A new approach for smart control of size-dependent nonlinear free vibration of viscoelastic orthotropic piezoelectric doubly-curved nanoshells

Abstract

• The active vibration control of a viscoelastic orthotropic piezoelectric doubly-curved nanoshell is studied. • A velocity feedback control law is introduced to obtain an efficient active damping for the present system. • The nonlinear vibration response of the system with surface effects is reduced due to the effect of active damping. • There exists a critical value of width to thickness ratio above which the natural frequency will monotonously increase. The focus of this paper is on the active control of nonlinear free vibration of viscoelastic orthotropic piezoelectric doubly-curved smart nanoshells with surface effects. To achieve an efficient active damping in the vibration control, a velocity feedback control law is introduced to carry out the present study. Within the framework of surface piezoelectricity theory and Kelvin–Voigt viscoelastic model, the nonlinear equations of motion, including the surface effect and internal damping effect, are derived from the generalized Hamilton's principle. By using the harmonic balance method to solve the equations of motion, the nonlinear vibration responses of the system with and without active vibration control are presented. The effects of the surface energy, viscous damping coefficient, initial displacement, aspect ratio and control gain on the nonlinear vibration responses of the system are studied. Numerical results show that these parameters, especially the control gain, play a significant role in the active vibration control of a viscoelastic orthotropic piezoelectric doubly-curved nanoshell.