The Effects of Symmetry on Optimal Transducer Location for Active Vibration Control

Abstract

In this article, the global optimal configuration of sensors and actuators has been investigated for active vibration reduction of plates with symmetrical and asymmetrical geometries and boundary conditions. An isotropic plate element stiffened by beam elements on its edges and with piezoelectric sensor/actuator pairs bonded to its surfaces is modeled, using Hamilton’s principle and the finite element method taking into account piezoelectric mass, stiffness and electromechanical coupling effects. The modeling is based on Mindlin-Reissner plate and Timoshenko beam theories. Optimization is obtained by means of a genetic algorithm using minimization of linear quadratic index is taken as an objective function. The program is written in Matlab m-code and incorporates results from an ANSYS finite element model of the basic structure to take the effects of the first six modes of vibration collectively. The plates with different boundary conditions and geometries are represented by the ANSYS package using two dimensional shell63 elements and three dimensional soild45 elements for the passive structure, and solid5 elements for the active piezoelectric components. The first six modes of vibration are validated experimentally. The genetic algorithm is used to obtain optimal placement of eight and ten piezoelectric sensor/actuator pairs to suppress the first six modes of vibration, investigating the effects of plate boundary conditions and geometry on the optimal distribution of piezoelectric actuators. It is shown that structures with symmetrical geometries and boundary conditions have optimal transducer locations distributed with the same axes of symmetry.