# Finite element-based system identification from experimental modal analysis results

#### Abstract

A process is developed to determine the physical attributes of a structure from experimental measurements of the natural frequencies of vibration and the corresponding mode shapes of the structure. The process is based upon minimization of a least squares measure of the difference between the measured vibrational characteristics and those characteristics determined from a finite element model of the structure. The solution is given by the parameters of the finite element model which yield a minimum least squares difference in the two sets of modal data. The accuracy of the solution is affected by the error in the finite element model and by the error in the experimental data. Procedures are given for minimizing the error introduced by the finite element model. The error in the experimental data is caused by non-controllable factors; therefore, its effect is minimized by using as much experimental data as possible. A conflict arises when determining the number of modes to include in the analysis because the effect of the finite element error increases as the number of modes increases but the effect of the experimental error decreases as the number of modes increases. A complete procedure for determining the physical attributes is developed. The procedure starts with the collection of experimental data, includes information on the development of an accurate finite element model and ends with a description of a computer algorithm for an efficient solution of the problem. Three examples are included to demonstrate the effectiveness of the stated system identification procedure.

#### Degree

Ph.D.

#### Advisors

Starkey, Purdue University.

#### Subject Area

Mechanical engineering

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