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Abstract

A mathematical model of the transverse vibration of a plate to be used for free and forced vi bration control purposes is presented. For the analysis of plate flexural vibration, the eigenfunctions of a Poisson-Kirchoff plate have been used as basis functions in a Galerkin formulation. Separation of variables and a double Fourier expansion coupled with Navier's method are used to find the optimal location of the sensors/actuators. A quadratic control objective is defined as a measure of system performance. The control objective is composed of those error variables that are important to the design, and they are used to approx imate the high-order plant system by a lower order model. To guarantee that the error in the reduced model is smaller than the desired error, a minimum required number of modes in the plate model has been derived analytically.

Keywords

Plate vibration control Galerkin formulation Navier's method order reduction optimal sensors/actua tors piezoelectric active vibration actuator sensor

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Development of Mathematical Model of a Plate for Active Vibration Suppression

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