Love Wave Propagation in an Anisotropic Viscoelastic Layer Over an Initially Stressed Inhomogeneous Half-Space
Love-type surface wave in a model comprising of an orthotropic viscoelastic layer supported by a half-space is investigated. The layer and half-space both are heterogeneous, and the half-space is in the state of initial stress. Employing relevant boundary
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Abstract Love-type surface wave in a model comprising of an orthotropic viscoelastic layer supported by a half-space is investigated. The layer and half-space both are heterogeneous, and the half-space is in the state of initial stress. Employing relevant boundary conditions, frequency equation is derived, based on which numerical computations are carried out to analyze the impact of different parameters on Love wave speed. It is discovered that dissipation function and heterogeneity of the layer and initial stress and heterogeneity of the half-space has a substantial effect on phase velocity. Keywords Love wave · Inhomogeneity · Orthotropic · Viscoelastic · Initial stress
1 Introduction The study of seismic waves gives us the most accurate results and information regarding Earth’s interior. It is a well-known fact that the Earth’s crust is not uniform; different sorts of heterogeneity and anisotropy exist within it. The presence of inhomogeneity and anisotropy drastically affects the seismic wave propagation. Detailed information related to seismic wave propagation in different types of medium is available in Ewing et al. [1], Love [2], Bullen [3], Gubbins [4], etc. The intrinsic viscosity of the Earth layer along with different parameters, such as heterogeneity and anisotropy, has a crucial effect on earthquake waves. Therefore, while investigating seismic waves, one should proceed in such a way that the studies interpret these factors simultaneously. Investigations are made by several authors (Cooper [5]; Shaw and Bugl [6]; Buchen [7]; Schoenberg [8]; Borcherdt and B. Prasad (B) · P. C. Pal · S. Kundu Department of Applied Mathematics, IIT (ISM) Dhanbad, 826004 Dhanbad, Jharkhand, India e-mail: [email protected] P. C. Pal e-mail: [email protected] S. Kundu e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. Dutta et al. (eds.), Advances in Structural Vibration, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-5862-7_38
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ˇ Wennerberg [9]; Carcione [10]; Cervený [11]) to analyze the effect of viscoelasticity of the Earth on the propagation of earthquake-generated waves. Chattopadhyay et al. [12] investigated shear waves in a model comprising of a layer over a half-space where both the mediums were viscoelastic and the boundary separating them was irregular. Kakar [13] discussed Love waves in a layer of Voigt-viscoelastic type supported by a gravitating half-space. Pandit et al. [14] investigated Love waves in an anisotropic viscoelastic layer over a half-space. The layer considered by him was prestressed having the orthotropic type of anisotropy, whereas the half-space was porous in nature saturated by fluids. Prasad et al. [15] discussed the scattering of SH waves through viscoelastic and reinforced media where the boundary separating the two mediums was sinusoidal in nature. Stresses, which are present in a body even when there are no external forces, are known by the name of initial stress. The presence of initial s
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