An improved displacement boundary condition of piezoelectric cantilever beams

Abstract

Based on the linear piezoelectric theory, three kinds of displacement boundary conditions are used to study the deformations of piezoelectric cantilever beams. The first two conditions are conventional simplified displacement boundary conditions, and the third one is an improved boundary condition determined by the least-squares method. Two load cases and six slenderness ratios of cantilever beams are investigated. Solutions are given by both the conventional boundary conditions and the improved boundary condition, and are then compared with solutions by finite element method. Results from the improved boundary condition are found to be much better than those from the conventional displacement boundary conditions especially for short beams. Among the three displacement boundary conditions of the fixed end, the boundary condition determined by the least-squares method is proved to be the most effective boundary condition.