Exact 2D piezoelasticity solution of hybrid beam with damping under harmonic electromechanical load

Two dimensional piezoelasticity solution is presented for steady state forced response of simply supported hybrid beams with embedded or surface bonded piezoelectric layers under electromechanical harmonic excitation with damping. For each layer, all entities are expanded in Fourier series to satisfy the boundary conditions at the ends. The governing equations reduce to ordinary differential equations in the thickness coordinate with constant coefficients. Their general solution for each layer involves six arbitrary constants. A transfer matrix approach is presented to obtain these from the electromechanical conditions at the top and bottom of the beam, the conditions of prescribed potentials at the interfaces with piezoelectric layers, and the conditions of continuity/jump at the layer interfaces. Results for the amplitude and phase lag of the deflection are presented for composite, sandwich, and hybrid beams. The reduction of deflection response by actuation of a piezoelectric layer is illustrated. The present benchmark solution would help to assess 1D beam theories for damped response under harmonic loads.