SHOCK RESPONSE SPECTRUM ANALYSER USING MATLAB SCRIPTS
|
|
- Harvey Moody
- 6 years ago
- Views:
Transcription
1 Scientific Bulletin of the Electrical Engineering Faculty Year 13 No. () ISSN SHOCK RESPONSE SPECTRUM ANALYSER USING MATLAB SCRIPTS C. DUMITRACHE 1, N. OLARIU 1, E. LAKATOS 1, G. MANTESCU, L. OLTEANU, M. BADEA 1 VALAHIA University Targoviste, Faculty of Electrical Engineering, 18, Unirii Boulevard, Targoviste, Romania, VALAHIA University Targoviste, Energy Environment Research Department, 18, Unirii Boulevard, Targoviste, Romania cristiandumitrache@gmail.com Abstract. We present in this article a complete arrangement, hardware and software, that enables analysis of shocks encountered in real operating conditions as well as those generated by simulation systems. The actual part of the analysis is based on Matlab scripts. After a theoretical introduction on the subject we make a detailed description of each script, its place and function in shock analysis methodology. The concept Shock Response Spectrum has been kept for historical reason, although a better term would be Maximum Response Spectrum. Our work has been accomplished through the use of digital signal acquisition systems and computerized data processing equipment. The analysis of data is therefore primarily a digital signal - processing task that use the ramp invariant method. Keywords: Shock response spectrum, Digital signal processing, Ramp invariant method. 1. INTRODUCTION The term Shock response spectrum was first introduced in 193 by M. A. Biot at California Institute of Technology, under the name Earthquake spectrum. Biot's apparatus consisted of a set of torsion pulum which simulated mechanical systems with one degree of freedom [3]. He defined the SRS (Shock Response Spectrum) as the maximum response motion from a set of single DOF oscillators covering the frequency range. After the World War, first in USA and later in Europe, the concept was used to standardize mechanical shock tests [4], [5]. In parallel, methods have evolved for obtaining this spectrum, analogue first (analogical computer and active filters) and then, numerical, with the computer (Duhamel or Laplace evaluation of convolution integral or digital filtering). After 1965, digital filtering to permit the changeover of transfer function H(s) to H(z) used either the trapezoidal method (Tustin) either the impulse invariant method. After 1980, is almost exclusively recommed the step invariance method presented by D. O. Smallwood in [].. MATHEMATICAL ASPECTS We briefly present the mathematical aspects related to the shock spectrum in [], [4], [5] and [6]. That way, the scripts, presented in the chapter that follows, will be clearer. In Figure 1 we present a single DOF mechanical system (without the influence of gravity). Figure 1. Single Degree of Freedom (DOF) System In Figure 1: mass=m; viscous damping coefficient=c; stiffness=k; absolute displacement of the mass=x; base input displacement=y. Q is the quality factor. Response acceleration: Base acceleration: d ( x ( t )) = a ( ) m t dt d dt ( yt ( )) = a ( ) 0 t c m = ξϖ n 1 Q ξ = ω = n k m Differential equation describing the system is:.. c. k c. k x+ x+ x = y+ y (1) m m m m If the mechanical system is without initially accumulated energy, the transfer function, connecting the response acceleration with base acceleration is: A () s ξϖ s+ ω H() s = = A s s s m n n 0 () + ξϖn + ωn (1 ) 10
2 ISSN Scientific Bulletin of the Electrical Engineering Faculty Year 13 No. () For s = jω, we can plot the Bode diagram (Figure ). Where: ωn A = Q (9) 1 B = ω n 1 (10) 4 Q The next step is to find the difference equation that connects the output acceleration x ( kt ) with the input acceleration y(kt). We use Z -1 transform and the recursive formula is: x = b y + b y + b y a x a x (11) k 0 k 1 k 1 k 1 k 1 k Figure. Bode Plot for H(jω) We wish to obtain a pulse transfer function using the step invariant method []. The key is to consider that sampling the response of the continuous system with a ramp invariant method would provide the same result as a discrete sequence, applied at the entry to digital system, described by H (z). Finally: ( ) H s T z = ( ) ( z 1 ) 1 Z L H z s t= nt Here T=1/fs - sampling period. () The result is given in [1] and [] and the calculation is made by Irvine in [6]. Here is the result: b + b z + b z H(z) = (3) a1 z a z We obtain the Bode plot for pulse transfer function H (z) (digital filter), using Matlab command dbode. It is represented in Figure 3. This should be compared with Figure, corresponding to continuous case. The frequency response of the ramp invariant discrete time filter is related to the frequency response of the analog filter as described in [7]. ω sin n π + j ω T n π + H( e ) = H j ω j + T ω + n π (1) The first term in the sum leads to aliasing and the second is a systematic one (sinc distortion). His value is 8 db at the Nyquist frequency. In our paper the maximum analysis frequency is one tenth of the sampling frequency. That leads to errors less than 5%. With the coefficients for the digital filter: sin( b) b0 = 1 exp( A) B (4) sin( B) b1 = exp( A) cos( B) B (5) sin( B) b = exp( A) exp( A) (6) B Figure 3. Bode plot for H(z=e jωt ) a = exp( A) cos( ) (7) 1 B ( A) a = exp (8) 11
