Journal ArticleDOI
Stable and Accurate Computation of Dispersion Relations for Layered Waveguides, Semi-Infinite Spaces and Infinite Spaces
Qiang Gao,Yanhui Zhang +1 more
Reads0
Chats0
TLDR
In this paper, the dispersion characteristics of guided waves in layered finite media, surface wave in layered semi-infinite spaces, and Stoneley wave in a layered infinite space were investigated using the Wittrick-Williams (W-W) algorithm.Abstract:
This paper studies the dispersion characteristics of guided waves in layered finite media, surface waves in layered semi-infinite spaces, and Stoneley waves in layered infinite spaces. Using the precise integration method (PIM) and the Wittrick–Williams (W-W) algorithm, three methods that are based on the dynamic stiffness matrix, symplectic transfer matrix, and mixed energy matrix are developed to compute the dispersion relations. The dispersion relations in layered media can be reduced to a standard eigenvalue problem of ordinary differential equations (ODEs) in the frequency-wavenumber domain. The PIM is used to accurately solve the ODEs with two-point boundary conditions, and all of the eigenvalues are determined by using the eigenvalue counting method. The proposed methods overcome the difficulty of seeking roots from nonlinear transcendental equations. In theory, the three proposed methods are interconnected and can be transformed into each other, but a numerical example indicates that the three methods have different levels of numerical stability and that the method based on the mixed energy matrix is more stable than the other two methods. Numerical examples show that the method based on the mixed energy matrix is accurate and effective for cases of waves in layered finite media, layered semi-infinite spaces, and layered infinite spaces.read more
Citations
More filters
Proceedings Article
The scaled boundary finite-element method – a primer: derivations
John P. Wolf,Chongmin Song +1 more
TL;DR: In this paper, the LCH-CONF-1998-009 Record created on 2007-04-24, modified on 2016-08-08, was used as a reference.
Journal ArticleDOI
An accurate method for guided wave propagation in multilayered anisotropic piezoelectric structures
Qiang Gao,Yanhui Zhang +1 more
TL;DR: In this paper, the authors extended the precise integration method and the Wittrick-Williams (W-W) algorithm to analyze the dispersion of guided waves in multilayered anisotropic piezoelectric structures.
Journal ArticleDOI
Stability analysis of the mixed variable method and its application in wave reflection and transmission in multilayered anisotropic structures
Yanhui Zhang,Qiang Gao +1 more
TL;DR: In this paper, the stability analysis of the mixed variable method (MVM) for computing the R/T coefficients of elastic waves in multilayered anisotropic structures is presented.
Journal ArticleDOI
Stress measurement for steel slender waveguides based on the nonlinear relation between guided wave group velocity and stress
TL;DR: In this article, an investigation of the nonlinear relation between guided wave group velocity and stress was carried out numerically and experimentally, and a stress measurement method based on the non-linear relation was developed.
Journal ArticleDOI
An accurate and efficient Chebyshev expansion method for large-scale transient heat conduction problems
TL;DR: An efficient and accurate Chebyshev expansion method is presented for solving large-scale transient heat conduction problems and it is indicated that under the given truncation criterion, the computational cost decreases with the increasing of the time step.
References
More filters
Book
Mathematical Methods of Classical Mechanics
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
Book ChapterDOI
The Dispersion of Surface Waves on Multilayered Media
TL;DR: In this paper, a matrix formalism developed by W. T. Thomson is used to obtain the phase velocity dispersion equations for elastic surface waves of Rayleigh and Love type on multilayered solid media.
Journal ArticleDOI
Transmission of Elastic Waves through a Stratified Solid Medium
TL;DR: In this article, the transmission of a plane elastic wave at oblique incidence through a stratified solid medium consisting of any number of parallel plates of different material and thickness is studied theoretically.
Journal ArticleDOI
Introduction to the spectral element method for three-dimensional seismic wave propagation
Dimitri Komatitsch,Jeroen Tromp +1 more
TL;DR: In this article, the spectral element method is used for the calculation of synthetic seismograms in 3D earth models using a weak formulation of the equations of motion, which are solved on a mesh of hexahedral elements.
Related Papers (5)
Dispersion Relation of Leaky Modes in Nonhomogeneous Waveguides and Its Applications
Jianxin Zhu,Zheqi Shen +1 more
Root-finding absorbing boundary conditions for scalar and elastic waves in infinite media
Jin Ho Lee,John L. Tassoulas +1 more
Convergence of infinite element methods for scalar waveguide problems
Thorsten Hohage,Lothar Nannen +1 more