Exact 3D piezoelasticity solution of hybrid cross-ply plates with damping under harmonic electro-mechanical loads

Three-dimensional (3D) piezoelasticity solution is presented for the steady-state forced response of simply supported hybrid cross-ply rectangular plates with embedded or surface-bonded piezoelectric layers under electromechanical harmonic excitation with damping. For each layer, all the entities are expanded in Fourier series to satisfy the boundary conditions at the edges. The governing equations reduce to ordinary differential equations in the thickness coordinate with constant coefficients. Their general solution is obtained using state-space technique. A transfer matrix approach is presented to obtain these from the electromechanical boundary conditions at the top and bottom of the plate, the conditions of prescribed potentials and the conditions of continuity/jump at the layer interfaces. Results for the amplitude and phase lag of the central deflection are presented for an elastic plate and for hybrid composite and sandwich plates. The reduction of deflection response by actuation of a piezoelectric layer is illustrated. The present benchmark solution would help assess 2D plate theories for damped response under harmonic loads.