Development of mathematical model of a plate for active vibration suppression

摘要

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 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 approximate 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. [References: 17]