Mechanics of surface wave propagation in a pre‐stressed and functionally graded piezoelectric‐hydrogel‐viscoelastic composite layered structure

Abstract This study introduces a mathematics‐based mechanics framework to analyze the surface wave propagation in a pre‐stressed and functionally graded composite structure while focusing on the internal field variables evolution, such as the stress field. It further explores the potential shear deformation of the composite, which comprises a pre‐stressed hydrogel layer bonded between a pre‐stressed functionally graded piezoelectric material layer and a pre‐stressed functionally graded viscoelastic substrate, effectively representing a potential micro‐electro‐mechanical system. Time‐dependent force balance equations in the ‐direction and Maxwell's equations for electric potential are solved within each domain, leading to a general analytical solution. Two sets of boundary conditions, considering the influence of inter‐layer adhesive material on the macro‐scale force equilibrium, resulting in separate analytical solutions for each medium using the wave mode method. The final system of equations is solved using the classical Newton‐Raphson method by uncoupling the coupled equations. The study examines the impact of various parameters on the field variable distribution, highlighting the coupled nature of the proposed analytical solution. It is concluded that gradient factors, pre‐stress, and fixed‐charge concentration within the pH‐sensitive hydrogel significantly influence surface wave propagation, leading to severe distortion of the hydrogel layer in a specific plane. This approach offers novel insights into the mechanics of multi‐layered composite systems and has potential applications in the design of vibration‐damping foundations, seismic isolation systems, and MEMS devices.