Abstract
Simulating the propagation of elastic waves in multi-layered media has many applications. A common approach is to use matrix methods where the elastic wave-field within each material layer is represented by a sum of partial-waves along with boundary conditions imposed at each interface. While these methods are well-known, coding the required matrix formation, inversion, and analysis for general multi-layered systems is non-trivial and time-consuming. Here, a new open-source toolbox called ElasticMatrix is described which solves the problem of acoustic and elastic wave propagation in multi-layered media for isotropic and transverse-isotropic materials where the wave propagation occurs in a material plane of symmetry. The toolbox is implemented in MATLAB using an object oriented programming framework and is designed to be easy to use and extend. Methods are provided for calculating and plotting dispersion curves, displacement and stress fields, reflection and transmission coefficients, and slowness profiles.
Highlights
Motivation and significanceMatrix models of wave propagation in multi-layered elastic solids have had a significant contribution to research areas such as acoustics, geophysics and electromagnetics
The algorithm implemented in ElasticMatrix only searches in the real domain of ζ which is a good-estimate for simple plate structures in a vacuum, it may be inaccurate for leaky solutions, for example a plate embedded in soil
The toolbox uses the partial-wave method which allows the calculation of slowness profiles, reflection and transmission coefficients, dispersion curves and stress and displacement fields
Summary
Matrix models of wave propagation in multi-layered elastic solids have had a significant contribution to research areas such as acoustics, geophysics and electromagnetics. A new open-source toolbox called ElasticMatrix is introduced which uses the partial-wave method for multi-layered structures with an arbitrary number of isotropic and transverse-isotropic materials. Where possible, it is validated against existing literature and has been implemented so that it is both easy to use and extend. Some potential uses of this software are: (1) plotting the slowness profiles of materials, (2) determining the reflection and transmission coefficients of multi-layered structures, (3) finding the dispersion curves of multi-layered structures, (4) plotting the displacement and stress fields, (5) extending the toolbox for other applications, for example modelling the directional response of Fabry–Perot ultrasound sensors [10,21].
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