3 Scientific Bulletin of the Electrical Engineering Faculty Year 13 No. () ISSN EXPERIMENTAL ARRANGEMENTS The experimental arrangement is represented in Figure 4. Figure 4. Experimental arrangement The first two levels are devices: the B&K piezotransducer has a resonance frequency higher than 40 khz. The charge amplifier has a flat frequency characteristic from 1Hz to 10 khz. The third level is a common sound card (Realtek) or a PC Daq Card (sampling frequency Hz). A more elaborate solution can be a digital event recorder. This arrangement is enough for shock due to transport or pyroshocks in the far region. Further we use Matlab [8]: Data Acquisition Toolbox and Signal Processing Toolbox. - Data Real Time (DRT.m): This script opens the channel for communication with the sound card and plots the real shock in time. The values are saved in DRT.mat. Here is this script: %DataRealTime (DRT.m) %In datareal is the real shock in time %The value are saved in DRT.mat and ploted = analoginput('winsound',0); chan = addchannel(,1); duration = 1; SampleRate = 44100;% due to Sound Card set(,'samplerate',samplerate); set(,'samplespertrigger',duration*samplerate); set(,'triggertype','manual'); start(); trigger(); K=100; %Scale factor for 1V=100g. datareal =getdata(); datareal=k*datareal t=1/44100:1/44100:1 %1sec. plot(t,datareal)%without t we can plot in sample title('real data versus time') xlabel('time in sec.') ylabel('aceleration in g.') save DRT.mat - Data Real Frequency (DRF.m): This is a function [9] with input parameter fs=44100-sampling frequency; Fmin - low frequency in Hz; fmax - maximum frequency in Hz; fno - number of frequency; Q - quality factor-10; This function plots the maximal shock spectrum and save this data in DRF.mat Function [datarealfreq,f] = DRF(fs,fmin,fmax,fno,Q) %SRS Max raspuns la soc cu inv. la rampa %DataRealFrequency % [datarealfreq,f] = DRF(fs,fmin,fmax,fno,Q) % y maxim este calculat % f este vectorul frecventelor masurat in Hz % fs este frecventa de esantionare in Hz-Adica=44100 %Hz (sound card) % fmin este frecventa minima in Hz % fmax este frecventa maxima in Hz % fno este numarul de frecvente % Q este facorul de calitate. Aici este 10 % In datareal data for real shock from DRT.mat load DRT.mat plot (t,datareal) %just for control pause datarealfreq = zeros(fno,1); % De aici f = zeros(fno,1); % k1 = log(fmax/fmin)/(fno-1); k = pi/q/fs; k3 = *pi/fs*sqrt(1-1/(4*q*q)); % for n = 1:fno; f0 = fmin*exp(k1*(n-1)); A = k*f0; B= k3*f0; a = [1, -*cos(b)*exp(-a), exp(-*a)]; b=[1-exp(-a)*sin(b)/b,*exp(-a)*(sin(b)/bcos(b)),exp(-*a)-exp(-a)*sin(b)/b]; % si pana aici z = filter(b,a,datareal); datarealfreq(n,1) = max(abs((z))); f(n,1) = f0; loglog(f,datarealfreq) grid title('shock Spectrum for Real Situation in log-log axes') xlabel('frequncy in Hz') ylabel('acceleration in g') save DRF.mat - Data Simulation Time (DST.m). This is a function with input arguments: AMP - amplitude in g of 1/sinus used currently for simulation and τ (in ms.) is the duration of 1/ sinus. All the values are plotted versus time and saved in DST.mat 1
4 ISSN Scientific Bulletin of the Electrical Engineering Faculty Year 13 No. () Here is the script: Function DST = DST(AMP,tau) %DataSimulation in time % AMP is amplitude in g. % tau is 1/ sinus duration % Function DST.m to plot 1/ sinus for simulation %DataSimulationTime t=1/44100:1/44100:0*tau; k=max(size(t)); for i=1:k if((t(i)>=0)&(t(i)<=tau)) datasim(i)=amp*sin(*pi*t(i)/(*tau)); else datasim(i)=0; plot(t,datasim) title('1/sinus for simulation') xlabel('time in sec.') ylabel('acceleration in g.') save DST.mat - Data Simulation Frequency (DSF.m): This function is similar to DRF.m- with the same input arguments as DRF.m This function plot the maximal shock spectrum for 1/ sinus and save this data in DSF.mat. Here is this function: Function [datasimfreq,f] = DSF(fs,fmin,fmax,fno,Q) [datasimfreq,f] = DSF(x,fs,fmin,fmax,fno,Q,A,T) % datasimfreq maximal is calculated % f este vectorul frecventelor in Hz % datasim -input vector from DST.mat % fs este frecventa de esantionare Hz % fmin este frecventa limita de jos Hz % fmax este frecventa limita de sus Hz % fno este numarul de frecvente % Q este factorul de calitate =10 % In datasim data for half-sinus load DST.mat datasimfreq = zeros(fno,1); f = zeros(fno,1); % Inserati de aici % 11 comenzi de mai sus adica din DRF % si pana aici datasimfreq(n,1) = max(abs((z))); f(n,1) = f0; loglog(f,datasimfreq) grid title('shock Spectrum for 1/sinus A=100g, tau=11ms.') xlabel('frequency in Hz ') ylabel('acceleration in g.') save DSF.mat - Comparison (COMP.m). This is a script that use all the four.mat files and the result is a plot of both maximal shock spectrum for the real shock and for the simulation shock. Here is this script: %COMP load DST.mat load DSF.mat load DRT.mat load DRF.mat loglog(f,datarealfreq,'om',f,datasimfreq,'*r') grid title('shock Spectrum: magenta-real and red -simulation') xlabel('frequency in HZ') ylabel('acceleration in g.') % FM is the Merit Function from last squares method ind=1:1:max(size(f)); for ind=1:max(size(f)) FM(ind)=sum((datarealfreq(ind)-datasimfreq(ind)).^); FM=sqrt(sum(FM(ind)))/max(size(f)) AMPLITUDE_in_g=AMP HALF_SINUS_TIME_in_s= τ *1000 FM function, calculated similarly to the method of least squares, gives a mathematical picture of the degree of overlap of the two spectra. But it is the duty of the engineer, who knows the exact situation, to search and assess how small can be the minimum. 4. REZULTS The real shock, produced by the fall of transducer from a height of 10 cm on a wood surface, is represented in Figure 5. Here we used B&K 4367 transducer, B&K 66 charge amplifier and PC Realtek sound card and DRT.m In Figure 6 is represented the maximal Shock Spectrum for this experimental real shock (see DRF.m) In Figure 7 is represented a simulation shock -1/ sinus, with 150 g. amplitude and duration 10 ms (see DST.m). Figure 5. Real shock (see DRT.m) 13
