An efficient coupled zigzag theory for dynamic analysis of piezoelectric composite and sandwich beams with damping

Abstract

An efficient new coupled zigzag theory is developed for dynamics of piezoelectric composite and sandwich beams with damping. Third order zigzag approximation is used for the axial displacement. The electric field is approximated as piecewise linear for the sublayers. The conditions of zero transverse shear stress at the top and bottom and its continuity at the layer interfaces, are for the first time enforced exactly in this theory. Using these conditions, the displacement field is expressed in terms of three primary displacement variables and potentials. The governing equations are derived from Hamilton's principle. Analytical solutions of simply-supported beams are obtained for natural frequencies and steady state forced response under harmonic electromechanical load with damping. These are compared with the exact two-dimensional piezoelasticity solution and the uncoupled first order shear deformation theory (FSDT) solution. The new results of forced damped response are more accurate than the FSDT solution and agree very well with the exact solution for both thin and thick hybrid beams. The developed theory adequately models open and closed circuit electric boundary conditions to accurately predict the response.