A simple closed form dispersion equation for shear types of surface waves propagating in periodic structures

1993 ◽  
Vol 40 (4) ◽  
pp. 421-423 ◽  
Author(s):  
V.P. Plessky
Keyword(s):  
Surface Waves ◽  
Closed Form ◽  
Dispersion Equation ◽  
Periodic Structures

Fundamental properties of surface waves in lossless stratified structures

2010 ◽  
Vol 466 (2120) ◽  
pp. 2447-2469 ◽  
Author(s):  
Guido Valerio ◽  
David R. Jackson ◽  
Alessandro Galli
Keyword(s):  
Surface Waves ◽  
Dispersion Equation ◽  
High Frequency ◽  
Low Frequency ◽  
Layered Structures ◽  
Graphical Solution ◽  
Fundamental Properties ◽  
The Past ◽  
Permittivity And Permeability ◽  
Constitutive Parameters

This paper is focused on dispersive properties of lossless planar layered structures with media having positive constitutive parameters (permittivity and permeability), possibly uniaxially anisotropic. Some of these properties have been derived in the past with reference to specific simple layered structures, and are here established with more general proofs, valid for arbitrary layered structures with positive parameters. As a first step, a simple application of the Smith chart to the relevant dispersion equation is used to prove that evanescent (or plasmonic-type) waves cannot be supported by layers with positive parameters. The main part of the paper is then focused on a generalization of a common graphical solution of the dispersion equation, in order to derive some general properties about the behaviour of the wavenumbers of surface waves as a function of frequency. The wavenumbers normalized with respect to frequency are shown to be always increasing with frequency, and at high frequency they tend to the highest refractive index in the layers. Moreover, two surface waves with the same polarization cannot have the same wavenumber at a given frequency. The low-frequency behaviours are also briefly addressed. The results are derived by means of a suitable application of Foster’s theorem.

scholarly journals Lamb Waves in Anisotropic Functionally Graded Plates: A Closed Form Dispersion Solution

2019 ◽  
Vol 36 (1) ◽  
pp. 1-6
Author(s):  
S. V. Kuznetsov
Keyword(s):  
Closed Form ◽  
Dispersion Equation ◽  
Lamb Waves ◽  
Functionally Graded ◽  
Stratified Media ◽  
Exponential Mapping ◽  
Functionally Graded Plates ◽  
Graded Materials ◽  
Transverse Inhomogeneity ◽  
Dispersion Solution

ABSTRACTPropagation of harmonic Lamb waves in plates made of functionally graded materials (FGM) with transverse inhomogeneity is studied by combination of the Cauchy six-dimensional formalism and matrix exponential mapping. For arbitrary transverse inhomogeneity a closed form implicit solution for dispersion equation is derived and analyzed. Both the dispersion equation and the corresponding solution resemble ones obtained for stratified media. The dispersion equation and the corresponding solution are applicable to media with arbitrary elastic (monoclinic) anisotropy.

scholarly journals Propagation of Torsional Surface Waves in a Nonhomogeneous Half-Space With Circular Irregularity in Free Surface

2018 ◽  
Vol 23 (4) ◽  
pp. 929-939
Author(s):  
M. Sethi ◽  
A.K. Sharma ◽  
A. Sharma
Keyword(s):  
Free Surface ◽  
Phase Velocity ◽  
Surface Waves ◽  
Dispersion Equation ◽  
Half Space ◽  
Analytical Solutions ◽  
Homogeneous Half Space ◽  
Depth Separation ◽  
Separation Of Variable ◽  
Torsional Surface Waves

Abstract The present paper studies the effect of circular regularity on propagation of torsional surface waves in an elastic non-homogeneous half-space. Both rigidity and density of the half-space are assumed to vary inversely linearly with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation of the torsional surface waves. Also, the effects of non-homogeneity and irregularity on the phase velocity of torsional surface waves have shown graphically.

Surface waves above thin porous layers and periodic structures

1999 ◽  
Vol 105 (2) ◽  
pp. 1385-1385 ◽  
Author(s):  
Walter Lauriks ◽  
Luc Kelders ◽  
Jean François Allard
Keyword(s):  
Surface Waves ◽  
Periodic Structures ◽  
Porous Layers
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