5 Scientific Bulletin of the Electrical Engineering Faculty Year 13 No. () ISSN Figure 6. Maximal Shock Spectrum for real shock (see DRF.m) Figure 9. The Maximal Shock Spectrum real and simulation (see COMP.m) Here FM is 5.3. Probably a better coefficient could be achieved. This is beyond the intention of our article. Farther, a good engineer must have a decision: to use for shock test real data, processed like this article (or something similar) or direct to use a norm. 5. CONCLUSIONS Figure 7. Simulation Shock in time (150g, 10 ms) (see DST.m) The Maximal Shock Spectrum (for this 1/ sinus) is represented in Figure 8 (see DSF.m) We presented in this article a complete (cheap) arrangement, experimental and software, that enables analysis of shocks encountered in real conditions as well as those generated by simulation systems. The actual part of the analysis is based on Matlab scripts and Digital Signal Processing. The analysis method is ramp invariant method and maximal shock spectrum. Finally, a real shock can be equalled with a simulation shock of form 1/ sinus with amplitude and duration predetermined. 6. REFERENCES Figure 8. Maximal Shock Spectrum for 1/ sinus -150 g, 10 ms. (see DSF.m) The last test is to compare the Spectrum via COMP.m The result is presented in Figure 9. [1] *** ISO/WD , Mechanical vibration and shock Signal processing Part 4, Shock response spectrum analysis. [] Smallwood, David, An Improved Recursive Formula for Calculating Shock Response Spectra, 51st Shockand Vibration Bulletin, [3] M. Biot, A Mechanical Analyzer for the Prediction of Earthquake Stresses, Bulletin of the Seismological Society of America, Volume 31, Number, April [4] G. A. Piersol, T. Paez, Harris Shock and Vibration Handbook, Sixth Edition, Mc Graw Hill, 010. [5] A. Lenk, J. Rehnitz, Schwingungsprutechnik, Auflage, Veb Verlag Technik Berlin, [6] T. Irvine, Derivation of the Filter Coefficients for the Ramp Invariant Method as Applied to Base 14
6 ISSN Scientific Bulletin of the Electrical Engineering Faculty Year 13 No. () Excitation of a Single-degree-of Freedom System, Vibration data, February, 01. [7] D. Schlichtharle, Digital Filters, Second Edition, Springer-Verlag, 011. [8] [9] K. Ahlin, Comparison of Test Specifications and Measured Field Data, Sound and Vibration, September
Direct Fatigue Damage Spectrum Calculation for a Shock Response Spectrum
Direct Fatigue Damage Spectrum Calculation for a Shock Response Spectrum By Tom Irvine Email: tom@vibrationdata.com June 25, 2014 Introduction A fatigue damage spectrum (FDS) was calculated for a number
More informationSHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 1B. Damping
SHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 1B. Damping By Tom Irvine Introduction Recall the homework assignment from Unit 1A. The data.txt time history represented a rocket vehicle dropped from
More informationDynamics of structures
Dynamics of structures 2.Vibrations: single degree of freedom system Arnaud Deraemaeker (aderaema@ulb.ac.be) 1 One degree of freedom systems in real life 2 1 Reduction of a system to a one dof system Example
More informationVibration Testing. an excitation source a device to measure the response a digital signal processor to analyze the system response
Vibration Testing For vibration testing, you need an excitation source a device to measure the response a digital signal processor to analyze the system response i) Excitation sources Typically either
More informationE2.5 Signals & Linear Systems. Tutorial Sheet 1 Introduction to Signals & Systems (Lectures 1 & 2)
E.5 Signals & Linear Systems Tutorial Sheet 1 Introduction to Signals & Systems (Lectures 1 & ) 1. Sketch each of the following continuous-time signals, specify if the signal is periodic/non-periodic,
More informationNumerical Solution of Equation of Motion
Class Notes: Earthquake Engineering, Ahmed Elgamal, September 25, 2001 (DRAFT) Numerical Solution of Equation of Motion Average Acceleration Method (Trapezoidal method) m a + c v + k d = f (t) In the above
More information1 The frequency response of the basic mechanical oscillator
Seismograph systems The frequency response of the basic mechanical oscillator Most seismographic systems are based on a simple mechanical oscillator really just a mass suspended by a spring with some method
More informationLaboratory handouts, ME 340
Laboratory handouts, ME 340 This document contains summary theory, solved exercises, prelab assignments, lab instructions, and report assignments for Lab 4. 2014-2016 Harry Dankowicz, unless otherwise
More informationFROM ANALOGUE TO DIGITAL
SIGNALS AND SYSTEMS: PAPER 3C1 HANDOUT 7. Dr David Corrigan 1. Electronic and Electrical Engineering Dept. corrigad@tcd.ie www.mee.tcd.ie/ corrigad FROM ANALOGUE TO DIGITAL To digitize signals it is necessary
More information2.161 Signal Processing: Continuous and Discrete
MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete Fall 28 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS
More informationIn-Structure Response Spectra Development Using Complex Frequency Analysis Method
Transactions, SMiRT-22 In-Structure Response Spectra Development Using Complex Frequency Analysis Method Hadi Razavi 1,2, Ram Srinivasan 1 1 AREVA, Inc., Civil and Layout Department, Mountain View, CA
More informationALOHA FEATURE ARTICLES. One of the purposes of this newsletter is to present an interdisciplinary view of acoustics, shock, and vibration.
