2D exact solutions for flat hybrid piezoelectric and magnetoelastic angle-ply panels under harmonic load

Abstract

A benchmark two-dimensional (2D) exact piezoelasticity solution is presented for the steady-state forced harmonic response of simply supported angle-ply laminated flat panels with embedded or surface-bonded piezoelectric layers, in cylindrical bending, under electromechanical and magneto-mechanical harmonic excitation with damping. The variables for each layer are expanded in Fourier series to satisfy the boundary conditions at the simply supported ends. The governing equations reduce to ordinary differential equations in thickness coordinates with constant coefficients. Their general solution is obtained using a state-space approach. A transfer matrix approach is presented to relate eight primary variables at the top and bottom using the electromechanical and magneto-mechanical boundary conditions at the top and bottom of the panel, 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 a hybrid piezoelastic highly inhomogeneous test panel, composite and sandwich panels, and a hybrid magnetoelastic panel. The present benchmark solution would help assess 1D panel theories for damped response under harmonic loads.