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The present work is aimed at deriving a finite element model for active constraining layer damping treatment (ACLD) of layered skew plates by incorporating zig-zag behaviour using a Murakami zig-zag function (MZZF). The ACLD in skew patch form comprises of 1–3 PZC material and viscoelastic material in the layer form placed on substrate skew plate. The overall skew substrate ACLD system deformation kinematics are derived using MZZF and the equations of motion for the same are derived by virtual work method. A MATLAB subroutine for the overall skew plate ACLD system has been developed to present the closed loop frequency responses by successful implementation of closed-loop feedback system. The substrate skew plates with different lamination schemes namely symmetric/antisymmetric cross-ply and antisymmetric angle-ply are considered to assess the damping behavior of the skew plates undergoing ACLD. Also, the piezo-fiber angle (obliquely reinforced) variation of the PZC layer on the damping responses of the skew plates have been thoroughly examined.

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This study is aimed at incorporating the zig-zag effect by Murakami zig-zag function in the development of a finite element model for active constraining layer damping treatment of functionally graded sandwich plates. The present sandwich construction consists of functionally graded facings distanced by a ceramic core. The substrate functionally graded plate is subjected to active constraining layer damping treatment, which in itself is a two-layered material system comprised of a viscoelastic layer and a 1–3 piezoelectric composite layer. The deformation kinematics of the functionally graded sandwich plate active constraining layer damping system is shaped using Murakami zig-zag function , and the finite element model is obtained by the virtual work principle. A standard feedback control system has been implemented, and a MATLAB subroutine has been developed to present the open- and closed-loop responses. Substrate plates with functionally graded configurations 1-1-1, 1-2-1, and 2-1-2 are considered to evaluate the effect of active constraining layer damping on damping the frequency responses of these plates. Investigation on damping performance has been carried out, bearing in mind the change in power-law index with top and bottom ceramic-/metal-rich surfaces. Also, the effect of variation in fiber orientation angle (obliquely reinforced) of the piezoelectric composite material on the active constraining layer damping performance has been examined thoroughly.

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