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Theoretical andExperimental Modal Analysis

Topics:

• Experimental and theoretical routes

• Introduction to model testing, vibration testing

• Models of vibrating structures

• Spatial model

• Modal model and

• Response model

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Introduction

Modal analysis is a method to describe a structure in terms of itsnatural characteristics which are the frequency, damping andmode shapes – its dynamic properties.

Theoretical [ Finite Element Analysis (FEA) ] and ExperimentalModal Analysis (EMA) have been very separate engineeringactivities aimed at solving above mentioned common problem.Now the two technologies are converging and powerful new toolsfor solving noise and vibration problems are emerging as aresult.

o Modal analysis involves process ofdetermining the modal parameters ofa structure to construct a modalmodel of the response

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Experimental and theoretical routes

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Experimental and theoretical routes

• The modal parameters may be determined by analytical means,

such as finite element analysis, and one of the common reasons

for experimental modal analysis is the verification/correction of

the results of the analytical approach (model updating).

• Often, though, an analytical model does not exist and the modal

parameters determined experimentally serve as the model for

future evaluations such as structural modifications.

• Predominately, experimental modal analysis is used to explain a

dynamics problem, vibration or acoustic, that is not obvious from

intuition, analytical models, or previous similar experience.

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Theoretical andExperimental Modal Analysis

Topics:

• Experimental and theoretical routes

• Introduction to model testing, vibration testing

• Models of vibrating structures

• Spatial model

• Modal model and

• Response model

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Introduction to Modal Testing

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Introduction to Modal Testing

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Introduction to Modal Testing

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Introduction to Modal Testing

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Introduction to Modal Testing

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Introduction to Modal Testing

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Modal Testing ( Linearity Assumption )

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Modal Testing

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Anatomy of FFT analyzer

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Modal Testing

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CURVE FITTING METHODSAll curve fitting methods fall into one of the followingcategories,

o Local SDOFo Local MDOFo Globalo Multi-Reference (Poly Reference)

• SDOF methods estimate modal parameters one mode at atime.

• MDOF, Global, and Multi-Reference methods cansimultaneously estimate modal parameters for two or moremodes at a time.

Curve Fitting Methods

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Curve fitting technique [ Peak picking method ]• Modal Damping as Peak Width

• The width of the resonance peak is a measure of modaldamping. The resonance peak width should also be the same forall FRF measurements, meaning that modal damping is thesame in every FRF measurement.

• The width is actually measured at the so-called half powerpoint, and is approximately equal to twice the modal damping (inHz).

• Mode Shape From Quadrature Peaks• From (displacement/force) or (acceleration/force) FRFs, the peak

values of the imaginary part of the FRFs are taken ascomponents of the mode shape.

• This is called the Quadrature method of curve fitting. From(velocity/force) FRFs, the peak values of the real part are usedas mode shape components.

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Curve fitting technique [ Peak picking method ]

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Curve fitting techniques [ Circle fit ]

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Local MDOF MethodsThe Complex Exponential and the Rational Fraction Polynomial methods

Complex Exponential (CE)This algorithm curve fits and analytical expression for a structural impulseresponse to experimental impulse response data. A set of impulse responsedata is normally obtained by applying the Inverse FFT to a set of FRFmeasurements, as shown in Figure .

Curve fitting techniques

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Rational Fraction Polynomial (RFP)This method applies the rational fraction polynomial expression shown inFigure directly to an FRF measurement. Its advantage is that it can be appliedover any frequency range of data, and particularly in the vicinity of a resonancepeak.

Curve fitting techniques

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Curve fitting techniques

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Theoretical andExperimental Modal Analysis

Topics:

• Experimental and theoretical routes

• Introduction to model testing, vibration testing

• Models of vibrating structures

• Spatial model

• Modal model and

• Response model

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Models of vibrating structures

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Acknowledgements

• Contents for some of the slides of the presentation have been taken from the B& K Application notes