Control of axi-symmetric vibrations of cylindrical shells using active constrained layer damping

Abstract

Distributed-parameter modeling of thin cylindrical shells which are fully treated with active constrained layer damping (ACLD) is presented. Hamilton's principle is utilized to develop the shell/ACLD model as well as the associated boundary conditions. A globally stable boundary control strategy is developed to damp out the vibration of the shell/ACLD system. The devised boundary controller is compatible with the operating nature of the ACLD treatments where the strain induced, in the active constraining layer, generates a control force acting at the boundary of the treated shell. As the boundary control strategy is based on a distributed-parameter model of the shell/ACLD system, the classical spillover problems resulting from using “truncated” finite element models is eliminated. Also, such an approach makes the boundary controller capable of controlling all the modes of vibration of the shell/ACLD and guarantees that the total energy norm of the system is continuously decreasing with time. Numerical examples are presented to demonstrate the effectiveness of the ACLD in damping out the vibration of cylindrical shells. Such effectiveness is determined for different control gains and compared with the performance of conventional passive constrained layer damping (PCLD). The results obtained demonstrate the high damping characteristics of the boundary controller particularly over broad frequency bands.