m # 1Hz, 1% damping, 1kg mass\n", "uD = F.sdof_Duhamel(1, 0.01, 0, 0)/m # zero initial conditions\n", "\n", "uE = uF - uD # solutions difference\n", "\n", "f2 = F.plot_time(2, figsize=(8,2), axis_t=(0, 32, -4.0, 4.0))\n", "f3 = uF.plot_time(3, figsize=(8,2), axis_t=(0, 32, -0.2, 0.2))\n", "f4 = uD.plot_time(4, figsize=(8,2), axis_t=(0, 32, -0.2, 0.2))\n", "f5 = uE.plot_time(5, figsize=(8,2), axis_t=(0, 32, -0.2, 0.2))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are many areas in engineering analysis where design codes define dynamic loads as power spectra.\n", "For instance, surface irregularities in pavements, earthquake accelerations, wind speeds, etc.\n", "In these cases, the equation:\n", "\n", "$$ U(\\omega) = H(\\omega) F(\\omega) $$\n", "\n", "which preserve phase information, is replaced by:\n", "\n", "$$ S_U(\\omega) = \\lvert H(\\omega) \\rvert^2 S_F(\\omega) $$\n", "\n", "where, instead of the complex Fourier transforms, the (real) spectral densities are used.\n", "In this new equation, the absolute squared mechanical admittance becomes:\n", "\n", "$$ \\lvert H(\\omega) \\rvert^2 = \\frac{1}{\\omega_{\\rm n}^4} \\; \\left[ \\frac{1}{(1 - \\beta^2)^2 + (2\\zeta\\beta)^2} \\right]$$\n", "\n", "with $\\beta = \\omega/\\omega_{\\rm n}$.\n", "The square root of the expression between brackets is also called _dynamic amplification factor_, $A(\\beta, \\zeta)$:\n", "\n", "$$ A(\\beta, \\zeta) = \\sqrt{\\frac{1}{(1 - \\beta^2)^2 + (2\\zeta\\beta)^2}} $$\n", "\n", "plotted below for some typical values of the damping ratio.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "bt = np.linspace(0, 3, 200)\n", "zt = [0.20, 0.10, 0.05, 0.01]\n", "\n", "plt.figure(6, figsize=(8,4))\n", "\n", "for z in zt:\n", " A = np.sqrt(1/((1 - bt**2)**2 + (2*z*bt)**2))\n", " f6 = plt.semilogy(bt, A)\n", "\n", "plt.legend(zt)\n", "plt.axis([0, 3, 0.1, 100])\n", "plt.ylabel('Dynamic Amplification (nondim)')\n", "plt.xlabel('Normalized frequency')\n", "plt.grid(True)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The most important features of the dynamic amplification factor are:\n", "\n", "* The factor represents the dynamic response increase with respect to the static response to a harmonic loading: <br> <br> $$ F(t) = F_{\\rm max} \\sin(\\omega t + \\theta) $$ <br> such that <br> $$ u_{\\rm max} = A(\\beta, \\zeta) \\; \\frac{F_{\\rm max}}{m \\omega_{\\rm n}^2} $$ <br> where we recall that $m \\omega_{\\rm n}^2$ is the stiffness coefficient and the phase information is lost.\n", "* For very low frequencies the amplification becomes $A(\\beta, \\zeta) = 1$, what means static response.\n", "* For $\\beta \\approx 1$ the amplification attains its maximum, which is approximatelly $A(1, \\zeta) = 1/(2\\zeta)$. This means, for instance, that for a typical damping ratio, $\\zeta = 1$%, the dynamic response is amplified approximately 50 times with respect to the static response.\n", "\n", "Lets take a look at this theory by running an example.\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Static displacement would be: 0.025m\n", "Peak of dynamic displacement: 1.261m\n", "Amplification factor is: 49.8 \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x144 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x144 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "m = 1.0 # system mass (kg)\n", "fn = 1.0 # system natural frequency (Hz)\n", "zt = 0.01 # system damping ratio (nondim)\n", "k = m*(2*np.pi*fn)**2 # implied stiffness\n", "\n", "Td = 32 # load duration (s)\n", "fs = 32 # sampling rate (Hz)\n", "N = Td*fs # signal length\n", "f0 = 1.0 # excitation frequency (Hz)\n", "F0 = 1.0 # excitation amplitude (N)\n", "phi = 0.0 # phase angle (rad)\n", "\n", "F = F0*MRPy.harmonic(1, N, fs, f0=f0, phi=phi) # harmonic loading\n", "\n", "ue = F0/k # static response\n", "ud = F.sdof_Fourier(fn, zt)/m # dynamic response\n", "up = ud[0].max() # peak response\n", "\n", "f7 = F.plot_time(7, figsize=(8,2), axis_t=(0,32,-1.5,1.5))\n", "f8 = ud.plot_time(8, figsize=(8,2), axis_t=(0,32,-1.5,1.5))\n", "\n", "print('Static displacement would be: {0:6.3f}m'.format(ue))\n", "print('Peak of dynamic displacement: {0:6.3f}m'.format(up))\n", "print('Amplification factor is: {0:4.1f} '.format(up/ue))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Example of application <a name=\"section_4\"></a> \n", "\n", "The aerodynamic force over a bluff body due to wind speed turbulence \n", "can be calculated as:\n", "\n", "$$ F(z, t) = \\frac{1}{2} \\rho V^2(z, t) C_{\\rm D} A $$\n", "\n", "where $z$ is the height above ground, $\\rho$ is the air density, $V(z,t)$ \n", "is the wind speed at height $z$, and the product $C_{\\rm D} A$ refers\n", "to the aerodynamic characteristics of the body.\n", "It can be shown that the spectral density of this aerodynamic force\n", "is related to the spectral density of the (fluctuating part) of the wind\n", "speed through:\n", "\n", "$$ S_F(z, f) = \\left [\n", " \\frac{2\\bar{F}(z)}{\\bar{V}(z)} \\right ]^2 S_v(z, f)$$\n", "\n", "where $f$ is the frequency, $\\bar{F}(z)$ is the mean force at height $z$,\n", "and $\\bar{V}(z)$ is the mean wind speed at height $z$. \n", "\n", "The wind speed turbulence, $v(t)$, may be modelled according to Harris' spectral density, $S_V(f)$:\n", "\n", "$$ \\frac{f S_V(f)}{\\sigma_V^2} = \\frac{0.6 Y}{\\left( 2 + Y^2 \\right)^{5/6}}$$\n", "with:\n", "\\begin{align*}\n", " Y &= 1800 f \\;/\\; \\bar{V}_{10} \\\\\n", " \\sigma_V^2 &= 6.66 \\; c_{\\rm as} \\; \\bar{V}_{10}^2\n", "\\end{align*}\n", "\n", "where $\\sigma_V^2$ is the wind speed variance, $c_{\\rm as}$ is the surface drag coefficient and $\\bar{V}_{10}$ is the mean wind speed at 10m height.\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x216 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cas = 6.5e-3 # NBR-6123 category II\n", "V10 = 20. # mean speed at 10m (m/s)\n", "sV2 = 6.66*cas*(V10**2) # wind speed variance \n", "\n", "fs = 64. # samplig rate\n", "N = 8192 # length of sample\n", "M = N//2 + 1 # length of periodogram\n", "df = fs/M # frequency step\n", "\n", "f = np.linspace(0, fs/2, M) # frequency axis\n", "Y = 1800*f[1:]/V10 # avoiding zero division\n", "\n", "SV0 = np.zeros((2, M))\n", "SV0[0,1:] = 0.6*sV2*Y/((2 + Y**2)**(5/6))/f[1:]\n", "SV0[1,1:] = SV0[0,1:] # (replicating)\n", "\n", "plt.figure(6, figsize=(8, 3))\n", "plt.loglog(f[1:], SV0[0,1:]);\n", "plt.grid(True)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5. Assignment <a name=\"section_5\"></a> \n", "\n", "1. Calcular as funções $K(\\omega)$ e $\\mu(\\omega)$ para o modelo reológico de Zener (escolha uma das\n", " duas versões, Maxwell ou Kelvin).\n", "2. Aplique as funções acima na equação de equilíbrio dinâmico no domínio da frequência e deduza\n", " a correspondente função de admitância mecânica.\n", "3. Plote esta admitância em função da frequência adimensionalizada.\n", "4. Apresente a expressão da frequência natural de vibração livre para este modelo.\n", "4. Relatório com deduções, gráficos e resultados (nome do arquivo T6_xxxxxxxx.ipynb).\n", "\n", "Prazo: 03 de junho de 2020.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.9" } }, "nbformat": 4, "nbformat_minor": 2 }