Nonlinear free vibration analysis of sandwich shell structures with a constrained electrorheological fluid layer

Nonlinear vibration analysis of sandwich shell structures with a constrained electrorheological (ER) fluid is investigated for different boundary conditions. To accomplish this, a nonlinear finite element model of a multi-layer shell structure with an ER fluid layer in the core of the sandwich shell has been developed. A new notation referred to as H-notation is presented, in place of the two well known notations referred to as B- and N-notation, in order to represent the nonlinear equations of motion. This notation leads to a considerable reduction in the computational costs caused by the time-consuming integrations in the nonlinear vibration analysis of the structure using a direct iteration technique. In particular, this notation is very useful for solving the nonlinear vibration analysis of sandwich layered shell structures in which large numbers of integrations are required to be repeatedly performed throughout the direct iteration technique. Finally, for different boundary conditions, the effects of small and large displacements, core thickness ratio and electric field intensity on the nonlinear vibration damping behavior of the sandwich shell structure are presented.