Shape control of coupled nonlinear piezoelectric beams

Abstract

This paper deals with the shape control of composite laminatedbeams with nonlinear piezoelectric patch actuators. The governingelectromechanical coupled equations for nonlinear material behaviour aredeveloped for a general three-dimensional structural element using Gibbsfree energy formulation. In the analysis, nonlinearity is accounted for byincorporating enough nonlinear terms in the Gibbs free energy expression.Since many of the higher-order material properties are not available formost of the piezoelectric materials, the experimental data that areavailable for the nonlinear relationship between the electric field andthe electric displacement are used. A finite element model is developedfor the beam with piezoelectric actuators using a modified bilinearfour-noded quadratic element. The expression for the actuation voltagesrequired for shape control is then obtained by minimizing an errorfunction, which is a measure of the area between the achieved and desiredshape. The final system of coupled equations is solved by an iterativefinite element procedure. Numerical results are obtained for severalpiezoelectric patch configurations on beams with various boundaryconditions. The results show the significance of nonlinear effects in theshape control of beams with piezoelectric actuators, which has hithertonot been accounted.