Forced vibration of the hydroelastic system consisting of an axially moving plate made of PZT Material, a compressible viscous fluid and a rigid wall

This study addresses a fundamental gap in the existing literature by developing a comprehensive hydro-electro-elastic model for the forced vibration of an axially moving piezoelectric (PZT) plate interacting with a compressible viscous fluid layer bounded by a rigid wall. The primary novelty of this work lies in the rigorous mathematical coupling of three distinct physical phenomena—axial transport mechanics, electromechanical transduction, and fluid viscosity—which have not been treated simultaneously in any prior study. Unlike previous works that rely on simplified inviscid assumptions or approximate plate theories, the present model solves the interaction simultaneously utilizing the exact equations of linear electro-elastodynamics and the linearized Navier-Stokes equations. It is further worth noting that when the electromechanical coupling effect is neglected, the model inherently reduces to the case of an anisotropic elastic structure, thereby demonstrating the robustness and generality of the proposed analytical framework. By transitioning from conventional stationary and inviscid approximations to a fully coupled, moving, and viscous formulation, this research is capable of capturing resonance frequency shifts and interface stress distributions that are otherwise entirely missed by classical models. The mathematical problems are solved using a discrete analytical method and the exponential Fourier transform. Numerical results explore the frequency response of the interface stress, electromechanical coupling, and the “gyroscopic” effect caused by simultaneous motion and vibration. Additionally, the occurrence of resonance-type cases and the influence of problem parameters on these responses are discussed.