Analysis of finite deformation of curved beams bonded with piezoelectric actuating layers

Piezoelectric laminated curved beams or laminated curved smart beams, one of the most popular elements, are widely used in nano- or micro-electromechanical systems due to their excellent properties such as small volume, lightweight, and quick response. In this article, the finite deformation of piezoelectric laminated curved beams is analyzed based on Lagrangian and Eulerian description. The piezoelectric actuating character for the deflection in the curved beams bonded with piezoelectric film (polyvinylidene fluoride) driving layers is investigated. Choosing the deformed radius of curvature and tangent slope angle as fundamental parameters, the governing equations of laminated curved smart beams under static mechanical and electrical loadings are derived. First, the equilibrium equations are deduced and decoupled using the deformed angle of tangent slope as the only variant. And then the analytical solutions of laminated curved smart beams are presented using harmonic functions. Finally, the static deformations of the laminated curved smart beams are calculated by this method and the finite element method. The results exhibit good consistency and show the validation of the present method. Circular and spiral beams covered with piezoelectric layers are researched further. Effects of radius, thickness ratios, and stacking sequence on deflections of the piezoelectric laminated beams are explored as well.