Modeling of piezoelectric materials on rubber beams

It is common to use piezoelectric materials to reduce vibrations or otherwise alter the dynamics of structures made of metal or composite materials. In contrast, this work addresses modeling of piezoelectric patches applied to a rubber substrate. An underlying goal of modeling, however, is to represent the significant physics of a problem with the simplest model possible. There were several simplified approaches to modeling piezoelectric actuation on classical beam and plate elements developed in the late 1980's and early 1990's. Of these, the "pin force," "extended pin force," and "Euler-Bernoulli" methods are assessed in this study. The basic concepts of the three approximation methods are developed, and the curvatures predicted by each is compared to predictions from a special-purpose finite element code. The final conclusion is that the constant-strain approaches (pin force and enhanced pin-force) are not accurate for very soft substrates. Future work includes adding the time dependence of rubber materials as well as the possibility of material of geometric nonlinearities.