Rayleigh wave at the surface of a general anisotropic poroelastic medium: derivation of real secular equation. (21st March 2018)

• Record Type: Journal Article
• Authors: Sharma, M. D.
• Is Part Of: Proceedings. Volume 474:Number 2211(2018)
• Publication Date: 2018-03-21
• Subjects: Rayleigh wave -- poroelastic solid -- arbitrary anisotropy -- secular equation -- phase velocity; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2017.0589
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : A secular equation governs the propagation of Rayleigh wave at the surface of an anisotropic poroelastic medium. In the case of anisotropy with symmetry, this equation is obtained as a real irrational equation. But, in the absence of anisotropic symmetries, this secular equation is obtained as a complex irrational equation. True surface waves in non-dissipative materials decay only with depth. That means, propagation of Rayleigh wave in anisotropic poroelastic solid should be represented by a real phase velocity. In this study, the determinantal system leading to the complex secular equation is manipulated to obtain a transformed equation. Even for arbitrary (triclinic) anisotropy, this transformed equation remains real for the propagation of true surface waves. Such a real secular equation is obtained with the option of boundary pores being opened or sealed. A numerical example is solved to study the existence and propagation of Rayleigh waves in porous media for the top three (i.e. triclinic, monoclinic and orthorhombic) anisotropies.