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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import scipy.fftpack\n",
"import check_lab03 as p"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"plt.rcParams.update({'font.size': 22})\n",
"plt.rcParams['lines.linewidth'] = 3\n",
"pi=np.pi"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ME 3263 Introduction to Sensors and Data Analysis\n",
"\n",
"## Lab #3 Measuring Natural Frequencies\n",
"\n",
"\n",
"### What are natural frequencies\n",
"\n",
"In free vibration (i.e., no external forcing), structural components\n",
"oscillate at specified frequencies or combinations of frequencies. Since\n",
"these vibrations are unforced, the associated frequencies are referred\n",
"to as natural frequencies; it's how the system vibrates if left to\n",
"behave on its own. In contrast, driven linear systems vibrate at the\n",
"driving frequency. An amplification of the response (called resonance)\n",
"occurs when the driving frequency coincides with one of the natural\n",
"frequencies. In short, the system is driven at a frequency at which it\n",
"likes to vibrate. Large amplitude oscillations are the result. So it is\n",
"important to know what the natural frequencies are *a priori* so you can\n",
"avoid driving the system into resonance."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In lab 2, we used the Euler-Bernoulli beam equation to describe static deflection of a cantilever beam. Here, we will use the Euler-Lagrange dynamic beam equation to account for inertial effects. The Euler-Lagrange beam equation relates bending stiffness and density as such\n",
"\n",
"$\\frac{\\partial^2}{\\partial x^2}\\left(EI\\frac{\\partial^2 w}{\\partial\n",
"x^2}\\right)=-\\mu\\frac{\\partial^2 w}{\\partial^2 t} +q(x)$ (1)\n",
"\n",
"where $E$ is the Young's modulus of the beam, $I$ is the second moment of area of the beam's cross-section, $\\mu$ is the mass per unit length of the beam, $q(x)$ is the applied load, and $w=w(x,t)$ is the displacement of the neutral axis that is a function of $x$-distance along beam-and $t$-time. \n",
"\n",
"Calculating the natural frequencies ignores the applied load $q(x)$ and if the cross-section is constant, Equation 1 becomes\n",
"\n",
"$EI\\frac{\\partial^4 w}{\\partial\n",
"x^4}=-\\mu\\frac{\\partial^2 w}{\\partial^2 t}$. (2)\n",
"\n",
"The full solution requires evaluation of the partial differential equation. We will use the derived mode shapes and natural frequencies for a cantilever beam [\\[1\\]](https://en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_theory#Example:_Cantilevered_beam). The solution for $w(x,t)$ is as such\n",
"\n",
"$w(x,t)=\\sum_{n=1}^{\\infty}(A_{n}\\cos\\omega_{n}t+B_{n}\\sin\\omega_{n}t)\n",
"\\left(\\cosh\\beta_n x-\\cos\\beta_n x+\n",
"\\frac{\\cos\\beta_n L + \\cosh\\beta_n L}{\\sin\\beta_n L+\\sinh\\beta_n L}\n",
"\\left(\\sin\\beta_n x -\\sinh\\beta_n x\\right)\\right)$ (3)\n",
"\n",
"where the formula $\\cosh(\\beta_n L)\\cos(\\beta_n L) +1 =0$ defines the constants $\\beta_n$, $L$ is the length of the beam, and $A_n$ and $B_n$ are constants derived from initial conditions. In the experiment, you will deliver an impulse to the cantilever specimens. An impulse will only require $\\sin(t)$ components, so $A_n$=0 for all n. The beam will vibrate similar to the following video [Beam vibrations](https://photos.app.goo.gl/t5a79MEz7PrM9vhf7). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Measuring natural frequencies\n",
"\n",
"In this lab, you will measure the first 3 natural frequencies of a rectangular beam.\n",
"Your goal is \n",
"to measure the free response time series data using a strain gage and accelerometer. With this data, you will\n",
"determine the first natural frequency in two ways: (i) by peak counting in the\n",
"time domain (which gives a very rough estimate of $\\omega_n$); and (ii) by a\n",
"formal frequency domain analysis (fast Fourier transform or FFT). For the\n",
"rectangular beam, you have analytical expressions for the natural frequencies\n",
"and you can confirm that you're doing everything properly by getting the\n",
"analytical frequencies to agree with the experimental frequencies.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Measuring vibrational modes has two components, the frequency and the amplitude. The amplitude of vibration can be determined by taking the difference between the maximum and minimum measurements. Measuring the frequency requiresmore attention. Consider 10 oscillations of a cos-wave of 1-Hz with amplitude of 1 a.u. (aribitrary units). Now, take N measurements over the given timeframe from 0-10 seconds. "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'a.u.')"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N=20\n",
