Elastic waves in periodically layered infinite and semi-infinite anisotropic media

Nougaoui, A.; Rouhani, B. Djafari

doi:10.1016/s0039-6028(87)80618-0

Cited by 50 publications

(35 citation statements)

References 24 publications

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“…We have observed these characteristics, both for the exact and for the NSWA calculations. However, 3 does not show this behavior as will be discussed below. Furthermore, 3 does not exist in the NSWA and therefore it must be associated with the behavior of the surface waves.…”

Section: Analysis Of the Resultsmentioning

confidence: 94%

“…8͑a͒ and 8͑c͒ we have the real and imaginary parts of 1 , respectively, and in Figs. 8͑b͒ and 8͑d͒ the real and imaginary parts of 3 , respectively. The figures shows four solid lines but only two dotted lines because in the NSWA 3 does not exist.…”

Section: Discussionmentioning

confidence: 99%

“…However, the direct analytical calculations become very cumbersome once the dimension of the propagator matrix is higher than 2 ϫ 2 due to the coupled-mode effect. It occurs, for instance, at a mixing of the sagittal acoustic modes in a symmetry plane of purely elastic stratified media [2][3][4][5][6] or at the shear horizontal ͑SH͒ waves propagation in the presence of electromechanical coupling. 2,[7][8][9][10][11] Theoretical treatment in those cases is largely numerical.…”

Section: Introductionmentioning

confidence: 99%

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Surface and shear horizontal waves in piezoelectric composites

2005

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Surface and shear horizontal waves in piezoelectric composite media consisting of piezoelectric layers of hexagonal 6mm symmetry are studied. We consider finite and infinite systems. For the finite case we study "periodic" and two types of nonperiodic structures: Fibonacci sequences and systems with a linear perturbation in the piezoelectric parameters which give rise to resonances of Stark-Ladder type. For the infinite case we only consider periodic systems. The transmission, dispersion relation, angular dispersion relation, and eigenmodes of vibration of the composites are analyzed. We discuss in detail the effect of surface waves on these properties. We use the transfer matrix formalisms of 4 ϫ 4 and 2 ϫ 2 dimensions to study the system in the exact approach and in the approximation where the surface waves are neglected, respectively. Numerical results are also presented.

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Section: Analysis Of the Resultsmentioning

confidence: 94%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Surface and shear horizontal waves in piezoelectric composites

2005

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“…Using the analytical solution of sagittal plane waves (19), the dispersion relations of infinitely periodic multilayered composites can be calculated along specific wavevector paths. Due to the homogeneous properties along x 1 -direction, wave motion in the infinitely periodic multilayered composites contains infinitely large j 1 components.…”

Section: Analytical Dispersion Relation and Spatial Aliasingmentioning

confidence: 99%

“…On the other hand, due to the complexity of the configuration, there have been limited analytical investigations on dispersion relation for wave motion at arbitrary angles in the sagittal plane, in which the pressure wave (P-wave) and vertical shear wave (SV-wave) propagate [18]. The analytical dispersion relations of infinitely periodic bilayered composites for sagittal plane waves can be found in several references [18][19][20][21]. However, only a few researchers [22,23] have presented the analytical dispersion relation of infinitely periodic multilayered composites for the sagittal plane waves, and their formulations are unduly complex.…”

Section: Introductionmentioning

confidence: 99%

Generalized Spatial Aliasing Solution for the Dispersion Analysis of Infinitely Periodic Multilayered Composites Using the Finite Element Method

Haque

Ghachi

Alnahhal

et al. 2017

Journal of Vibration and Acoustics

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The finite element (FE) method offers an efficient framework to investigate the evolution of phononic crystals which possess materials or geometric nonlinearity subject to external loading. Despite its superior efficiency, the FE method suffers from spectral distortions in the dispersion analysis of waves perpendicular to the layers in infinitely periodic multilayered composites. In this study, the analytical dispersion relation for sagittal elastic waves is reformulated in a substantially concise form, and it is employed to reproduce spatial aliasing-induced spectral distortions in FE dispersion relations. Furthermore, through an anti-aliasing condition and the effective elastic modulus theory, an FE modeling general guideline is provided to overcome the observed spectral distortions in FE dispersion relations of infinitely periodic multilayered composites, and its validity is also demonstrated.

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Sagittal Elastic Waves at the Interface between a Superlattice and a Substrate: Theoretical Analysis of the Density of States and Reflection Coefficientsrik

Bria

Boudouti

Nougaoui

et al. 2000

phys. stat. sol. (b)

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We investigate the existence and behavior of localized and resonant acoustic modes of sagittal polarization associated with the interface between a superlattice (SL) and a substrate. These modes appear as well‐defined peaks in the density of states, either inside the minigaps or inside the bulk bands of the SL and the substrate. It is shown that the interface modes strongly depend on the acoustic impedances of the substrate. Furthermore, a phonon incident on the superlattice from a substrate is partially reflected in the substrate, therefore the amplitudes and the phases of the reflection coefficients enable us to deduce the frequency ranges of the bulk bands and the minigaps of the superlattice as well as the frequency levels of the interface resonant modes. The densities of states and reflection coefficients, which are calculated as function of the frequency ω and the wave vector k∥(parallel to the interfaces), are obtained from an analytical determination of the Green's function for the superlattice/substrate interface. Specific application of our analytical results are given for a W/Al isotropic superlattice in contact with a substrate with different acoustic impedances.

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Elastic waves in periodically layered infinite and semi-infinite anisotropic media

Cited by 50 publications

References 24 publications

Surface and shear horizontal waves in piezoelectric composites

Surface and shear horizontal waves in piezoelectric composites

Generalized Spatial Aliasing Solution for the Dispersion Analysis of Infinitely Periodic Multilayered Composites Using the Finite Element Method

Sagittal Elastic Waves at the Interface between a Superlattice and a Substrate: Theoretical Analysis of the Density of States and Reflection Coefficientsrik

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