Analysis of multilayered structures embedding viscoelastic layers by higher-order, and zig-zag plate elements

In this work, a number of higher-order plate elements and an improved theory based on a zig-zag power function have been applied to metallic and composite layered structures with viscoelastic layers. The kinematic field is written by using an arbitrary number of continuous piecewise polynomial functions. The polynomial expansion order of a generic subdomain is a combination of zig-zag power functions depending on the plate thickness coordinate. Damped free-vibrations and frequency response analysis are performed modelling the viscoelastic properties with the complex modulus approach, and taking into account different damping laws for the viscoelastic layers included a five-parameter fractional-derivative model. The governing equations are derived from the Principle of Virtual Displacements and solved using the Finite Element (FE) method, and both full and reduced-order formulation are taken into account. Furthermore, the Mixed Interpolated Tensorial Components (MITC) method is employed to contrast the shear locking phenomenon. The Carrera Unified Formulation (CUF) has been employed to derive the governing FE equations for the various theories considered in this paper in an unified form. Several numerical investigations are carried out to validate and demonstrate the accuracy and efficiency of the present plate element. The results are reported in terms of frequencies, modal loss factors and frequency responses, and they are compared with solutions published in the literature and with solid finite element models.