Qiang Gao

Bio: Qiang Gao is an academic researcher from Dalian University of Technology. The author has contributed to research in topics: Space (mathematics) & Eigenvalues and eigenvectors. The author has an hindex of 1, co-authored 1 publications receiving 8 citations.

Stable and Accurate Computation of Dispersion Relations for Layered Waveguides, Semi-Infinite Spaces and Infinite Spaces

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.

The scaled boundary finite-element method – a primer: derivations

Abstract: Note: [255] Reference LCH-CONF-1998-009 Record created on 2007-04-24, modified on 2016-08-08

An accurate method for guided wave propagation in multilayered anisotropic piezoelectric structures

Abstract: The purpose of this paper is to extend and generalize the precise integration method (PIM) and the Wittrick–Williams (W–W) algorithm to analyze the dispersion of guided waves in multilayered anisotropic piezoelectric structures. The analysis shows that the W–W algorithm cannot be directly applied to piezoelectric materials. This is due to the fact that a submatrix of the Hamiltonian matrix is not positive definite for piezoelectric materials such that the eigenvalue count of sublayers is not zero when the divided sublayers are sufficiently small. The reason for this issue is explored by a theoretical analysis, and then, a symplectic transformation is introduced to ensure that the W–W algorithm can conveniently be applied to solve wave propagation problems in multilayered anisotropic piezoelectric structures. The present method not only guarantees that the computation is accurate and stable, but also finds all eigenfrequencies without being missed. Three numerical examples are provided to illustrate the performance of the method, and the results obtained by the method are compared with the published results and the results obtained by the semi-analytical finite element method. The effects of boundary conditions, wave propagation direction, thickness ratios and stacking sequences on the dispersion behavior of guided waves are discussed.

Stability analysis of the mixed variable method and its application in wave reflection and transmission in multilayered anisotropic structures

Abstract: This paper focuses on the reflection and transmission (R/T) problem of elastic waves in multilayered anisotropic structures. Stability analysis of the mixed variable method (MVM) for computing the R/T coefficients of elastic waves in multilayered anisotropic structures is presented. For this purpose, a detailed comparison of the MVM with the other two widely used methods, namely the transfer matrix method (TMM) and the stiffness matrix method (SMM), is made. Although the TMM, the SMM and the MVM are mathematically equivalent, they are quite different in numerical stability. The theoretical analysis shows that the MVM is unconditionally stable for arbitrary wavenumber–thickness products, whereas the TMM and the SMM may become unstable for large or small wavenumber–thickness products, respectively. This conclusion is numerically verified by various examples. Finally, the R/T coefficients of elastic waves in generally anisotropic multilayered structures bounded by two semi-infinite spaces are calculated using the MVM for a quasi-longitudinal or quasi-transverse wave incidence, and the effects of incident angles and wavenumber–thickness products on the R/T coefficients are discussed in detail through an example.