2.5D modelling of wave propagation in longitudinally curved viscoelastic structure using a coupled FEM-PML approach

Abstract

Wave propagation in a longitudinally curved viscoelastic structure with a large or infinite cross section is a common problem frequently encountered. To study this problem, a coupled finite element method-perfectly matched layer (FEM-PML) modelling methodology based on a curved two-and-a-half-dimensional (2.5D) formulation is proposed in light of the fact that only the wave propagation in a key interested domain is important for general practice problems. In this methodology, the perfectly matched layer (PML) domain is introduced and clamped at the edges of the interested domain of the viscoelastic structure to account for the radiation of waves towards infinity or far away from the interested domain. To facilitate the 2.5D modelling of the longitudinally curved viscoelastic structure, a longitudinal extension that extends both the interested domain and the PML domain to infinity in the longitudinal direction is made, and the cross sections of both domains are assumed to be longitudinally invariant. Then the finite elements and displacement-based PML elements based on a curved 2.5D formulation are developed to model both domains, with their equilibrium equations formulated in a weak form by means of the Galerkin approach. Based on these formulations, a frequency-dependent finite element solution with high computational accuracy and efficiency to the problem concerned is finally obtained. The validations and applications of the proposed methodology are also presented, demonstrating its efficiency, accuracy and potential in simulating the corresponding wave propagation problems.