Smart control of cylindrical shells incorporating Murakami Zig-Zag function

Abstract

The work is devoted towards incorporating the Murakami zig-zag function (MZZF) for modelling the active constraining layer damping (ACLD) treatment of ‘N’ layered laminate cylindrical shells. The ACLD treatment in the patch form comprises of two material layers with the viscoelastic material layer constrained between the host shell and the smart 1–3 piezoelectric composite (PZC) material layer. The kinematics of deformation are derived successfully implementing the MZZF in the displacement fields. Virtual work principle has been employed for the finite element (FE) model to deduce governing equations of shell ACLD system in complete form. A feed-back control system has been considered to arrive at closed loop governing equations of motion. Considering the above, a MATLAB code for the same is generated to emphasise on dynamics of the cylindrical shell ACLD system. Cylindrical shells with various lamination schemes have been considered to assess the validity and implementation of MZZF for ACLD treatment of shells. Also, the oblique orientation of the 1–3 PZC material layer and its effect on the damping behavior of the cylindrical shell has been thoroughly explored.