Precise deflection analysis of laminated piezoelectric curved beam

The piezoelectric laminated curved beams are currently one of the most popular elements used in nano- or micro-electromechanical systems because of the fact that the piezoelectric driving parts are small, lightweight, and quick response. This article presents an analytical model of the piezoelectric laminated curved beams with variant curvature. And the influence of secondary converse piezoelectric effect on the deflection of the curved beams fully covered with piezoelectric actuators is investigated. Using the radius of curvature and the tangent slope angle of the laminated curved beam as the basic parameters, the quantities of rotation angle, radial, and tangential displacements are decoupled and expressed as harmonic functions. The results of the isotropic curved beams are compared with the existing solutions and the data show the validation of the present method. The presented method can be used to analyze the curved piezoelectric beams being any curve. Some closed-form solutions of circular beams fully covered with piezoelectric layers are presented. Two kinds of ply angle (0/θ) and (θ'θ) are investigated in this article. The effects of aspect ratio, thickness ratio, and stacking sequence on the characters of the piezoelectric laminated circular beams with and without secondary converse piezoelectric effect are explored.