Optimization of clamped circular piezoelectric composite actuators

Abstract

This paper addresses the design of clamped circular piezoceramic composite unimorph and bimorph configurations, specifically the conflicting requirements of maximum volume displacement for a prescribed bandwidth. An optimization problem is formulated that implements analytical solutions for unimorph and bimorph configurations using laminated plate theory, including the use of oppositely polarized piezoceramic patches. A range of actuator geometric parameters are studied, and bounds for volume displacement and natural frequency of optimal designs are determined and presented via design curves. In the selected design space, Pareto optimization results for unimorph and bimorph configurations show that optimal volume displacement is related to the bandwidth by a universal power law such that the product of the square of the natural frequency and the displaced volume, a “gain-bandwidth” product, is a constant. Characteristic trends are also described that are independent of the actuator radius for the Pareto optimal piezoceramic patch thickness and radius versus normalized bandwidth. The results are relevant, for example, in the design of zero-net mass-flux or synthetic jet actuators used in flow control applications.