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Archive of Applied Mechanics
Erschienen in: Archive of Applied Mechanics 1/2020

21.09.2019 | Original

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

verfasst von: Yanhui Zhang, Qiang Gao

Erschienen in: Archive of Applied Mechanics | Ausgabe 1/2020

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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.
Vorheriger Artikel A review of friction damping modeling and testing
Nächster Artikel Analysis of dynamic characteristics of viscoelastic frame structures

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Metadaten
Titel
Stability analysis of the mixed variable method and its application in wave reflection and transmission in multilayered anisotropic structures
verfasst von
Yanhui Zhang
Qiang Gao
Publikationsdatum
21.09.2019
Verlag
Springer Berlin Heidelberg
Erschienen in
Archive of Applied Mechanics / Ausgabe 1/2020
Print ISSN: 0939-1533
Elektronische ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-019-01601-5

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