Acoustics Shock Vibration Signal Processing August 00 Newsletter ALOHA One of the purposes of this newsletter is to present an interdisciplinary view of acoustics, shock, and vibration. Potential topics
More informationCITY UNIVERSITY LONDON. MSc in Information Engineering DIGITAL SIGNAL PROCESSING EPM746
No: CITY UNIVERSITY LONDON MSc in Information Engineering DIGITAL SIGNAL PROCESSING EPM746 Date: 19 May 2004 Time: 09:00-11:00 Attempt Three out of FIVE questions, at least One question from PART B PART
More informationOptimized PSD Envelope for Nonstationary Vibration
Optimized PSD Envelope for Nonstationary Vibration Tom Irvine Dynamic Concepts, Inc NASA Engineering & Safety Center (NESC) 3-5 June 2014 The Aerospace Corporation 2010 The Aerospace Corporation 2012 Vibrationdata
More informationLaboratory handout 5 Mode shapes and resonance
laboratory handouts, me 34 82 Laboratory handout 5 Mode shapes and resonance In this handout, material and assignments marked as optional can be skipped when preparing for the lab, but may provide a useful
More informationLine Spectra and their Applications
In [ ]: cd matlab pwd Line Spectra and their Applications Scope and Background Reading This session concludes our introduction to Fourier Series. Last time (http://nbviewer.jupyter.org/github/cpjobling/eg-47-
More informationDynamics of structures
Dynamics of structures 2.Vibrations: single degree of freedom system Arnaud Deraemaeker (aderaema@ulb.ac.be) 1 Outline of the chapter *One degree of freedom systems in real life Hypothesis Examples *Response
More informationCHAPTER 6 STATE SPACE: FREQUENCY RESPONSE, TIME DOMAIN
CHAPTER 6 STATE SPACE: FREQUENCY RESPONSE, TIME DOMAIN 6. Introduction Frequency Response This chapter will begin with the state space form of the equations of motion. We will use Laplace transforms to
More informationMEG6007: Advanced Dynamics -Principles and Computational Methods (Fall, 2017) Lecture DOF Modeling of Shock Absorbers. This lecture covers:
MEG6007: Advanced Dynamics -Principles and Computational Methods (Fall, 207) Lecture 4. 2-DOF Modeling of Shock Absorbers This lecture covers: Revisit 2-DOF Spring-Mass System Understand the den Hartog
More informationChapter 7. Digital Control Systems
Chapter 7 Digital Control Systems 1 1 Introduction In this chapter, we introduce analysis and design of stability, steady-state error, and transient response for computer-controlled systems. Transfer functions,
More information2A1H Time-Frequency Analysis II
2AH Time-Frequency Analysis II Bugs/queries to david.murray@eng.ox.ac.uk HT 209 For any corrections see the course page DW Murray at www.robots.ox.ac.uk/ dwm/courses/2tf. (a) A signal g(t) with period
More informationChapter 7 Vibration Measurement and Applications
Chapter 7 Vibration Measurement and Applications Dr. Tan Wei Hong School of Mechatronic Engineering Universiti Malaysia Perlis (UniMAP) Pauh Putra Campus ENT 346 Vibration Mechanics Chapter Outline 7.1
More informationComputer simulation and modeling in virtual physics experiments
1198 Current Developments in Technology-Assisted Education (006) Computer simulation and modeling in virtual physics experiments W. Tłaczała *,1, G. Gorghiu, A. E. Glava 3, P. Bazan 4, J. Kukkonen 5, W.
