MODULE 10 EXPERIMENTAL MODAL ANALYSIS Most vibration problems are related to resonance phenomena where operational forces excite one or more mode of vibration. Modes of vibration which lie within the frequency range of the operations dynamic forces, always represent potential problems. An important property of modes is that any dynamic response (forced or free) of a structure can be reduced to a response of discrete set of modes.

2DOF.SLDASM DISCRETE SYSTEMS

multi pendulum.SLDASM DISCRETE SYSTEMS

1 st mode 2 nd mode 3 rd mode 4 th mode 5 th mode LEGO.SLDASM DISTRIBUTED SYSTEMS Experimental analysis to follow

Experiment 4 Shaker LEGO

Detailed geometrySimplified geometry Experiment 4 Shaker LEGO

Modulus of elasticity as for the ABS plastic Material density has been adjusted so that the simplified block have the same mass as real blocks 2.323g 1.261g Experiment 4 Shaker LEGO

The first vibration mode in the direction of excitation lego cantilever.SLDASM Note that there are gaps between blocks indicated by red arrows. Experiment 4 Shaker LEGO

pan.SLDPRT 1 st mode 2 nd mode 3 rd mode 4 th mode 5 th mode 6 th mode DISTRIBUTED SYSTEMS

The modal parameters are: Modal frequency Modal shape Modal damping Modal parameters represent the inherent properties of a structure which are independent of any excitation. Modal analysis is the process of determining all the modal parameters which is sufficient for formulating a mathematical model of a dynamic response. Modal analysis may be accomplished either through analytical, numerical or experimental techniques. EXPERIMENTAL MODAL ANALYSIS

EXPERIMENTAL MODAL ANALYSIS EXCITATION TECHNIQUES Impact testing

EXPERIMENTAL MODAL ANALYSIS EXCITATION TECHNIQUES Impact testing

EXPERIMENTAL MODAL ANALYSIS EXCITATION TECHNIQUES Impact testing

EXPERIMENTAL MODAL ANALYSIS EXCITATION TECHNIQUES Shaker testing

EXPERIMENTAL MODAL ANALYSIS EXCITATION TECHNIQUES Shaker testing

EXPERIMENTAL MODAL ANALYSIS EXCITATION TECHNIQUES Shaker testing

EXPERIMENTAL MODAL ANALYSIS EXCITATION TECHNIQUES Shaker testing

Note: sine excitation is NOT the only one available SHAKERS Shaker can provide both force and base excitation

shaker.sldprt SHAKERS

pan.SLDPRT Mode 1 Mode 2 Shakers

Experimental kit to demonstrate modes of vibration of a cantilever beam Mode 13.5Hz Mode 2 23Hz Mode 3 63Hz Mode 4127Hz CANTILEVER BEAM EXPERIMENT

CANTILEVER BEAM ANALYTICAL SOLUTION

cantilever beam MME9500.SLDPRT This model should give the same results as the experiment in previous slide. CANTILEVER BEAM NUMERICAL SOLUTION

Mode 1Mode 2Mode 3Mode 5 Where is Mode 4 ? CANTILEVER BEAM NUMERICAL SOLUTION

Most common means of Implementing the excitation Non-attached exciters Hammers Pendulum impactors Attached exciters Shakers Eccentric rotating devices EXPERIMENTAL MODAL ANALYSIS Hammers The excitation is transient The duration and thus the shape of the spectrum of the impact is determined by the mass and stiffness of both the hammer and the structure. For a relatively small hammer used on a hard structure, the stiffness of the hammer determines the spectrum.

Force excitation time historybase 010.sldprt Fixed geometry 1000N

Force excitation time historybase 010.sldprt Fixed geometry 500N UzUy

Fourier beam.sldprt Response time history It is not immediately obvious what frequencies are present in the response Transformation from the time to the frequency domain (Fourier transformation) Response spectrum In the frequency domain it is clear that two frequencies have been excited: 8Hz and 53Hz

The Fourier transform is a mathematical operation that decomposes a signal into its constituent frequencies. Thus the Fourier transform of a musical chord is a mathematical representation of the amplitudes of the individual notes that make it up. The original signal depends on time, and therefore is called the time domain representation of the signal, whereas the Fourier transform depends on frequency and is called the frequency domain representation of the signal. The term Fourier transform refers both to the frequency domain representation of the signal and the process that transforms the signal to its frequency domain representation.musical chordtimetime domainfrequency domaintransforms FOURIER TRANSFORM

What is a Fourier Transform? A Fourier Transform is a mathematical operation that transforms a signal from the time domain to the frequency domain. We are accustomed to time-domain signals in the real world. In the time domain, the signal is expressed with respect to time. In the frequency domain, a signal is expressed with respect to frequency. What is a DFT? What is an FFT? What's the difference? A DFT (Discrete Fourier Transform) is simply the name given to the Fourier Transform when it is applied to digital (discrete) rather than an analog (continuous) signal. An FFT (Fast Fourier Transform) is a faster version of the DFT that can be applied when the number of samples in the signal is a power of two. An FFT computation takes approximately N * log2(N) operations, whereas a DFT takes approximately N2 operations, so the FFT is significantly faster. FOURIER TRANSFORM

Continuous function Discrete function

Fourier beam.sldprt

Mode 1 4.5Hz 0.22s Mode 1 26Hz 0.038s Mode 3 42Hz 0.023s Mode 4 75Hz 0.013s

Fourier beam.SLDPRT Study 01dtimpulse duration

Study 01dt Response time historyFFT of response time history Only mode 1 and mode 2 are excited. Larger impulse (longer duration) caused larger displacement amplitude response

Fourier beam.SLDPRT Study 02dtimpulse duration 0.05

Study 02dt Response time historyFFT of response time history Only mode 1 is excited. Larger impulse (longer duration) caused larger displacement amplitude response

Study 03dtimpulse duration

Study 03dt Response time historyFFT of response time history Mode 1 and mode 2 are excited.

Study 04dtimpulse duration

Study 04dt Response time historyFFT of response time history Mode 1 and mode 2 are excited.

Fourier beam.SLDPRT Study 05dtimpulse duration 0.05 Based on one mode only 1% damping

How to excite mode 3- side hit How to excite mode 4? Hit here! and here!

The format is: freq(Hz)real amplitude (units)imaginary amplitude (units) fft_half.outdouble sided half amplitude magnitude fft_full.outsingle-sided full amplitude output fft_full_mpfull amplitude magnitude & phase output

fourier.exe or fft.exe can be used

elipse.sldprt in /vibration experiments PREPARATION FOR LAB

hex.sldprt in /vibration experiments PREPARATION FOR LAB

tree.sldprt in /vibration experiments