Coupled Consistent Third-order Theory for Hybrid Piezoelectric Composite and Sandwich Beams

Abstract

A new coupled consistent third-order theory (CTOT) is presented which, unlike the existing third-order theory (TOT), satisfies exactly the shear traction-free conditions at the top and bottom of a hybrid beam for any electrical boundary condition. The potential field is discretized layerwise as piecewise linear. The axial and transverse electric fields are considered. The deflection is approximated as uniform across the thickness and the longitudinal displacement is approximated as a third-order variation. The field equations and the boundary conditions are derived from the Hamilton’s principle. Analytical solutions are obtained for simply-supported beams for static and harmonic electromechanical load, and for natural frequencies. The theory is assessed by comparing the results with 2D exact piezoelasticity solution.