Overview

ABOUT THE COURSE:This course is about the fundamentals and basic concepts of Experimental Modal Analysis (EMA) and its applications. EMA, also known as Modal Testing, is a technique for experimentally determining the natural frequencies, mode shapes, and damping factors of a physical system or structure. One primary application of EMA is for the avoidance of resonant operation and troubleshooting vibration and noise problems. Another important application is in validating and updating structural dynamic FE models. EMA also enables deriving an experimental mathematical model of a physical system, which can be used for response simulation, force identification, structural modification, and structural control. The course will start from the theoretical basis of EMA, followed by signal processing for modal analysis. Then it will cover how the frequency and impulse response functions (FRFs and IRFs) can be measured by exciting the structure and measuring the input force and output response and how the modal parameters can be estimated from these measured FRFs and IRFs. In the end, the course will briefly cover Phase resonance testing, Operational Modal Analysis, and applications of EMA.INTENDED AUDIENCE:• Masters and doctoral students from Mechanical, Aerospace, Automotive, Civil, and Naval architecture disciplines• Undergraduate students of the above disciplines in their third and final year can also take this course as an elective• Practicing engineers working on modal analysis and testing, vibration and noise• Teachers interested in modal analysisPREREQUISITES: Students with a Bachelor’s degree or in their third or final year of Mechanical, Aerospace, Automotive, Civil engineering, and Naval architectureINDUSTRY SUPPORT: Automotive, aerospace, machine tool, and marine industries; Modal testing is widely used in many other industries, and they also may be interested.

Syllabus

Week 1: Introduction, need and applications of EMA, lumped parameter models, Analytical modal analysis of SDOF undamped and damped systems; Free and forced response, FRFWeek 2:Analytical modal analysis of undamped and damped MDOF systems; eigenvalue problem (EVP), free response, Forced response, FRF matrix, modal space, modal responseWeek 3:IRF, Convolution integral, FRF characteristics, FRF types, FRF Plots, stiffness and mass lines; modal contributions; antiresonancesWeek 4:Signal processing for experimental modal analysis, Fourier series, Fourier transform, Discrete Fourier Series, Discrete Fourier transformWeek 5:Time sampling; aliasing, sampling theorem, quantization, windowing; window functions, random signals, correlation, spectral density, white noiseWeek 6:FRF measurement with an impact hammer, FRF estimation, Impact hammer, response measurement, accelerometer, mounting and selection, LDVWeek 7:Auto and cross spectrums, H1- H2 estimates, spectrum averaging, coherence function, FRF measurement simulation, boundary conditions, calibrationWeek 8:FRF measurement with shaker, electromagnetic shaker, shaker-structure interaction, force transducer, impedance head; FRF measurement simulation, pseudo-random, periodic random, burst random, chirp excitationWeek 9:Modal parameter estimation using SDOF curve fitting, Peak-picking method, Circle fit method, Line fit, residualsWeek 10:Modal parameter estimation using MDOF curve fitting, RFP, Global method, Complex exponential method, Stabilization diagram, SVD, Eigensystem realization algorithm Week 11:Phase resonance testing, Operational modal analysis Week 12:EMA applications, local structural modification, Response simulation, Force identification, Coupled structural analysis, MAC correlation, FE Model validation and updating