A refined spectral element model for wave propagation in multiscale hybrid epoxy/carbon fiber/graphene platelet composite shells

Abstract

The propagation of elastic waves in heterogeneous media is of interest for impact dynamics and non-destructive detection. This work presents a refined spectral element model (RSEM) to study the wave propagation in multiscale hybrid composite (MHC) shells subjected to impulsive loadings. The doubly-curved MHC shell consists of epoxy, carbon fibers, and graphene platelets (GPLs). The GPLs are functionally distributed along the thickness of the shell. For the three-phase MHC, the Halpin-Tsai micromechanical model in conjunction with the Mori-Tanaka approach is exploited to determine the effective material properties. In the framework of four-variable shear deformation theory, the governing equations along with the natural boundary conditions are derived using Hamilton's principle. A two-node spectral shell element is developed according to the closed-from solutions. The accuracy of the RSEM is verified by comparison with published results in aspects of the natural frequency and transient responses. The wave dispersion characteristics, including the wave number, phase velocity, and group velocity are examined. In the context of high frequency and short wavelength, the proposed RSEM achieves high computational efficiency benefiting from its independence of mesh structure. The time domain responses clearly indicate the wave-boundary interactions, e.g., wave reflection, dispersion, and interference. It is revealed that the present model can well capture the fundamental wave modes of the MHC shell. Moreover, the inclusion of GPLs plays a significant role in improving transverse moduli and mitigating the discontinuities of inter-laminar shear stress.