Dispersion relations for electroelastic shear waves in a periodically layered medium

Zinchuk, L. P.; Podlipenets, A. N.; Shul’ga, N. À.

doi:10.1007/bf00887470

Cited by 10 publications

(6 citation statements)

References 5 publications

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“…Interestingly, taking into account absorption by setting complex does not violate this property, for, the statement (37) remains valid (though the interpretations invoking the Floquet spectrum and the physical/nonphysical solutions for surface waves certainly modify). On the other hand, the considered invariance property is no longer valid for the SH waves in piezoelectric periodic structures (see Zinchuk et al, 1988Zinchuk et al, , 1990Podlipenets et al, 1996), because the electromechanical coupling increases the algebraic dimension of the problem, which in this sense becomes similar to the case of coupled in-plane polarized waves.…”

Section: Discussionmentioning

confidence: 95%

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

2006

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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.

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Section: Discussionmentioning

confidence: 95%

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

2006

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“…Zinchuk et al (1990Zinchuk et al ( , 1992 have studied the propagation properties of a shear surface wave in the regularly periodic layered half-space.…”

Section: Introductionmentioning

confidence: 99%

Surface electro-elastic Love waves in a layered structure with a piezoelectric substrate and two isotropic layers

Piliposian

Danoyan

2009

International Journal of Solids and Structures

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a b s t r a c tPropagation of electro-elastic surface Love waves in a structure consisting of a piezoelectric half-space substrate of crystal class 6, 4, 6 mm or 4 mm and two layers, one of which (adjacent to the substrate) is a conducting material and the second is either a conducting or a dielectric material, is considered. The mathematical model obtained includes all the above crystal classes i.e. the surface wave problems related to all these classes are presented in a single mathematical model. The dispersion equation for the existence of Love surface waves with respect to phase velocity is obtained. Numerical calculations are carried out for three different layered structures. The effect of the second layer on the propagation behaviour of the surface Love wave in the structure is revealed.

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“…The Love waves generating in an elastic layer SiO 2 deposited on a piezoelectric substrate ST-90X were analytically studied by Liu and He [ 5 ]. The investigation of surface waves in structures with more than one layer was a subject of many papers (see, for example, [ 6 , 7 , 8 ]). In [ 7 ] the behavior of elastic waves in the three-layered piezoelectric media with inhomogeneous initial stresses was analyzed through the method of transfer matrix.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Micro-Inertia and Flexoelectricity on Love Wave Propagation in Layered Piezoelectric Structures

Hrytsyna

Sládek

2021

Nanomaterials

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The non-classical linear governing equations of strain gradient piezoelectricity with micro-inertia effect are used to investigate Love wave propagation in a layered piezoelectric structure. The influence of flexoelectricity and micro-inertia effect on the phase wave velocity in a thin homogeneous flexoelectric layer deposited on a piezoelectric substrate is investigated. The dispersion relation for Love waves is obtained. The phase velocity is numerically calculated and graphically illustrated for the electric open-circuit and short-circuit conditions and for distinct material properties of the layer and substrate. The influence of direct flexoelectricity, micro-inertia effect, as well as the layer thickness on Love wave propagation is studied individually. It is found that flexoelectricity increases the Love-wave phase velocity, while the micro-inertia effect reduces its value. These effects become more significant for Love waves with shorter wavelengths and small guiding layer thicknesses.

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Dispersion relations for electroelastic shear waves in a periodically layered medium

Cited by 10 publications

References 5 publications

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

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

Surface electro-elastic Love waves in a layered structure with a piezoelectric substrate and two isotropic layers

The Effect of Micro-Inertia and Flexoelectricity on Love Wave Propagation in Layered Piezoelectric Structures

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