More informationFilter Analysis and Design
Filter Analysis and Design Butterworth Filters Butterworth filters have a transfer function whose squared magnitude has the form H a ( jω ) 2 = 1 ( ) 2n. 1+ ω / ω c * M. J. Roberts - All Rights Reserved
More informationDynamics of Structures
Dynamics of Structures Elements of structural dynamics Roberto Tomasi 11.05.2017 Roberto Tomasi Dynamics of Structures 11.05.2017 1 / 22 Overview 1 SDOF system SDOF system Equation of motion Response spectrum
More information2A1H Time-Frequency Analysis II Bugs/queries to HT 2011 For hints and answers visit dwm/courses/2tf
Time-Frequency Analysis II (HT 20) 2AH 2AH Time-Frequency Analysis II Bugs/queries to david.murray@eng.ox.ac.uk HT 20 For hints and answers visit www.robots.ox.ac.uk/ dwm/courses/2tf David Murray. A periodic
More informationScienceDirect. Response Spectrum Analysis of Printed Circuit Boards subjected to Shock Loads
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 144 (2016 ) 1469 1476 12th International Conference on Vibration Problems, ICOVP 2015 Response Spectrum Analysis of Printed
More informationFREE VIBRATION WITH COULOMB DAMPING Revision A
By Tom Irvine Email: tomirvine@aol.com June 5, 010 FREE VIBRATION WITH COULOMB DAMPING Revision A g m F sgn () & Figure 1. Coulomb damping is dry friction damping. Consider the free vibration response
More informationChapter 5 Design. D. J. Inman 1/51 Mechanical Engineering at Virginia Tech
Chapter 5 Design Acceptable vibration levels (ISO) Vibration isolation Vibration absorbers Effects of damping in absorbers Optimization Viscoelastic damping treatments Critical Speeds Design for vibration
More informationELEN E4810: Digital Signal Processing Topic 11: Continuous Signals. 1. Sampling and Reconstruction 2. Quantization
ELEN E4810: Digital Signal Processing Topic 11: Continuous Signals 1. Sampling and Reconstruction 2. Quantization 1 1. Sampling & Reconstruction DSP must interact with an analog world: A to D D to A x(t)
More informationHomework 4. May An LTI system has an input, x(t) and output y(t) related through the equation y(t) = t e (t t ) x(t 2)dt
Homework 4 May 2017 1. An LTI system has an input, x(t) and output y(t) related through the equation y(t) = t e (t t ) x(t 2)dt Determine the impulse response of the system. Rewriting as y(t) = t e (t
More informationEE Experiment 11 The Laplace Transform and Control System Characteristics
EE216:11 1 EE 216 - Experiment 11 The Laplace Transform and Control System Characteristics Objectives: To illustrate computer usage in determining inverse Laplace transforms. Also to determine useful signal
More informationSHOCK RESPONSE OF MULTI-DEGREE-OF-FREEDOM SYSTEMS Revision F By Tom Irvine May 24, 2010
SHOCK RESPONSE OF MULTI-DEGREE-OF-FREEDOM SYSTEMS Revision F By Tom Irvine Email: tomirvine@aol.com May 4, 010 Introduction The primary purpose of this tutorial is to present the Modal Transient method
More informationSHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 29. Shock Response Spectrum Synthesis via Wavelets
SHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 29. Shock Response Spectrum Synthesis via Wavelets By Tom Irvine Email: tomirvine@aol.com Introduction Mechanical shock can cause electronic components
More informationECEN 420 LINEAR CONTROL SYSTEMS. Lecture 2 Laplace Transform I 1/52
1/52 ECEN 420 LINEAR CONTROL SYSTEMS Lecture 2 Laplace Transform I Linear Time Invariant Systems A general LTI system may be described by the linear constant coefficient differential equation: a n d n
More informationVibration Testing. Typically either instrumented hammers or shakers are used.
Vibration Testing Vibration Testing Equipment For vibration testing, you need an excitation source a device to measure the response a digital signal processor to analyze the system response Excitation
More informationLaboratory handouts, ME 340
Laboratory handouts, ME 34 This document contains summary theory, solved exercises, prelab assignments, lab instructions, and report assignments for Lab 6. 214-216 Harry Dankowicz, unless otherwise noted
More informationTopic 3: Fourier Series (FS)
ELEC264: Signals And Systems Topic 3: Fourier Series (FS) o o o o Introduction to frequency analysis of signals CT FS Fourier series of CT periodic signals Signal Symmetry and CT Fourier Series Properties
More informationLECTURE 12 Sections Introduction to the Fourier series of periodic signals
Signals and Systems I Wednesday, February 11, 29 LECURE 12 Sections 3.1-3.3 Introduction to the Fourier series of periodic signals Chapter 3: Fourier Series of periodic signals 3. Introduction 3.1 Historical
More informationEE 224 Signals and Systems I Review 1/10
EE 224 Signals and Systems I Review 1/10 Class Contents Signals and Systems Continuous-Time and Discrete-Time Time-Domain and Frequency Domain (all these dimensions are tightly coupled) SIGNALS SYSTEMS
More informationThe Laplace Transform
The Laplace Transform Syllabus ECE 316, Spring 2015 Final Grades Homework (6 problems per week): 25% Exams (midterm and final): 50% (25:25) Random Quiz: 25% Textbook M. Roberts, Signals and Systems, 2nd
More informationAPPLICATIONS FOR ROBOTICS
Version: 1 CONTROL APPLICATIONS FOR ROBOTICS TEX d: Feb. 17, 214 PREVIEW We show that the transfer function and conditions of stability for linear systems can be studied using Laplace transforms. Table
More informationSistemas de Aquisição de Dados. Mestrado Integrado em Eng. Física Tecnológica 2016/17 Aula 3, 3rd September
Sistemas de Aquisição de Dados Mestrado Integrado em Eng. Física Tecnológica 2016/17 Aula 3, 3rd September The Data Converter Interface Analog Media and Transducers Signal Conditioning Signal Conditioning
More informationRozwiązanie zagadnienia odwrotnego wyznaczania sił obciąŝających konstrukcje w czasie eksploatacji
Rozwiązanie zagadnienia odwrotnego wyznaczania sił obciąŝających konstrukcje w czasie eksploatacji Tadeusz Uhl Piotr Czop Krzysztof Mendrok Faculty of Mechanical Engineering and Robotics Department of
More informationOptimized PSD Envelope for Nonstationary Vibration Revision A
ACCEL (G) Optimized PSD Envelope for Nonstationary Vibration Revision A By Tom Irvine Email: tom@vibrationdata.com July, 014 10 FLIGHT ACCELEROMETER DATA - SUBORBITAL LAUNCH VEHICLE 5 0-5 -10-5 0 5 10
More informationDynamic Response. Assoc. Prof. Enver Tatlicioglu. Department of Electrical & Electronics Engineering Izmir Institute of Technology.
