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 |
本文献已被 SpringerLink 等数据库收录! |
|