Transition Behavior in Large Deflection of Simply Supported Plate with Piezoelectric Patches under Pretension

The transition behavior of a simply supported circular plate embedded with symmetric piezoelectric patches under pretension in large deflection due to lateral load is studied, von Karman's large deflection theory is employed but extended to a layered case that accounts for piezoelectric force terms. For a primary insight, however, a simplified linear case is considered to deal with a modified Bessel or standard Bessel equation for the lateral slope, depending on the relative magnitude of the piezoelectric load. The associated analytical solutions are developed following the boundary conditions of simply support ends and the interface continuity between the piezoelectric layered boss and the annular area. A further integration is carried out to obtain the expressions for lateral deflection and thus which at the center of the patched plate. The behavior of how the center deflection varies with the increase of pretension is thoroughly illustrated to show the transition behavior, i.e., how the bossed plate transfers from a plate mode to a membrane mode as the pretension proceeds. The developed approach is implemented with typical silicon-based materials commonly used for a sensing or actuating device. An extensive parametric study is conducted to explore the effects of varying the dimension of the patched region and applied voltage across the piezoelectric patches. The results indicate that, piezoelectric effect appears to be present only in a low pretension regime. In this case, the higher the applied voltage, the easier the plate under pretension may transmit to the membrane mode. Moreover, varying the radial size of the patched region may have a substantial effect on the transition behavior, as well, in a low pretension condition.