Active control of nonlinear piezoelectric circular shallow spherical shells

Nonlinear electromechanics and active control of a piezoelectric laminated circular spherical shallow shell are quantitatively investigated in this paper. It is assumed that the piezoelectric layers are uniformly distributed on the top and the bottom surfaces of the shell and the thickness of piezoelectric layers is much thinner than that of the shell. The governing equations for the nonlinear dynamics of active control of the circular spherical shallow shell with piezoelectric actuator are formulated and a semi-analytical method is employed to solve the nonlinear governing equations. The numerical results show that the con®guration of nonlinear deformation and the natural frequency of the shell structures can be actively controlled by means of high control voltages across the piezoelectric layers and the jumping phenomenon may occur for the case of geometrical parameter g ˆ ‰3…1 ÿ m2†Š1=2f=he1. In addition the e€ect of large amplitude on the vibrating frequency is discussed by the Galerkin method and the KBM perturbation.