Nonlinear deformations of piezoelectric composite beams

Abstract

This study presents large deformations of slender elastic and viscoelastic beams with multiple piezoelectric patches attached on their top and bottom surfaces. The slender beams can undergo large in-plane 2-D deformations due to electric fields applied through the piezoelectric patches and mechanical actuations. A nonlinear electro-mechanical constitutive equation is considered for the piezoelectric patches, while linear elastic and viscoelastic constitutive equations are used for the beams. Reissner’s finite-deformation beam theory is adopted in formulating the large 2-D deformation, and modified in order to incorporate the deformation due to the electric field input. For an elastic beam, closed form solutions are obtained for the deformations of the beam under electric field actuation, while a nonlinear shooting method is used to analyze the deformation of the beam under both electrical- and mechanical stimuli. For viscoelastic beams, time-dependent deformations of the beams under electric field actuations through the piezoelectric patches are solved numerically. By applying electric fields with different amplitude at different locations of patches, desired deformed shapes in active flexible beams can be achieved, which is useful for analyses and designs of active foldable systems. This study also highlights the effect of viscoelastic materials on the shape changes in foldable electro-active beams.