TITLE:
Proposal to Study Uniqueness Problem of Rayleigh Wave in Half-Space Kelvin Viscoelastic Media
AUTHORS:
Hua Cheng, Takashi Takiguchi
KEYWORDS:
Rayleigh Wave, Viscoelastic, Wave Equation, Characteristic Equation, Kelvin Model
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.9,
September
24,
2019
ABSTRACT: Rayleigh wave is an interference wave of longitudinal wave and transverse wave which propagate along the free surface of solids. There remains a dispute about the number of Rayleigh waves in viscoelastic media until now, which is an essential problem of Rayleigh wave propagation. The purpose of this study is to propose a brief way of handling this essential problem within half-space Kelvin viscoelastic media. Starting from the dynamic equations of transverse wave and longitudinal wave based on Kelvin viscoelastic model, this study sets the complex wave number as a variable, introduces complex moduli and complex exponential factors, then a characteristic equation of Kelvin viscoelastic Rayleigh wave in half space is derived and simplified support for analysis of its uniqueness. After reviewing mathematical models describing phenomena of having multiple solutions but uniqueness when a natural condition is taken into account, a conjecture is given that the Rayleigh wave in Kelvin viscoelastic media must be unique if we assume a natural condition in accordance with the natural phenomena.