Power Input to non-deterministic Subsystems via Piezoelectric Patch Actuators: Effect of the patch size and location

Many engineering systems such as aircraft and automotive are considered built-up structures, fabricated from components that are classified as deterministic subsystems (DS) and non-deterministic subsystems (Non-DS). The response of Non-DS is sensitive to uncertainties therefore presents problems in vibration control. Therefore, analytical solution to estimate average power delivered by a piezoelectric (PZT) patch actuator when attached to a Non-DS needs to be established. The response of Non-DS is estimated using statistical modelling technique such as statistical energy analysis (SEA), in which any external input to the subsystem must be represented in terms of power input. In this paper, ensemble average of power given by a PZT patch actuator to a simply-supported plate when subjected to structural uncertainties is studied using Lagrangian method. The effects of size and location of the PZT actuators on the power delivered to the plate are investigated. It is found that changing the patch location on the structure will not affect the average power supplied while changing the patch size will change the power magnitude proportionally but with some variations at higher frequency.