"t_collect=10 # time to collect data\n",
"t=np.linspace(0,t_collect,1000)\n",
"y=np.cos(2*pi*t)\n",
"tsample=np.linspace(0,10,N+1)\n",
"ysample=np.cos(2*pi*tsample)\n",
"plt.figure(20)\n",
"plt.plot(t,y,label='signal')\n",
"plt.plot(tsample,ysample,'o-',label='measure')\n",
"plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n",
"plt.xlabel('time (s)')\n",
"plt.ylabel('a.u.')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For N=20, it would appear that we can capture a minimal example of our signal (just the peaks occuring at 1 Hz). Collecting data for N=20 over 10 seconds is equivalent to sampling at 20 samples/10 seconds = 2 Hz. This is called the Nyquist rate which is given as such\n",
"\n",
"$f_{Nyquist}=2f_{signal}$. (4)\n",
"\n",
"In Equation 4, the Nyquist rate (also Shannon Sampling) [\\[2\\]](./jerri_1977-shannon_sampling.pdf)[\\[3\\]](./nyquist.pdf), $f_{Nyquist}$, is the minimum sampling rate necessary to capture the signal at frequency, $f_{signal}$. Try changing N<20 and consider the apparent signal frequencies. \n",
"\n",
"If you try N=11 in the above python code, you will see a phenomenon called \"aliasing\" or the \"wagon-wheel effect\" [\\[3\\]](http://www.onmyphd.com/?p=aliasing). When you look at the measured signal, it appears to have a frequency of 1 cycle/10 seconds = 0.1 Hz. This phenomenon is called the wagon-wheel effect because it is noticeable when recording spinning objects like a wagon wheel [or turbine](https://www.youtube.com/watch?v=vIsS4TP73AU). The wheel spins at a given frequency and the camera records at another frequency. When the ratio of the wheel frequency to camera recording frequency reaches certain values the wheel appears to stop, spin slower, or even backwards. \n",
"\n",
"Experimentally, we avoid aliasing by sampling above the Nyquist rate from equation 4. This poses a chicken and the egg problem. In order to measure the frequency, we need to double the measured frequency and measure the frequency. The result is that we cannot trust measured frequencies below half of the sampling frequency. We use a method called the fast Fourier transform to compare amplitudes measured at different frequencies.\n",
"\n",
"The fast Fourier transform (FFT) is a numerical implementation of the Fourier transform [\\[4\\]](./cooley_and_tukey-FFT.pdf). A Fourier transform of the function introduced earlier, $\\cos(2\\pi t)$, is two dirac delta functions at 1 Hz and -1 Hz. The FFT, if the sampling is well above the Nyquist rate, will produce two peaks, one at 1 Hz and another at the $f_{sampling} - 1Hz$, where $f_{sampling}$ is the sampling frequency. The signal is produced in the previous example with 1000 data points using `linspace(0,10,1000)`. In the next block of code we can compare different numbers of data points collected and the effect on the FFT results. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 5.0)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Y = 2/1000*np.fft.fft(y)\n",
"freq = np.linspace(0,1000/t_collect,len(Y))\n",
"plt.figure()\n",
"for N in range(20,50,10):\n",
" tsample=np.linspace(0,10,N+1)\n",
" ysample=np.cos(2*pi*tsample)\n",
" Ysample= 2/N*np.fft.fft(ysample)\n",
" freqsample = np.linspace(0,N/t_collect,len(Ysample))\n",
"\n",
" plt.plot(freqsample, np.abs(Ysample),'o-',label='N=%i'%N)\n",
"plt.plot(freq, np.abs(Y) ,label='signal')\n",
"plt.xlabel('frequency (Hz)')\n",
"plt.ylabel('Amplitude (a.u.)')\n",
"plt.title(r'FFT of $\\cos(2\\pi t)$ 10-s collection')\n",
"plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)\n",
"plt.xlim((0,5))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the figure plotted above, for N=20, $f_{sampling}=20/10~s=2~Hz$, for N=30, $f_{sampling}=30/10~s=3~Hz$, for N=40, $f_{sampling}=40/10~s=4~Hz$. The Nyquist rate is $2~Hz$. For each sampling rate above the Nyquist rate we see two peaks, $1~Hz$ and $f_{sampling}-1~Hz$. As a rule of thumb, do not trust any peaks you find above $f_{sampling}/2$. The FFT calculation produces the same amplitude in either direction from the point $f_{sampling}/2$. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 1\n",
"\n",
