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On the guided and surface shear horizontal waves in monoclinic transversely periodic layers and halfspaces with arbitrary variation of material properties across the unit cell
Authors:AL Shuvalov  O Poncelet  AN Podlipenets
Institution:(1) Laboratoire de Mécanique Physique, Université Bordeaux 1, UMR CNRS 5469, 351, F-33405 Talence Cedex, France;(2) Department of Superconductor Electronics, Institute for Metal Physics, UNAS, UA-03680 Kyiv, Ukraine
Abstract:The paper outlines analytically and exemplifies numerically the basic aspects, characterizing dispersion spectra of the shear horizontal (SH) waves in transversely periodic layers and half-spaces with a monoclinic functionally graded unit cell. On introducing the background, the ’quasi-orthorhombic’ formulation is pointed out. Further analytical consideration bypasses explicit intricacy of the wave solutions in continuously varying media and relies only on a few basic traits of the governing equation of SH motion. An elementary reasoning pinpoints the key features of the Floquet eigenmodes and their link to the traction-free boundary conditions in question. This simple grounds suffices to generalize the remarkable property, previously restricted to the orthorhombic piecewise homogeneous periodic stacks, which implies that the SH dispersion spectrum for a unit cell, assumed free of traction at the faces, is embedded into the spectrum for the finite periodic structure of these unit cells and contains the locus of surface-wave solutions for the semi-infinite periodic structure. The conclusion is valid for an arbitrary continuous and/or discrete transverse periodic inhomogeneity. Numerical results, presented for the case of continuously inhomogeneous unit cell, are based on the Peano series of multiple integrals.
Keywords:periodically inhomogeneous medium  SH guided and surface waves
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