A semi-analytical method and the circumferential dominant modal control of circular cylindrical shells with active constrained layer damping treatment

TLDR: In this paper, an integrated first-order differential equation for active constrained layer damped (ACLD) circular cylindrical shells is derived by reformulating the integrated firstorder differential equations for the PCLD circular cylinders, and a high precision semi-analytical method is developed for solving the dynamic problem.

Abstract: To enhance the generality and flexibility of active constrained layer damped (ACLD) forms used in vibration control for circular cylindrical shells, the piezoelectric layer of the ACLD form is divided into several sub-blocks by thin insulated layers, and the sub-blocks are integrated on the viscoelastic layer continuously in the circumferential direction. In addition, on the basis of the authors' recent research on passive constrained layer damped (PCLD) circular cylindrical shells, the piezoelectric effects of the constrained layer (made of piezoelectric material) are further considered. Then, the integrated first-order differential equation for such an ACLD (partially treated in the axial direction) circular cylindrical shell is derived by reformulating the integrated first-order differential equation for the PCLD circular cylindrical shell. Next, employing the extended homogeneous capacity precision integration approach and the superposition principle, a high precision semi-analytical method is developed for solving the dynamic problem for such ACLD circular cylindrical shells. Subsequently, several kinds of circumferential modal control strategy are compared by the method presented. Furthermore, the concept of a circumferential dominant modal control strategy is proposed, which is different from the traditional modal control method. The numerical results show that, on applying the circumferential dominant modal control strategy, the ACLD cylindrical shell attenuates the vibration better. Lastly, some influence factors for the circumferential dominant modal control strategy affecting the damping effect of ACLD circular cylindrical shells are also investigated.