Dispersion Analysis of Three-Dimensional Elastic Wave Propagation in Transversely Isotropic Media Using Optimally Blended Spectral-Element Method
Publication: Journal of Engineering Mechanics
Volume 149, Issue 6
Abstract
The accuracy of the optimally blended spectral-element method for wave propagation in a homogeneous transversely isotropic elastic medium was investigated. A nonstandard quadrature rule obtained by combining Gauss quadrature rule and Gauss–Lobatto–Legendre quadrature rule was used to compute elementary matrixes. The mass and stiffness matrixes were represented as the triple tensor-product of elementary matrixes as second-order tensors. The solution of the eigenvalue problem representing the semidiscretized version of elastic wave equation for plane harmonic wave propagation was obtained using the Rayleigh quotient approximation technique. The resulting eigenvalues subsequently were used to estimate the phase and group velocity of three bulk waves. The variations of the errors in these velocities of the bulk waves with the number of grid points per wavelength were depicted graphically. These variations were shown for different polynomial orders and various angles of deviation from the symmetry axis. The effect of a change in the order of time discretization on error variation also was shown. The solution obtained by the optimally blended spectral-element method was found to be more accurate than that from the classical spectral-element method for low-order polynomials. The improvement in solution accuracy was demonstrated through dispersion analysis.
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Data Availability Statement
All data used during the study appear in the published paper. The codes used during the study are available from the corresponding author by request.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 149 • Issue 6 • June 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Jun 2, 2022
Accepted: Feb 18, 2023
Published online: Apr 13, 2023
Published in print: Jun 1, 2023
Discussion open until: Sep 13, 2023
ASCE Technical Topics:
- Analysis (by type)
- Continuum mechanics
- Dynamics (solid mechanics)
- Elastic analysis
- Engineering fundamentals
- Engineering mechanics
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid mechanics
- Fluid velocity
- Frequency analysis
- Hydrologic engineering
- Isotropy
- Material mechanics
- Material properties
- Materials engineering
- Mathematical functions
- Mathematics
- Matrix (mathematics)
- Solid mechanics
- Structural analysis
- Structural engineering
- Three-dimensional analysis
- Water and water resources
- Wave equations
- Wave propagation
- Wave spectrum
- Wave velocity
- Waves (mechanics)
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