Dispersion and attenuation of SH‐waves in a temperature‐dependent Voigt‐type viscoelastic strip over an inhomogeneous half‐space

A mathematical model is presented to explore the SH‐wave (horizontally polarized shear wave) propagation in a temperature‐dependent viscoelastic medium laid on a vertically heterogeneous elastic half‐space. Heterogeneity in the half‐space arises due to nth order depth variation in the elastic consta...

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Published inZeitschrift für angewandte Mathematik und Mechanik Vol. 101; no. 12
Main Authors Alam, Parvez, Singh, Kuvar Satya, Ali, Rifaqat, Badruddin, Irfan Anjum, khan, T.M. Yunus, Kamangar, Sarfaraz
Format Journal Article
LanguageEnglish
Published Weinheim Wiley Subscription Services, Inc 01.12.2021
Subjects
2010 Mathematics Subject Classification: 74Hxx
35Q74
74Dxx
74E05
74J15
74L10
Attenuation coefficients
Boundary conditions
damped velocity
Damping
Dissipation factor
Elastic properties
Heterogeneity
heterogeneous
Horizontal polarization
Parameters
phase velocity
SH‐ wave
Temperature dependence
Temperature ratio
Viscoelasticity
Wave attenuation
Wave propagation
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Summary:A mathematical model is presented to explore the SH‐wave (horizontally polarized shear wave) propagation in a temperature‐dependent viscoelastic medium laid on a vertically heterogeneous elastic half‐space. Heterogeneity in the half‐space arises due to nth order depth variation in the elastic constants. Bessel's and Whittaker's functions have been used to derive the internal deformations. The expression of the complex frequency equation has been obtained with the aid of suitable boundary conditions. The decomposition of the complex frequency equation into real and imaginary parts provides dispersion and damping equations. These equations exhibited their reliance on the temperature ratio parameter, attenuation coefficient and dissipation factor due to viscoelasticity, heterogeneity and order of heterogeneity function. The impacts of the aforesaid parameters on the propagation of SH‐wave have been studied numerically and demonstrated by 2D/3D graphs. A mathematical model is presented to explore the SH‐wave (horizontally polarized shear wave) propagation in a temperature‐dependent viscoelastic medium laid on a vertically heterogeneous elastic half‐space. Heterogeneity in the half‐space arises due to nth order depth variation in the elastic constants. Bessel's and Whittaker's functions have been used to derive the internal deformations. The expression of the complex frequency equation has been obtained with the aid of suitable boundary conditions.…
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ISSN:0044-2267
1521-4001
DOI:10.1002/zamm.202000223