The effect of incompressibility of a layer on the propagation of guided elastic waves in anisotropic layered materials is examined. The layer is either overlying a half-space (host material) or is imbedded in an infinite host material, which is compressible. To gain an understanding of the propagation characteristics and their dependence on the material parameters the mathematically tractable case of material orthotropy is considered. The strain energy of the two materials is otherwise arbitrary. For propagation along a material axis of symmetry the dispersion equation is obtained in an explicit form when the axes of symmetry of the two materials coincide and one of them is normal to the plane separating the layer from the host material. Analysis of the dispersion equation reveals the propagation characteristics of interfacial waves and their dependence on the material parameters. Propagation occurs either in single or multiple modes depending on the material parameters of both the layer and the host material. For a thin layer the guided wave phase speed is obtained in explicit form in terms of the material parameters. Parameter conditions are also defined under which the generation of guided waves is not permitted by the structure.
The propagation of guided elastic waves in an orthotropic compressible layer imbedded in a difference orthotropic compressible material is examined. The strain energy of the two materials is otherwise arbitrary with the material constants satisfying the strong ellipticity conditions. To extract the propagation characteristics, propagation is considered along a material axis of symmetry which lies in the interfacial plane. For the two materials having common axes of symmetry, the dispersion equation is derived in explicit form. Analysis of the dispersion equation reveals the propagation characteristics and their dependence on frequency and material parameters. Low and high-frequency asymptotes are defined and their existence is discussed, the high frequency asymptote corresponding to a Stoneley wave. For low frequencies, the interfacial wave speed is derived in explicit form yielding a simple material parameter condition for the existence of interfacial waves.
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Smart Nondestructive Evaluation and Health Monitoring of Structural and Biological Systems
3 March 2003 | San Diego, California, United States