"Take the Fourier transform of a function $\\sin(2\\pi t)$ recorded for 10 seconds. Plot the results for:\n",
"\n",
"a. N=20\n",
"\n",
"b. N=30\n",
"\n",
"c. N=40\n",
"\n",
"*Hint: use the same code from above*"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Rectangular beam dynamics\n",
"\n",
"Use the physical dimensions of your beam and calculated modulus from Lab #1. Calculate the first\n",
"three natural frequencies of a cantilever beam using the formula\n",
"\n",
"$\\omega_i=\\beta_i^2\\sqrt{\\frac{EI}{\\bar{m}L^4}}$ (5)\n",
"\n",
"where the $i^{th}$ natural frequency, $\\omega_i$ is given in\n",
"rad/s,$\\beta_1=1.875104$, $\\beta_2=4.694091$, $\\beta_3=7.854757$, $\\bar{m}$ is\n",
"the mass per unit length, $E$ is Young's modulus, and $I$ is the second moment\n",
"of area of the beam. Ensure that the units of $\\omega_i$ are rad/s e.g. 1/s.\n",
"\n",
"As an example, the function `natural_frequency(i,E,I,mbar,L)` returns the $i^{th}$ natural frequency of a cantilever beam given \n",
" Youngs modulus, `E`,second moment of area, `I`, mass per unit length, `mbar`=density*(cross-sectional area), and Length, `L`. An example for aluminum is given with a cross-section of $12\\times4$ mm in the cell following the function definition."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def natural_frequency(i,E,I,mbar,L):\n",
" '''returns the i^th natural frequency of a cantilever beam with \n",
" Youngs modulus, E \n",
" second moment of area, I\n",
" mass per unit length, mbar=density*(cross-sectional area)\n",
" Length, L'''\n",
" # solutions to cosh(pi*x)*cos(pi*x)+1=0 are saved in beta array below\n",
" # first 19 mode shapes are solved\n",
" beta=np.array([ 1.87510407, 4.69409113, 7.85475744, 10.99554073,\n",
" 14.13716839, 17.27875953, 20.42035225, 23.5619449 ,\n",
" 26.70353756, 29.84513021, 32.98672286, 36.12831552,\n",
" 39.26990817, 42.41150082, 45.55309348, 48.69468613, \n",
" 51.83627878, 54.97787144, 58.11946409])\n",
" if i>len(beta):\n",
" print('Error: choose a natural frequency less than %i'%(len(beta)))\n",
" omega=np.NaN\n",
" else:\n",
" omega=beta[i-1]**2*np.sqrt(E*I/(mbar*L**4))\n",
" return omega\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the 1st natural frequency is 11.239 Hz\n",
"the 2nd natural frequency is 70.433 Hz\n",
"the 3rd natural frequency is 197.214 Hz\n"
]
}
],
"source": [
"E=70E9 # 70,000,000 Pa=70 GPa\n",
"b=12e-3 # width in m\n",
"t=4e-3 # thickness in m\n",
"I=b*t**3/12 # second moment of area for rectangular cross-section (m^4)\n",
"mbar=7500*b*t # 7500 kg/m^3*(cross-section area) -> mbar [kg/m]\n",
"L=16.5*25.4e-3 # length in m\n",
"\n",
"f1=natural_frequency(1,E,I,mbar,L)\n",
"f2=natural_frequency(2,E,I,mbar,L)\n",
"f3=natural_frequency(3,E,I,mbar,L)\n",
"print('the 1st natural frequency is %1.3f Hz'%(f1/2/np.pi)) \n",
"print('the 2nd natural frequency is %1.3f Hz'%(f2/2/np.pi)) \n",
"print('the 3rd natural frequency is %1.3f Hz'%(f3/2/np.pi)) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Problem 2\n",
"\n",
"What are the first three natural frequencies of a steel beam that is 2 mm x 6 mm x 300 mm (in Hertz)?"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Whoops, try again\n"
]
},
{
"data": {
"text/plain": [
"0"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# your work here\n",
"\n",
"p.check_p02(f1/2/pi,f2/2/pi,f3/2/pi)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, use the LabView program provided to take data from the strain gage. \n",
"Use a sampling frequency at least twice as large as the highest\n",
"frequency you're trying to capture (this is the Nyquist limit). You can do this\n",
"estimation in a trial-and-error fashion as you carry out the analysis that\n",
"follows.\n",
"\n",
"Begin recording data. Make sure that when you apply an impact to your\n",
"beam that you get a decaying vibration on your LabView time series plot.\n",
"Measuring the frequency: you'll do this in two ways:\n",
"\n",
"1. Estimate the $1^{st}$ natural frequency from the decaying\n",
" oscillation. The time between the peaks is the oscillation period,\n",
" relate this to the frequency as \n",
"\n",
" $f=\\frac{1}{T}~Hz$\n",
"\n",
"2. Second, use a frequency domain approach: the\n",
" Fast Fourier Transform (FFT). \n",
"\n",
"In the second approach, you need to explore 'windowing' and 'low-pass\n",
"filtering' your data. You should do this all in LabView. Try to\n",
"investigate the following:\n",
"\n",
"1. Use a Hanning window. Windowing allows us to\n",
" smooth the edges of the data recorded [\\[6\\]](./harris-1978.pdf).\n",
