Estimation of dispersion and attenuation of Rayleigh waves in viscoelastic inhomogeneous layered half-space based on spectral method

The dispersion and attenuation characteristics of Rayleigh waves in a non-uniform viscoelastic half-space with a covering layer are studied in this paper. The half-space and the covering layer are modeled by the fractional-order Zener viscoelastic solid. Compared with the traditional integer-order v...

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Vydané v:	Acta mechanica Ročník 235; číslo 12; s. 7789 - 7805
Hlavní autori:	Li, Caiguang, Wei, Peijun, Guo, Xiao
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Vienna Springer Vienna 01.12.2024 Springer Springer Nature B.V
Predmet:	Attenuation Boundary conditions Classical and Continuum Physics Control Dynamical Systems Eigenvalues Engineering Engineering Fluid Dynamics Engineering Thermodynamics Fractional calculus Half spaces Heat and Mass Transfer Mechanical properties Original Paper Polynomials Rayleigh waves Seismic engineering Solid Mechanics Spectral methods Surface waves Theoretical and Applied Mechanics Vibration Viscoelasticity Wave propagation Window functions
ISSN:	0001-5970, 1619-6937
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Abstract	The dispersion and attenuation characteristics of Rayleigh waves in a non-uniform viscoelastic half-space with a covering layer are studied in this paper. The half-space and the covering layer are modeled by the fractional-order Zener viscoelastic solid. Compared with the traditional integer-order viscoelastic model, the viscoelastic model with fractional-order derivative is more flexible in describing the complicated history-dependent mechanical behavior. Legendre and Laguerre orthogonal polynomials are used to approximate the displacement field of surface waves. The rectangular window function is used to merge the surface boundary conditions. The complicated problem of solving the complex wave number in the complex region is ultimately transformed into an eigenvalue problem. The correctness of the method is verified by comparing our outcomes with those in the literature. It is found that the present spectrum method avoids the complicated iterative process of root-finding and the pseudo-root and root-missing problem compared to the traditional root-finding method. Moreover, the uneven gradient distribution of the cover layer and half-space has opposite effects on the propagation of Rayleigh waves at low and high frequencies, and the same influence applies to fractional-order effects. The present study has important theoretical significance and application potential in the geophysical exploration and earthquake engineering.
AbstractList	The dispersion and attenuation characteristics of Rayleigh waves in a non-uniform viscoelastic half-space with a covering layer are studied in this paper. The half-space and the covering layer are modeled by the fractional-order Zener viscoelastic solid. Compared with the traditional integer-order viscoelastic model, the viscoelastic model with fractional-order derivative is more flexible in describing the complicated history-dependent mechanical behavior. Legendre and Laguerre orthogonal polynomials are used to approximate the displacement field of surface waves. The rectangular window function is used to merge the surface boundary conditions. The complicated problem of solving the complex wave number in the complex region is ultimately transformed into an eigenvalue problem. The correctness of the method is verified by comparing our outcomes with those in the literature. It is found that the present spectrum method avoids the complicated iterative process of root-finding and the pseudo-root and root-missing problem compared to the traditional root-finding method. Moreover, the uneven gradient distribution of the cover layer and half-space has opposite effects on the propagation of Rayleigh waves at low and high frequencies, and the same influence applies to fractional-order effects. The present study has important theoretical significance and application potential in the geophysical exploration and earthquake engineering.
Audience	Academic
Author	Wei, Peijun Guo, Xiao Li, Caiguang
Author_xml	– sequence: 1 givenname: Caiguang surname: Li fullname: Li, Caiguang organization: Department of Applied Mechanics, University of Science and Technology Beijing – sequence: 2 givenname: Peijun orcidid: 0000-0002-2965-314X surname: Wei fullname: Wei, Peijun email: weipj@ustb.edu.cn organization: Department of Applied Mechanics, University of Science and Technology Beijing – sequence: 3 givenname: Xiao surname: Guo fullname: Guo, Xiao organization: School of Mathematics and Physics, University of Science and Technology Beijing
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Snippet	The dispersion and attenuation characteristics of Rayleigh waves in a non-uniform viscoelastic half-space with a covering layer are studied in this paper. The...
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SubjectTerms	Attenuation Boundary conditions Classical and Continuum Physics Control Dynamical Systems Eigenvalues Engineering Engineering Fluid Dynamics Engineering Thermodynamics Fractional calculus Half spaces Heat and Mass Transfer Mechanical properties Original Paper Polynomials Rayleigh waves Seismic engineering Solid Mechanics Spectral methods Surface waves Theoretical and Applied Mechanics Vibration Viscoelasticity Wave propagation Window functions
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Title	Estimation of dispersion and attenuation of Rayleigh waves in viscoelastic inhomogeneous layered half-space based on spectral method
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