ULTRASONIC WAVE INTERACTION WITH A THIN ANISOTROPIC LAYER BETWEEN 2 ANISOTROPIC SOLIDS .2. 2ND-ORDER ASYMPTOTIC BOUNDARY-CONDITIONS

In this paper, using a transfer matrix method, second-order asymptotic boundary conditions (B.C.) are introduced to model an anisotropic int erfacial layer when the layer is thin compared to the wavelength. Comp ared with the first-order asymptotic B.C. which have previously been i ntroduced by Rokhlin and Huang [J. Acoust. Soc. Am. 92, 1729-1742 (199 2)], the second-order B.C. greatly improve the accuracy and consistenc y of approximation and at the same time preserve the same order of sim plicity. Other attractive features are that unlike the first-order app roximation the wave solutions for the second-order B.C. exactly satisf y energy balance and give zero scattering from a homogeneous substrate /layer/substrate system. Furthermore, for decoupled symmetric and anti symmetric problems, the second-order B.C. can be simplified through lo wer-order stiffness matrices so that the rank of the system of equatio ns is reduced by half. Here the second-order B.C. are presented for a thin orthotropic layer between two solids which is rotated about one o f its axes of symmetry with respect to the incident plane. Such bounda ry conditions couple the in-plane and out-of-plane stresses and displa cements on the interface even for isotropic substrates. The results ar e illustrated by numerical examples of ultrasonic wave scattering from an imperfect interface between anisotropic solids by comparison with exact solutions.