Optimized Design of Piezoelectric Flap Actuators for Active Flow Control

Piezoelectric ?ap actuators are often used in active ?ow-control applications. However, effective design tools are lacking in the ?ow-control community. This paper discusses theoretical modeling, experimental validation, and optimal design of piezoelectric unimorph and bimorph ?ap actuators. First, two different ?nite element models are described. One is a simple beam model that assumes a perfect bond exists between the piezoelectric patch and the shim, whereas the second incorporates a linear elastic shear element for the bond layer. These models are then used to predict the magnitude of the dc response (tip displacement per unit applied voltage) and the natural frequency (a measure of the bandwidth) of these actuators. Next, an approximate analytical model is developed to facilitate design optimization. The models are compared with experimental data obtained from a parametric study in which 10 otherwise identical unimorph piezoelectric actuators with varying piezoelectric patches are fabricated and characterized using a laser displacement sensor. All models produce estimates that are accurate to within +/- 15% and +/- 10% for the dc response and natural frequency, respectively. The analytical model is also extended to bimorph actuators. Finally, a general design optimization procedure is presented, and representative results are provided.