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

Haque, A.; Ghachi, Ratiba F.; Alnahhal, Wael; Aref, Amjad J.; Shim, Jongmin

doi:10.1115/1.4036469

Cited by 7 publications

(2 citation statements)

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“…TMM and k1(ω, k2) solutions The transfer matrix method has been explained in detail in 65 and it is treated only briefly here for completeness (see Appendix-A for some more details). Following 65 we define our laminate as a periodically layered structure in the x 1 direction with the layer interfaces in the x 2 -x 3 plane and infinite in this plane. In the direction of periodicity the laminated composite is characterized by a unit cell Ω of length h (0 ≤ x 1 ≤ h).…”

Section: Dispersion Calculationsmentioning

confidence: 99%

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Scattering under Linear Non Self-Adjoint Operators: Case of in-Plane Elastic Waves

Mokhtari,

Lu,

Zhou

et al. 2020

Preprint

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In this paper, we consider the problem of the scattering of in-plane waves at an interface between a homogeneous medium and a metamaterial. The relevant eigenmodes in the two regions are calculated by solving a recently described non self-adjoint eigenvalue problem particularly suited to scattering studies. The method efficiently produces all propagating and evanescent modes consistent with the application of Snell's law and is applicable to very general scattering problems. In a model composite, we elucidate the emergence of a rich spectrum of eigenvalue degeneracies. These degeneracies appear in both the complex and real domains of the wave-vector. However, since this problem is non self-adjoint, these degeneracies generally represent a coalescing of both the eigenvalues and eigenvectors (exceptional points). Through explicit calculations of Poynting vector, we point out an intriguing phenomenon: there always appears to be an abrupt change in the sign of the refraction angle of the wave on two sides of an exceptional point. Furthermore, the presence of these degeneracies, in some cases, hints at fast changes in the scattered field as the incident angle is changed by small amounts. We calculate these scattered fields through a novel application of the Betti-Rayleigh reciprocity theorem. We present several numerical examples showing a rich scattering spectrum. In one particularly intriguing example, we point out wave behavior which may be related to the phenomenon of resonance trapping. We also show that there exists a deep connection between energy flux conservation and the biorthogonality relationship of the non self-adjoint problem. The proof applies to the general class of scattering problems involving elastic waves (under self-adjoint or non self-adjoint operators).

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Section: Dispersion Calculationsmentioning

confidence: 99%

“…(A4). So that if k 1 is a solution, then so are ±(k 1 ± 2nπ/h) for all integer n (details in 65 ). This class of problem, termed k 1 (ω, k 2 ), is generally associated with a non-normal differential operator 27 This generally gives rise to complex eigenvalues and linearly dependent eigenvectors.…”

Section: Dispersion Calculationsmentioning

confidence: 99%