Dynamic Response Assoc. Prof. Enver Tatlicioglu Department of Electrical & Electronics Engineering Izmir Institute of Technology Chapter 3 Assoc. Prof. Enver Tatlicioglu (EEE@IYTE) EE362 Feedback Control
More informationME scope Application Note 28
App Note 8 www.vibetech.com 3/7/17 ME scope Application Note 8 Mathematics of a Mass-Spring-Damper System INTRODUCTION In this note, the capabilities of ME scope will be used to build a model of the mass-spring-damper
More informationDIGITAL SIGNAL PROCESSING UNIT III INFINITE IMPULSE RESPONSE DIGITAL FILTERS. 3.6 Design of Digital Filter using Digital to Digital
DIGITAL SIGNAL PROCESSING UNIT III INFINITE IMPULSE RESPONSE DIGITAL FILTERS Contents: 3.1 Introduction IIR Filters 3.2 Transformation Function Derivation 3.3 Review of Analog IIR Filters 3.3.1 Butterworth
More informationLecture 9 Infinite Impulse Response Filters
Lecture 9 Infinite Impulse Response Filters Outline 9 Infinite Impulse Response Filters 9 First-Order Low-Pass Filter 93 IIR Filter Design 5 93 CT Butterworth filter design 5 93 Bilinear transform 7 9
More informationCMPT 889: Lecture 3 Fundamentals of Digital Audio, Discrete-Time Signals
CMPT 889: Lecture 3 Fundamentals of Digital Audio, Discrete-Time Signals Tamara Smyth, tamaras@cs.sfu.ca School of Computing Science, Simon Fraser University October 6, 2005 1 Sound Sound waves are longitudinal
More information2.161 Signal Processing: Continuous and Discrete Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Massachusetts
More informationVibration Measurements Vibration Instrumentation. MCE371: Vibrations. Prof. Richter. Department of Mechanical Engineering. Handout 11 Fall 2011
MCE371: Vibrations Prof. Richter Department of Mechanical Engineering Handout 11 Fall 2011 Overview of Vibration Measurements Follow Palm, Sect. pp 425-430 and 559-562. Additional references: Holman, J.P.,
More informationDamping of materials and members in structures
Journal of Physics: Conference Series Damping of materials and members in structures To cite this article: F Orban 0 J. Phys.: Conf. Ser. 68 00 View the article online for updates and enhancements. Related
More informationProblem Weight Score Total 100
EE 350 EXAM IV 15 December 2010 Last Name (Print): First Name (Print): ID number (Last 4 digits): Section: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO Problem Weight Score 1 25 2 25 3 25 4 25 Total
More informationSHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 6B. Notes on the Fourier Transform Magnitude
SHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 6B. Notes on the Fourier Transform Magnitude By Tom Irvine Introduction Fourier transforms, which were introduced in Unit 6A, have a number of potential
More informationWaveform Parameters. Correlation of Count Rate and Material Properties. Emission Hits and Count. Acoustic Emission Event Energy
Cumulative representations of these parameters can be defined as a function of time or test parameter (such as pressure or temperature), including: () total hits, (2) amplitude distribution and (3) accumulated
More informationAn Estimation of Error-Free Frequency Response Function from Impact Hammer Testing
85 An Estimation of Error-Free Frequency Response Function from Impact Hammer Testing Se Jin AHN, Weui Bong JEONG and Wan Suk YOO The spectrum of impulse response signal from the impact hammer testing
More informationLecture 3 - Design of Digital Filters
Lecture 3 - Design of Digital Filters 3.1 Simple filters In the previous lecture we considered the polynomial fit as a case example of designing a smoothing filter. The approximation to an ideal LPF can
More informationHomework: 4.50 & 4.51 of the attachment Tutorial Problems: 7.41, 7.44, 7.47, Signals & Systems Sampling P1
Homework: 4.50 & 4.51 of the attachment Tutorial Problems: 7.41, 7.44, 7.47, 7.49 Signals & Systems Sampling P1 Undersampling & Aliasing Undersampling: insufficient sampling frequency ω s < 2ω M Perfect
More informationGrades will be determined by the correctness of your answers (explanations are not required).
6.00 (Fall 2011) Final Examination December 19, 2011 Name: Kerberos Username: Please circle your section number: Section Time 2 11 am 1 pm 4 2 pm Grades will be determined by the correctness of your answers
More informationDOING PHYSICS WITH MATLAB FOURIER ANALYSIS FOURIER TRANSFORMS
DOING PHYSICS WITH MATLAB FOURIER ANALYSIS FOURIER TRANSFORMS Ian Cooper School of Physics, University of Sydney ian.cooper@sydney.edu.au DOWNLOAD DIRECTORY FOR MATLAB SCRIPTS maths_ft_01.m mscript used
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering Dynamics and Control II Fall 2007
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering.4 Dynamics and Control II Fall 7 Problem Set #9 Solution Posted: Sunday, Dec., 7. The.4 Tower system. The system parameters are
More informationIndex. Index. More information. in this web service Cambridge University Press
A-type elements, 4 7, 18, 31, 168, 198, 202, 219, 220, 222, 225 A-type variables. See Across variable ac current, 172, 251 ac induction motor, 251 Acceleration rotational, 30 translational, 16 Accumulator,
More informationEQUIVALENT STATIC LOADS FOR RANDOM VIBRATION Revision B
EQUIVALENT STATIC LOADS FOR RANDOM VIBRATION Revision B By Tom Irvine February 20, 2001 Email: tomirvine@aol.com Introduction A particular engineering design problem is to determine the equivalent static
More informationStep Response for the Transfer Function of a Sensor
Step Response f the Transfer Function of a Sens G(s)=Y(s)/X(s) of a sens with X(s) input and Y(s) output A) First Order Instruments a) First der transfer function G(s)=k/(1+Ts), k=gain, T = time constant
More informationECE 301 Fall 2011 Division 1 Homework 10 Solutions. { 1, for 0.5 t 0.5 x(t) = 0, for 0.5 < t 1
ECE 3 Fall Division Homework Solutions Problem. Reconstruction of a continuous-time signal from its samples. Let x be a periodic continuous-time signal with period, such that {, for.5 t.5 x(t) =, for.5
More informationUNIT - III PART A. 2. Mention any two techniques for digitizing the transfer function of an analog filter?
