Efficient semi-analytical simulation of elastic guided waves in cylinders subject to arbitrary non-symmetric loads

Abstract

In this paper, we present an approach to model the propagation of high-frequency elastic guided waves in solid or hollow cylinders. This formulation requires only discretization of the radial direction, whereas the circumferential direction is approximated via a truncated Fourier series, and the axial direction is described analytically. The model is extended to allow applying arbitrary non-symmetric loads f(r,θ) on the flat cylinder surface. Efficiency is increased by a proposed methodology to limit the number of Fourier coefficients and by the implementation of hierarchical shape functions to dynamically adjust discretization with respect to frequency. Results are validated against conventional finite element applications, demonstrating the accuracy of the model and a reduction of the computing time by three orders of magnitude. Additionally, we apply a matrix function solution for the scaled boundary finite element method leading to a linear solution in the static case.

Keywords: Axisymmetry; FFEM; Guided waves; Hierarchical shape functions; SBFEM.