An asymptotic approach for the analysis of piezoelectric fiber composite beams

Abstract

An asymptotic-expansion-method-based approach is developed to analyze piezoelectricfiber composite beams by employing the virtual work principle. Starting from thethree-dimensional linear piezoelectricity, a microscopic two-dimensional model and amacroscopic one-dimensional model are systematically derived by taking advantage of theslenderness of the beam. This enables us to derive a sophisticated yet efficient tool for themodeling and analysis of piezoelectric fiber-based composites, which can provide us withgood physical insights on the behavior of slender adaptive structures in terms of actuationand sensing. The non-classical boundary conditions of the beam are obtained by applyingthe orthogonality of asymptotic displacements to the beam fundamental solutions. Theaccuracy and efficiency of the proposed approach are demonstrated by comparing itsanalytical/numerical predictions with the experimental results, three-dimensional finiteelement solutions, and one-dimensional beam solutions obtained by the classical rule ofmixture.