Optimal placement of sensors and actuators for active vibration reduction of a flexible structure using a genetic algorithm based on modified Hinfinity

This paper is concerned with active vibration reduction of a square isotropic plate, mounted rigidly along one edge to form a cantilever. Optimal placement of ten piezoelectric sensor/actuator pairs is investigated using a genetic algorithm to suppress the first six modes of vibration. A new objective function is developed based on modified Hinfinity to locate the sensor/actuator pairs. The plate, with piezoelectric sensor/actuator pairs bonded to its surfaces, is modelled using the finite element method and Hamilton's principle based on first order shear deformation theory including bending, membrane, and shear deformation effects. The effects of piezoelectric mass, stiffness and electromechanical coupling are taken into account. The first six natural frequencies are validated by comparison with the finite element ANSYS package using two dimensional SHELL63 and three dimensional SOLID45 elements and also experimentally. Vibration reduction for the cantilever plate with piezoelectric patches bonded in the optimal location was investigated to attenuate the first six modes of vibration using a linear optimal control scheme. The new fitness function has reduced the computational cost and given greater vibration reduction than other previously published results.