An arbitrarily curved three-dimensional anisotropic thin interphase between two anisotropic solids is considered. The purpose of this study is to model this interphase as a surface between its two neighbouring media by means of appropriately devised interface conditions on it. The analysis is carried out in the setting of unsteady heat conduction and dynamic elasticity, and makes use of the simple idea of a Taylor expansion of the relevant fields in thin regions. It consists of a generalization of a previous study by Bovik [1994. On the modelling of thin interface layers in elastic and acoustic scattering problems. Q. J. Mech. Appl. Math. 47, 17–42] which was confined to the isotropic setting. The remarkable feature of the presently derived anisotropic interface model is that formally it has a more compact form than that of Bovik's isotropic version. This is achieved by a judicious choice of surface differential operators which have been used in the derivation, and makes possible to show that several previously known classical interface models are recovered as special cases of the one obtained in this study, once suitable assumptions are made on the magnitude of the conductivity and elasticity tensors of the interphase.

A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media

Guided waves in a layered elastic plate of rectangular cross section (finite width and thickness) has been studied in this paper A semianalytical finite element method in which the deformation of the cross section is modeled by two-dimensional finite elements and analytical representation of propagating waves along the length of the plate has been used The method is applicable to arbitrary number of layers and general anisotropic material properties of each layer, and is similar to the stiffness method used earlier to study guided waves in a laminated composite plate of infinite width Numerical results showing the effect of varying the width of the plate on the dispersion of guided waves are presented and are compared with those for an infinite plate In addition, effect of thin anisotropic coating or interface layers on the guided waves is investigated

Elastic guided waves in a layered plate with rectangular cross section.

Some properties of surface acoustic waves in anisotropic-coated solids, studied by the impedance method

A thin isotropic three-dimensional curved interphase of thickness h between two isotropic media is considered in the setting of thermal conduction This interphase is modelled by a surface between the two neighbouring media, and appropriate interface conditions on it are derived for the temperature and normal heat flux fields The derivation makes use of Taylor expansions for the fields and is correct to O(h N ), where h denotes the thickness of the interphase The jumps for the temperature and normal heat flux in the interface model are given in terms of a hierarchy of surface differential forms, which depend on the conductivities of the interphase and surrounding media, and involve surface derivatives of the temperature and normal heat flux along the interface The analysis is directly transferable to the analogous physical phenomena of electrical conduction, dielectrics, magnetism, diffusion, flow in porous media and anti-plane elasticity

An O(hN) interface model of a three-dimensional curved interphase in conduction phenomena

Approximate dynamic boundary conditions for a thin piezoelectric layer

In this paper, dispersion of guided waves in a three-layered sandwich plate is considered. The focus here is on a configuration consisting of a thin anisotropic layer sandwiched between two identical isotropic layers. This configuration could model, for example, a superconducting tape where the middle layer is a brittle superconductor and the surrounding layers are isotropic and ductile. An approximate dispersion relation correct to O(h) governing the guided waves is obtained by expanding the field inside the thin middle layer in powers of the small thickness h of the layer. Numerical examples are given for two specific systems with superconducting middle layers. Some characteristic features, particularly at low frequencies, are investigated. Comparison between the exact and approximate dispersion relations are made to show that the approximation works well in the frequency interval of interest. The characteristic features may be useful for ultrasonic measurements of the anisotropic elastic constants of the thin layer.

AJ Niklasson

Papers

On ultrasonic guided waves in a thin anisotropic layer lying between two isotropic layers