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.
Highlights
The Rayleigh wave is a surface wave that propagates along the surface of a medium [1]
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
We derived the characteristic equation of Rayleigh surface wave in Kelvin viscoelastic half-space in a brief way and in terms of complex wave number
Summary
The Rayleigh wave is a surface wave that propagates along the surface of a medium [1]. He took advantage of complex modulus to analyze the root number of the characteristic equation of viscoelastic half-space Rayleigh wave His derivation process contained multiple variable substitutions, which appeared complicated and obscure, he deemed that there is only one complex root valid, while the other two are invalid. The results obtained in the papers by Chirita et al [17] and Currie et al [6] [7] [8] claimed “a viscoelastic Rayleigh wave may propagate with a speed greater than either the P or S body-waves, whereas in the elastic case the speed is always less than that of P and S waves” Their results clearly conflict with the real natural condition that the Rayleigh wave is an interference wave of longitudinal wave and transverse wave. The uniqueness problem is addressed, followed by discussion and future work
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