Spatial Dispersion of Elastic Waves in Transversely Isotropic Media Using Lagrange Spectral Element Method
Publication: Journal of Engineering Mechanics
Volume 148, Issue 7
Abstract
Dispersion is studied for the two-dimensional propagation of elastic waves in transversely isotropic media using the Lagrange spectral element method. Spectral element matrices are derived as the tensor product of elementary second-order tensors. Gauss-Lobatto-Legendre points are used for the interpolation of Lagrange-type shape functions as well as for the numerical integration to obtain elementary matrices. The Rayleigh quotient approximation technique is employed to find the solution of the eigenvalue problem, which is obtained from the semidiscretized form of the elastic wave equation for propagation of plane harmonic waves. Variations of errors in the phase/group velocities of bulk waves are depicted graphically with the order of interpolation polynomial, angle with the symmetry axis, and the time discretization. Error analysis clearly demonstrated the effectiveness of the Lagrange spectral element method for wave simulation in a transversely isotropic medium.
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Data Availability Statement
All data used during the study appear in the published article, while the codes used during the study are available from the corresponding author by request.
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Published In
Journal of Engineering Mechanics
Volume 148 • Issue 7 • July 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Oct 17, 2021
Accepted: Feb 15, 2022
Published online: Apr 28, 2022
Published in print: Jul 1, 2022
Discussion open until: Sep 28, 2022
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Cited by
- Poonam Saini, Dispersion Analysis of Three-Dimensional Elastic Wave Propagation in Transversely Isotropic Media Using Optimally Blended Spectral-Element Method, Journal of Engineering Mechanics, 10.1061/JENMDT.EMENG-6781, 149, 6, (2023).