Two‐dimensional transient analysis of in‐plane vibration in rectangular plates of piezoelectric ceramics

Abstract

AbstractIn‐plane vibration in rectangular plates of piezoelectric ceramics which were polarized along the direction of plate thickness was investigated by two‐dimensional transient analysis. In this analysis, it was assumed that both the top and bottom surfaces of the rectangular ceramic plates were electroded entirely and the four‐edge surfaces were not constrained. The spatial network method was employed for numerical analyses. Transient responses were evaluated numerically first for the cases where stepwise input voltages were applied to square plates.In‐plane wave motion and displacements of free edges were calculated. The results indicate the following behaviors: 1) a longitudinal wave is created at the free edge and propagates along the surface of the plate; 2) a part of the longitudinal wave is transformed to a shear wave at a free boundary parallel to the direction of the wave propagation; and 3) these two waves experience repeated reflections at the free boundaries and thus form a complicated vibration. Transient responses of a rectangular ceramic plate were analyzed next. Prior to the analysis, the vibratory behaviors of the rectangular plate were predicted approximately based on the results for the square plate. The detailed numerical analyses performed could confirm the validity of the predictions.