UNIT - III PART A. Mention the important features of the IIR filters? i) The physically realizable IIR filters does not have linear phase. ii) The IIR filter specification includes the desired characteristics
More informationANNEX A: ANALYSIS METHODOLOGIES
ANNEX A: ANALYSIS METHODOLOGIES A.1 Introduction Before discussing supplemental damping devices, this annex provides a brief review of the seismic analysis methods used in the optimization algorithms considered
More informationANALOG AND DIGITAL SIGNAL PROCESSING CHAPTER 3 : LINEAR SYSTEM RESPONSE (GENERAL CASE)
3. Linear System Response (general case) 3. INTRODUCTION In chapter 2, we determined that : a) If the system is linear (or operate in a linear domain) b) If the input signal can be assumed as periodic
More informationSHOCK RESPONSE SPECTRUM ANALYSIS VIA THE FINITE ELEMENT METHOD Revision C
SHOCK RESPONSE SPECTRUM ANALYSIS VIA THE FINITE ELEMENT METHOD Revision C By Tom Irvine Email: tomirvine@aol.com November 19, 2010 Introduction This report gives a method for determining the response of
More informationECE 301 Fall 2010 Division 2 Homework 10 Solutions. { 1, if 2n t < 2n + 1, for any integer n, x(t) = 0, if 2n 1 t < 2n, for any integer n.
ECE 3 Fall Division Homework Solutions Problem. Reconstruction of a continuous-time signal from its samples. Consider the following periodic signal, depicted below: {, if n t < n +, for any integer n,
More informationDiscrete-Time David Johns and Ken Martin University of Toronto
Discrete-Time David Johns and Ken Martin University of Toronto (johns@eecg.toronto.edu) (martin@eecg.toronto.edu) University of Toronto 1 of 40 Overview of Some Signal Spectra x c () t st () x s () t xn
More informationMultirate Digital Signal Processing
Multirate Digital Signal Processing Basic Sampling Rate Alteration Devices Up-sampler - Used to increase the sampling rate by an integer factor Down-sampler - Used to decrease the sampling rate by an integer
More informationSHOCK AND VIBRATION RESPONSE SPECTRA COURSE Unit 6A. The Fourier Transform. By Tom Irvine
SHOCK ND VIBRTION RESPONSE SPECTR COURSE Unit 6. The Fourier Transform By Tom Irvine Introduction Stationary vibration signals can be placed along a continuum in terms of the their qualitative characteristics.
More information6.003 Homework #6 Solutions
6.3 Homework #6 Solutions Problems. Maximum gain For each of the following systems, find the frequency ω m for which the magnitude of the gain is greatest. a. + s + s ω m = w This system has poles at s
More informationLecture 8 - IIR Filters (II)
Lecture 8 - IIR Filters (II) James Barnes (James.Barnes@colostate.edu) Spring 2009 Colorado State University Dept of Electrical and Computer Engineering ECE423 1 / 27 Lecture 8 Outline Introduction Digital
More informationModeling of Resonators
. 23 Modeling of Resonators 23 1 Chapter 23: MODELING OF RESONATORS 23 2 23.1 A GENERIC RESONATOR A second example where simplified discrete modeling has been found valuable is in the assessment of the
More informationExperimental Investigation of the Dynamics of a Wilberforce Pendulum
Friday 2 5 Lab 3 Experimental Investigation of the Dynamics of a Wilberforce Pendulum Barbara Hughey Lab Partner: Thalia Rubio 3/6/09 2.671 Measurement and Instrumentation Prof. Neville Hogan Abstract
More informationExperimental Modal Analysis of a Flat Plate Subjected To Vibration
American Journal of Engineering Research (AJER) 2016 American Journal of Engineering Research (AJER) e-issn: 2320-0847 p-issn : 2320-0936 Volume-5, Issue-6, pp-30-37 www.ajer.org Research Paper Open Access
More informationINSTRUMENTAL ENGINEERING
INSTRUMENTAL ENGINEERING Subject Code: IN Course Structure Sections/Units Section A Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Section B Section C Section D Section E Section F Section G Section H Section
More informationCorrelation, discrete Fourier transforms and the power spectral density
Correlation, discrete Fourier transforms and the power spectral density visuals to accompany lectures, notes and m-files by Tak Igusa tigusa@jhu.edu Department of Civil Engineering Johns Hopkins University
More informationChapter 5 Frequency Domain Analysis of Systems
Chapter 5 Frequency Domain Analysis of Systems CT, LTI Systems Consider the following CT LTI system: xt () ht () yt () Assumption: the impulse response h(t) is absolutely integrable, i.e., ht ( ) dt< (this
More information2.161 Signal Processing: Continuous and Discrete Fall 2008
MI OpenCourseWare http://ocw.mit.edu.6 Signal Processing: Continuous and Discrete Fall 008 For information about citing these materials or our erms of Use, visit: http://ocw.mit.edu/terms. Massachusetts
More informationSignals, Instruments, and Systems W5. Introduction to Signal Processing Sampling, Reconstruction, and Filters
