##### From Harris' Shock and Vibration Handbook

## MODAL PARAMETER ESTIMATION

Modal parameter estimation, or modal identification, is a special case of system identification where the a priori model of the system is known to be in the form of modal parameters. *Modal parameters* include the complex-valued modal frequencies ? _{ r}, modal vectors { ? _{ r}}, and modal scaling (modal mass or modal *A*). Additionally, most algorithms estimate modal participation vectors { *L* _{ r}} and residue vectors { *A* _{ r}} as part of the overall process.

Modal parameter estimation involves estimating the modal parameters of a structural system from measured input-output data. Most modal parameter estimation is based upon the measured data being the frequency response function or the equivalent impulse-response function, typically found by inverse Fourier transforming the frequency response function. Therefore, the form of the model used to represent the experimental data is normally stated in a mathematical frequency response function (FRF) model using temporal (time or frequency) and spatial (input degree-of-freedom and output degree-of-freedom) information.

In general, modal parameters are considered to be global properties of the system. The concept of global modal parameters simply means that there is only one answer for each modal parameter and that the modal parameter estimation solution procedure enforces this constraint. Every frequency response or impulse-response function measurement theoretically contains the information that is represented by the characteristic equation, the modal frequencies, and damping. If individual measurements are treated as independent of one another in the solution procedure, there is nothing to guarantee...

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MODAL DATA PRESENTATION/VALIDATION Once the modal parameters are determined, there are several procedures that allow the modal model to be validated. Some of the procedures that are used are...

MODAL ANALYSIS THEORY While modal analysis theory has not changed over the last century, the application of the theory to experimentally measured data has changed significantly. The advances of...

EXPERIMENTAL MODAL ANALYSIS METHODS In order to understand the various experimental approaches used to determine the modal parameters of a structure, some sort of outline of the various techniques is...

MODAL DATA ACQUISITION Acquisition of data that are used in the formulation of a modal model involves many important technical concerns. The primary concern is the digital signal processing, or the...

Randall J. Allemang, David L. Brown INTRODUCTION Experimental modal analysis is the process of determining the modal parameters (natural frequencies, damping factors, modal vectors, and modal...