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The purpose of this study is to suggest a new formulation for active vibration control of a rectangular plate based on the optimal positions/orientations of piezoelectric actuators/sensors attached to the plate. The free vibration and modal properties are derived by using Rayleigh–Ritz and the transient response by assumed modes methods based on the classical plate theory. Three criteria are proposed for optimal location of piezoelectric patches attached to the simply supported plate. In other words, the optimal positions/orientations of piezoelectric patches can be determined based on spatial controllability/observability gramians of the structure, as well as the consideration of residual modes to reduce the spillover effect. These criteria are used to achieve the optimal fitness function defined for a genetic algorithm optimizer to find the optimal locations/orientations of piezoelectric sensors/actuators. To control the vibrations of the plate, a negative velocity feedback control algorithm is designed. The results of simulations indicate that by locating piezoelectric patches in the optimal positions, the depreciation rate of the structure increases and the amplitudes of the plate vibrations reduce effectively. The effect of number of piezoelectric devices on the active damping property of the system is also analyzed.

Optimal configuration of piezoelectric sensors and actuators for active vibration control of a plate using a genetic algorithm