Signals, Instruments, and Systems W5 Introduction to Signal Processing Sampling, Reconstruction, and Filters Acknowledgments Recapitulation of Key Concepts from the Last Lecture Dirac delta function (
More information10 Measurement of Acceleration, Vibration and Shock Transducers
Chapter 10: Acceleration, Vibration and Shock Measurement Dr. Lufti Al-Sharif (Revision 1.0, 25/5/2008) 1. Introduction This chapter examines the measurement of acceleration, vibration and shock. It starts
More informationEXPERIMENTAL DETERMINATION OF DYNAMIC CHARACTERISTICS OF STRUCTURES
EXPERIMENTAL DETERMINATION OF DYNAMIC CHARACTERISTICS OF STRUCTURES RADU CRUCIAT, Assistant Professor, Technical University of Civil Engineering, Faculty of Railways, Roads and Bridges, e-mail: rcruciat@utcb.ro
More informationSolutions to Problems in Chapter 4
Solutions to Problems in Chapter 4 Problems with Solutions Problem 4. Fourier Series of the Output Voltage of an Ideal Full-Wave Diode Bridge Rectifier he nonlinear circuit in Figure 4. is a full-wave
More informationCONTRIBUTION TO THE IDENTIFICATION OF THE DYNAMIC BEHAVIOUR OF FLOATING HARBOUR SYSTEMS USING FREQUENCY DOMAIN DECOMPOSITION
CONTRIBUTION TO THE IDENTIFICATION OF THE DYNAMIC BEHAVIOUR OF FLOATING HARBOUR SYSTEMS USING FREQUENCY DOMAIN DECOMPOSITION S. Uhlenbrock, University of Rostock, Germany G. Schlottmann, University of
More informationChapter 3 Data Acquisition and Manipulation
1 Chapter 3 Data Acquisition and Manipulation In this chapter we introduce z transf orm, or the discrete Laplace Transform, to solve linear recursions. Section 3.1 z-transform Given a data stream x {x
More informationVIBRATION ANALYSIS OF ROTARY DRIER
Engineering MECHANICS, Vol. 14, 2007, No. 4, p. 259 268 259 VIBRATION ANALYSIS OF ROTARY DRIER František Palčák*, Martin Vančo* In this paper the transfer of vibration from motor to the bottom group of
More informationComparison of different seat-to-head transfer functions for vibrational comfort monitoring of car passengers
Comparison of different seat-to-head transfer functions for vibrational comfort monitoring of car passengers Daniele Carnevale 1, Ettore Pennestrì 2, Pier Paolo Valentini 2, Fabrizio Scirè Ingastone 2,
More informationSTRONG -MOTION EARTHQUAKE
53 STRONG -MOTION EARTHQUAKE RECORDS P. W. Taylor* SYNOPSIS: This article reviews, at an elementary level, the ways in which information from strong-motion earthquake records may be presented. The various
More informationPatrick F. Dunn 107 Hessert Laboratory Department of Aerospace and Mechanical Engineering University of Notre Dame Notre Dame, IN 46556
Learning Objectives to Accompany MEASUREMENT AND DATA ANALYSIS FOR ENGINEERING AND SCIENCE Second Edition, Taylor and Francis/CRC Press, c 2010 ISBN: 9781439825686 Patrick F. Dunn pdunn@nd.edu 107 Hessert
More informationTransactions on the Built Environment vol 22, 1996 WIT Press, ISSN
A shock damage potential approach to shock testing D.H. Trepess Mechanical Subject Group, School of Engineering, Coventry University, Coventry CVl 5FB, UK A shock damage (excitation capacity) approach
More informationDynamic circuits: Frequency domain analysis
Electronic Circuits 1 Dynamic circuits: Contents Free oscillation and natural frequency Transfer functions Frequency response Bode plots 1 System behaviour: overview 2 System behaviour : review solution
More informationStudy of Rupture Directivity in a Foam Rubber Physical Model
Progress Report Task 1D01 Study of Rupture Directivity in a Foam Rubber Physical Model Rasool Anooshehpoor and James N. Brune University of Nevada, Reno Seismological Laboratory (MS/174) Reno, Nevada 89557-0141
More informationEach of these functions represents a signal in terms of its spectral components in the frequency domain.
N INTRODUCTION TO SPECTRL FUNCTIONS Revision B By Tom Irvine Email: tomirvine@aol.com March 3, 000 INTRODUCTION This tutorial presents the Fourier transform. It also discusses the power spectral density
More informationDynamic Analysis on Vibration Isolation of Hypersonic Vehicle Internal Systems
International Journal of Engineering Research and Technology. ISSN 0974-3154 Volume 6, Number 1 (2013), pp. 55-60 International Research Publication House http://www.irphouse.com Dynamic Analysis on Vibration
More informationVibration isolation experimental setup Part I: Experimental setup description
Vibration isolation experimental setup Part I: Experimental setup description Svetlin Stoyanov Vibration isolation experimental setup: The paper justifies the necessity to introduce the students to machinery
More informationMECH : a Primer for Matlab s ode suite of functions
Objectives MECH 4-563: a Primer for Matlab s ode suite of functions. Review the fundamentals of initial value problems and why numerical integration methods are needed.. Introduce the ode suite of numerical
More information