Nonlinear Dynamic Response and Active Control of Piezoelastic Laminated Shallow Spherical Shells with Damage

Abstract

Based on Talreja’s damage model with tensor valued internal state variables and geometric nonlinear theory, the constitutive relations for a moderately thick shallow spherical shell with damage are derived. The distribution of electric potential along the thickness direction in the piezoelectric layer is simulated by a sinusoidal function, and accordingly the dynamic analytical model for the cross-ply laminated moderately thick piezoelectric shallow spherical shell is established. Using the negative velocity feedback control algorithm, an analytical model for active vibration control of the piezoelectric laminated moderately thick piezoelectric shallow spherical shell is built when the damage effect is considered. And the solutions to the whole problem are obtained with synthetical utilization of the orthogonal collocation point method and the Newark method. In numerical examples, the effects of damage, piezoelectric effect, and the structure’s geometrical parameters on the dynamic response and vibration control of the piezoelastic laminated shallow spherical shells with damage are investigated.