This paper presents a mathematical modelling of a novel multiphysics (electro-mechanic coupling) problem of the shear wave propagation in laminated structures (piezoelectric - hydrogel - elastic substrate) using the wave mode method while finding the general solution for each medium. A dynamic mechanical equilibrium equation (for transverse deflection) and Maxwell equation (for electric potential) are solved in a coupled manner over each domain resulting a general closed-form solution. A specific analytical solution is then obtained enforcing the boundary conditions at the top of piezoelectric layer and the interface continuity requirements between each layer and the elastic half-space. A novel approach, to uncouple the coupled equations, is presented resulting in a final systematic solution. The effect of x coordinate (thickness) on the field variables is carefully examined for the electrically open and short cases. The jump in the stress and electric displacement components (causing delamination due to shearing mode of fracture) is present across all the interfaces due to the different bulk material constants. The key contribution of the current work is demonstrating the influence of fixed-charge concentration inside the hydrogel layer on the shear wave propagation. The present study thus provides a new concept for adjusting and controlling the elastic wave propagation in the composite structures, and provides a proper theoretical understanding of wave propagation in the damage tolerance-based design of piezotronics devices.
