Development of mathematical model of a plate for active vibration suppression

A mathematical model of the transverse vibration of a plate to be used for free and forced vibration control purposes is presented. For the analysis o f 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 u sed to find the optimal location of the sensors/actuators. A quadratic cont rol objective is defined as a measure of system performance. The control ob jective is composed of those error variables that are important to the desi gn, and they are used to approximate the high-order plant system by a lower order model. To guarantee that the error in the reduced model is smaller t han the desired error, a minimum required number of modes in the plate mode l has been derived analytically.