Scattering of SH waves by an elastic thin-walled rigidly supported inclusion

Abstract

Explicit forms of the first-order approximate boundary conditions are derived for a 2D problem of SH waves scattering by a thin, curvilinear, elastic, rigidly supported inclusion in a uniform background. The effects of varying elastic modulus and geometrical forms of the inclusion on the stress and strain states of the body near and far from the ends of the inhomogeneity are examined. The method of investigation is based on the matching of asymptotic expansions with the thickness-to-length ratio as the perturbation parameter. IntroductionThe study of wave propagation in inhomogeneous media consisting of thin-walled layers, confronts with the problem of appropriate approximations for boundary conditions and equilibrium equations of thin-walled inhomogeneities. The general purpose of the approximated boundary conditions, usually referred to as effective boundary conditions, [1, 2], or imperfect interface conditions, [3], is to simplify the analytical or numerical solutions of the wave scattering problem involving complex structures by, e.g., converting a three-media problem into a two-media problem. Such boundary conditions have been widely used in problems of wave propagation and diffraction in inhomogeneous layered media, [4, 5, 6], antenna and radar cross-section studies, [2,7], nondestructive testing of materials, [8-10], modeling of interphases in fiber-reinforced composites, [3,11,12], etc. In the latter case, the interphases constitute thin elastic layers between the fibers and the matrix, where the fiber is usually much stiffer that the matrix material. For this class of structures, only cylindrical or plane unit cell models have been used, see, e.g., [11,12].The goal of the present investigation is to obtain effective boundary conditions for elastodynamic interactions between a thin-walled, curvilinear, elastic, rigidly supported inclusion and the surrounding matrix that would hold for arbitrary values of mechanical parameters of the matrix and the inclusion in the 2D case of SH-waves scattering. The displacement asymptotic near the ends of the scatterer and the approximation of displacements over the scatterer thickness are also considered.

SH-Wave at a Plane Interface between Homogeneous and Inhomogeneous Fibre-Reinforced Elastic Half-Spaces

“…Chattopadhyay and Singh [13] studied the problem of -type seismic waves in fibre-reinforced media and obtained the dispersion equation for the propagation of -type seismic wave in fibre-reinforced layer lying over an inhomogeneous fibre-reinforced elastic half-space. Literatures showed many problems of propagation of SH-waves and notable among them are Bath and Arroyo [14], Gupta [15], Tomar et al [16], Kumar et al [17], Chaudhary et al [18,19], Emets et al [20], Chattopadhyay and Michel [21], Tomar and Singh [22], Tomar and Kaur [23,24], Abd-Alla and Alsheikh [25], Chattopadhyay et al [26], Singh [27], Wang and Zhao [28], and Sahu et al [29].…”

Scattering of a SH-wave by an elastic fiber of nonclassical cross section with an interface crack

“…The null field (T-matrix) method is applied for the solution of the scattering problem. The method was originally developed for acoustic scattering by Waterman [9], and has later been extended to the scattering of waves in elastic solids by voids, perfectly bonded rigid and elastic inclusions, inclusions with thin interface layers by Varatharajulu and Pao [10], Olsson and Boström [11], Boström et al [12], Emets et al [13]. Longer lists of references on the subject can be found in the review works by Martin [14], Beskos [15], and Boström [16].…”

Wave propagation in 2D elastic composites with partially debonded fibres by the null field approach

“…Previously this method has been successfully applied for the timeharmonic analysis of electromagnetic and acoustic scattering by Waterman [9]. Many references on the subject can be found in the papers by Varatharajulu and Pao [10], Olsson and Bostro¨m [11], Bostro¨m et al [12], Emets et al [13] and in the review works by Martin [14], Beskos [15], and Bostro¨m [16]. Bostro¨m and Olsson [17] proposed a modification of the null field approach to study the scattering of elastic waves by non-planar cracks, where the 'square-root' behaviour of the solution at the crack-tip is explicitly considered.…”