Forced vibration analysis of bi-axially pre-stressed piezoelectric plates under a harmonic point load

In this paper, a discussion on the forced vibration of a transversely isotropic piezoelectric plate with finite dimensions subjected to a time-harmonic force resting on a rigid foundation is carried out. Here, we assume that the plate is poled along the perpendicular surface and bi-axial initially stressed in their reference configuration. The three-dimensional linearized theory of electro-elastic waves in initially stressed bodies (TLTEEWISB) is applied to the initially-stressed piezoelectric plate. A general formulation of the governing equations of motions is provided according to the piece-wise homogeneous body model, and then the three-dimensional finite element modeling (3D-FEM) is developed as a solution procedure in terms of weak formulation and virtual work principle. The objective of this paper is to present the results regarding the frequency response of the piezoelectric rectangular plate and the influence of the initial stress factor on the system. Numerical examples imply that while the increasing aspect ratio of the plate prevents the resonance mode of the dynamic force, the increasing thickness ratio exceeds this mode. Further, it is also demonstrated and discussed in detail that the initial stress state has a considerable influence on this mode.