"\n",
"2. Use a low-pass filter in your experiment.\n",
" Low-pass filtering allows us to eliminate unwanted high frequencies\n",
" due to various effects including *aliasing*. You need to change the\n",
" cut-off frequency values and see the effects in FFT analysis.\n",
" The frequency content above the cut-off frequency will\n",
" be filtered out, which is why we can call this procedure 'low-pass\n",
" filtering'. But be careful about making this too low as it may throw\n",
" out the frequencies that you're trying to measure. Strike the beam\n",
" and identify the first, second, third natural frequencies. Compare these to your theoretical\n",
" predictions. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# References\n",
"\n",
"1. [https://en.wikipedia.org/wiki/Euler-Bernoulli_beam_theory](https://en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_theory#Example:_Cantilevered_beam)\n",
"\n",
"2. Jerri, A. J. (1977). The Shannon sampling theorem—Its various extensions and applications: A tutorial review. Proceedings of the IEEE, 65(11), 1565-1596.\n",
"\n",
"3. Nyquist, H. (1928). Certain topics in telegraph transmission theory. Transactions of the American Institute of Electrical Engineers, 47(2), 617-644.\n",
"\n",
"4. [http://www.onmyphd.com/?p=aliasing](http://www.onmyphd.com/?p=aliasing)\n",
"\n",
"5. Cooley, J. W., & Tukey, J. W. (1965). An algorithm for the machine calculation of complex Fourier series. Mathematics of computation, 19(90), 297-301.\n",
"\n",
"6. Harris, F. J. (1978). On the use of windows for harmonic analysis with the discrete Fourier transform. Proceedings of the IEEE, 66(1), 51-83."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Appendix: Example Calculations from Labview output with 70 Hz-filter"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"the 1st natural frequency is 15 Hz\n",
"the 2nd natural frequency is 92 Hz\n",
"the 3rd natural frequency is 258 Hz\n"
]
}
],
"source": [
"E=200e9 # 200,000,000 Pa=200 GPa\n",
"b=25.5e-3\n",
"t=3.2e-3\n",
"I=b*t**3/12 # second moment of area for rectangular cross-section (m^4)\n",
"mbar=8000*b*t # 8000 kg/m^3*(cross-section area) -> mbar [kg/m]\n",
"L=16.5*25.4e-3 # length in mm\n",
"\n",
"f1=natural_frequency(1,E,I,mbar,L)\n",
"f2=natural_frequency(2,E,I,mbar,L)\n",
"f3=natural_frequency(3,E,I,mbar,L)\n",
"print('the 1st natural frequency is %1.0f Hz'%(f1/2/np.pi)) \n",
"print('the 2nd natural frequency is %1.0f Hz'%(f2/2/np.pi)) \n",
"print('the 3rd natural frequency is %1.0f Hz'%(f3/2/np.pi)) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Import the csv from the Labview output"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"data=pd.read_csv('beam_04.csv')\n",
"t=data['delta time'].values\n",
"y=data['accel (Filtered)'].values"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot the time-series (not for frequency measure, but just to see values)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Voltage (V)')"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(1)\n",
"plt.plot(t,y,'o')\n",
"plt.title('Amplitude of Strain gage Measure')\n",
"plt.xlabel('time (s)')\n",
"plt.ylabel('Voltage (V)')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Take Fourier transform of data from index i1 to index i2\n",
"## Here we use t=3.49 s to t=4.99 s"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([3.49999485, 4.99999363])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t[[7000,10000]]"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
" def fY(i1,i2): \n",
" ts=t[i1:i2];ys=y[i1:i2] \n",
" Y=2/len(ts)*np.fft.fft(ys) \n",
" f= np.linspace(0,len(ts)/(max(ts)-min(ts)),len(Y)) \n",
" return f,Y"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 100.0)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"f,Y=fY(7000,10000)\n",
"plt.figure(2)\n",
"plt.plot(f,abs(Y))\n",
"plt.title('FFT of SG Measure')\n",
"plt.xlabel(r'$f~(Hz)$')\n",
"plt.xlim((0,100))"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Measured first natural frequency from lab output: 14.00927679127636 Hz\n",
"Predicted first natural frequency from model: 14.71515776208809 Hz\n"
]
}
],
"source": [
"print('Measured first natural frequency from lab output: ',f[abs(Y)==np.max(abs(Y))][0], ' Hz')\n",
"print('Predicted first natural frequency from model: ', f1/2/pi, 'Hz')"
]
}
],
"metadata": {
"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": "3.8.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}