EXTENSIONAL WAVE PROPAGATION IN PRE-STRESSED IMPERFECTLY BONDED INCOMPRESSIBLE LAYERED ELASTIC COMPOSITES SOMSAK LEUNGVICHCHAROEN AND ANIL C. WIJEYEWICKREMA Department of Civil Engineering, Tokyo Institute of Technology, O-okayama, Meguro-ku, Tokyo 152-8552, Japan Ｅ-mail: anil@cv.titech.ac.jp In the present analysis harmonic extensional wave propagation in a pre-stressed, incompressible, symmetric layered composite is considered. The bi-material composite consists of two isotropic elastic materials. The imperfect interface is simulated by a shear spring type resistance model that can accommodate the extreme cases of perfect bonding or a sliding interface. Using the technique of the propagator matrix, the dispersion relation is obtained. Four possible cases of dispersion curves that depend on the limiting shear wave speeds of the bi-material composite are discussed. The effect of the imperfect interface is more pronounced for low wave numbers. 1 Introduction Elastic wave propagation in infinite layers has previously been discussed in the monographs of Achenbach [1], Eringen and Suhubi [2] and Graff [4], where it has been shown that there are two uncoupled modes of wave propagation, viz. symmetric mode (extensional waves) and antisymmetric mode (flexural waves). The effect of finite primary deformations on waves in elastic layers have been studied by Ogden and Roxburgh [6] and Rogerson and Fu [7]. Motivated by the wide usage of layered composites in engineering practice, wave propagation in pre-stressed layered composites have been considered by Rogerson and Sandiford [8-10]. In general, layered composites are assumed to be perfectly bonded, although in practice due to defects in manufacturing or damage due to loading, the interface may be unable to perfectly transfer stresses due to displacement discontinuities at the interface. Such a case is considered in this paper where a shear spring type resistance model is used to simulate an imperfect interface. Both perfect bonding or a sliding interface can be accommodated by such a resistance model. The basic theory and equations of incremental elastic deformations are given by Ogden [5]. The bi-material, symmetric composite is assumed to consist of isotropic incompressible elastic material. Four possible cases of dispersion curves that depend on the limiting shear wave speeds of the bi-material composite are discussed, for the case of extensional wave propagation. 2 Formulation of the problem The layered incompressible composite shown in Fig. 1 consists of outer layers of identical isotropic material of thickness h and an inner layer of isotropic material of thickness 2d . x 2 o h h 2d x 1 01-06-24-ACAM-6pages submitted to World Scientific 7/3/2003 : 6:46 PM 1/1