Numerical analysis of elastic wave propagation in unbounded structures

The main objective of this paper is to show the effectiveness and usefulness of the concept of an absorbing layer with increasing damping (ALID) in numerical investigations of elastic wave propagation in unbounded engineering structures. This has been achieved by the authors by a careful investigation of three different types of structures characterised by gradually increasing geometrical and mathematical description complexities. The analysis includes propagation of longitudinal elastic waves in a 1-D semi-infinite isotropic rod, modelled according to the classical 1-mode theory of rods, propagation of coupled shear and flexural elastic waves in a 1-D semi-infinite isotropic beam modelled according to the Timoshenko beam theory, as well as propagation of elastic waves in a 3-D semi-infinite isotropic half-pipe shell modelled by a 6-mode theory of shells. The concept of the ALID has been not only presented by the authors, but certain relations between the ALID properties and the characteristics of propagating elastic waves have been given that can help to maximise the ALID performance in terms of its damping capability. All results of numerical calculations presented by the authors in this work have been obtained by the use of the Time-domain Spectral Finite Element Method (TD-SFEM).