Plane SH‐waves at a corrugated interface between two dissimilar perfectly conducting self‐reinforced elastic half‐spaces

In this paper, we have attempted a problem of reflection and refraction of plane harmonic SH‐wave at a corrugated interface between two different perfectly conducting self‐reinforced elastic half‐spaces. Rayleigh's method is employed to find out the expressions of reflection and refraction coefficients for first‐ and second‐order approximation of the corrugation. The expressions of these coefficients show that they depend on the properties of half‐spaces, angle of incidence, frequency of the incident wave and are strongly influenced by the corrugation of the interface. Numerical computations are performed for a particular model having special type of interface and the variation of these coefficients are depicted graphically against the angles of incidence, frequency parameter, corrugation parameter at different values of reinforcement parameters. Results of some earlier works are reduced as a particular case of this formulation. Copyright © 2005 John Wiley & Sons, Ltd.     

Reflection and refraction of SH‐waves at a corrugated interface between two monoclinic elastic half‐spaces

A problem of reflection and transmission of shear wave incident upon a corrugated interface between two monoclinic solid half‐spaces have been investigated. Rayleigh's method of approximation is used to investigate the reflection and transmission coefficients for first and second approximation of the corrugation. For a special interface, closed‐form expressions of these coefficients for the first order approximation of the corrugation are obtained. It is found that these coefficients are functions of amplitude of corrugation, elastic parameters of the media, frequency of the incident wave and angle of incidence. The numerical computations are performed for a specific model and the results obtained are presented graphically. It is found that the reflection and transmission coefficients are strongly influenced by the corrugation and the elastic properties of the media. Results of some earlier workers in this field have been reduced as particular case from the present formulation. Copyright © 2004 John Wiley & Sons, Ltd.     

Response of shear wave from a corrugated interface between elastic solid/viscoelastic half‐spaces

The propagation of plane shear wave at a corrugation interface between elastic solid and viscoelastic liquid half‐spaces has been investigated. Adopting Rayleigh's method of approximation, the reflection and refraction coefficients corresponding to reflected and refracted SH‐waves have been derived for the first order of approximation of the corrugated interface. These coefficients are derived in the closed form for a periodic interface. Numerical computation has been performed for a particular model and the results are depicted graphically. The results of Asano (Bull. Earthquake Res. Inst. 1960; 38 (2):177–197) and Kielczynski and Pajewski (J. Acoust. Soc. Am. 1987; 81 (3):599–605) are recovered from this study. Copyright © 2010 John Wiley & Sons, Ltd.     

Frictional contact of laminated elastic half‐spaces allowing interface cavities. Part 2: Numerical results

The paper presents some numerical results of the problem on contact of stratified elastic half‐spaces possessing unevenness of their surface layers. The approach of the Jacobi polynomials is used to reduce the singular integral equation of the problem to a system of linear algebraic equations. On the basis of the system's solution the dependence of gaps' geometric characteristics on external load and friction is investigated for two types of initial boundary disturbances, namely a local symmetric recess and a periodic set of recesses at a flat boundary. Numerical results are presented in figures for a few elastic and geometric parameters of joint components. The analysis shows that elastic properties and geometric structure of a laminated half‐space have a significant influence on the shape of interface gaps and their location. Copyright © 2001 John Wiley & Sons, Ltd.     

Dynamic responses of a pile embedded in a layered poroelastic half‐space to harmonic lateral loads

A single pile embedded in a layered poroelastic half‐space subjected to a harmonic lateral load is investigated in this study. Based on Biot's theory, the frequency domain fundamental solution for a horizontal circular patch load applied in the layered poroelastic half‐space is derived via the transmission and reflection matrices method. Utilizing Muki and Sternberg's method, the second kind of Fredholm integral equation describing the dynamic interaction between the layered half‐space and the pile subjected to a top harmonic lateral load is constructed. The proposed methodology is validated by comparing results of this paper with some existing results. Numerical results show that for a two‐layered half‐space, the thickness of the upper softer layer has pronounced influences on the dynamic response of the pile and the half‐space. For a three‐layered half‐space, the presence of a softer middle layer in the layered half‐space will enhance the compliance for the pile significantly, while a stiffer middle layer will diminish the dynamic compliance of the pile considerably. Copyright © 2009 John Wiley & Sons, Ltd.