Perfectly matched layers for flexural waves in Kirchhof–Love plates

Morvaridi, Maryam; Brun, Michele

doi:10.1016/j.ijsolstr.2017.11.009

Cited by 7 publications

(4 citation statements)

References 18 publications

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“…The absorbing boundaries are designed using the approach described in 21 , with eight different areas that surround the model zone that represents the space-dependent attenuation (which increases exponentially from the boundary of the propagating zone to the end of the simulation box). Finally, the full computation takes approximatively 1 h in the frequency domain (around 45 s per frequency).…”

Section: Numerical Simulationsmentioning

confidence: 99%

Negative index metamaterial through multi-wave interactions: numerical proof of the concept of low-frequency Lamb-wave multiplexing

Lott

Roux

Rupin

et al. 2021

Sci Rep

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We study numerically the potential of a multimodal elastic metamaterial to filter and guide Lamb waves in a plate. Using a sub-wavelength array of elongated beams attached to the plate, and combining the coupling effects of the longitudinal and flexural motion of these resonators, we create narrow transmission bands at the flexural resonances of the beams inside the wide frequency bandgap induced by their longitudinal resonance. The diameter of the beams becomes the tuning parameter for selection of the flexural leakage frequency, without affecting the main bandgap. Finally, by combination of the monopolar and dipolar scattering effects associated with the coupled beam and plate system, we create a frequency-based multiplexer waveguide in a locally resonant metamaterial.

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Section: Numerical Simulationsmentioning

confidence: 99%

Negative index metamaterial through multi-wave interactions: numerical proof of the concept of low-frequency Lamb-wave multiplexing

Lott

Roux

Rupin

et al. 2021

Sci Rep

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“…where p1 and p2 are given in (30), (f k , g k ) represent the Dirichlet data of the total field u PML on Γ k for k = 1, 2.…”

Section: Convergence Analysismentioning

confidence: 99%

“…It has found extensive applications in solving various wave scattering problems, including, for example, acoustic waves [23], electromagnetic waves [24][25][26], and elastic waves [27,28]. The PML method has also been utilized numerically in solving biharmonic wave scattering problems [29][30][31], highlighting its convenience and accuracy. However, to our knowledge, a comprehensive discussion regarding the well-posedness of the PML method and its convergence has not been documented in existing literature.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Difficulty Levels of Examples in High School Mathematics Textbooks

Jiang

Wang

2021

School Mathematics Textbooks in China

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In this paper, we address exponential ergodicity for Lévy driven Langevin dynamics with singular potentials, which can be used to model the time evolution of a molecular system consisting of N particles moving in R d and subject to discontinuous stochastic forces. In particular, our results are applicable to the singular setups concerned with not only the Lennard-Jones-like interaction potentials but also the Coulomb potentials. In addition to Harris' theorem, the approach is based on novel constructions of proper Lyapunov functions (which are completely different from the setting for Langevin dynamics driven by Brownian motions), on invoking the Hörmander theorem for non-local operators and on solving the issue on an approximate controllability of the associated deterministic system as well as on exploiting the time-change idea.

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“…There has been a growing interest over the past years in the analysis of elastic waves in thin plates in the metamaterial community with the theoretical proposal [1,2], and its subsequent experimental validation [3,4] of a broadband cloak for flexural waves. Square [5] and diamond [6] cloaks are based on an improved transformed plate model, while form-invariance of the transformed equations in the framework of pre-stressed anisotropic plates is analized in [7,8,9].…”

Section: Introductionmentioning

confidence: 99%

Transformation design of in-plane elastic cylindrical cloaks, concentrators and lenses

Brun¹,

Guenneau²

2021

Preprint

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We analyse the elastic properties of a class of cylindrical cloaks deduced from linear geometric transforms x → x in the framework of the Milton-Briane-Willis cloaking theory [New Journal of Physics 8, 248, 2006]. More precisely, we assume that the mapping between displacement fields u(x) → u (x ) is such that u (x ) = A −t u(x), where A is either the transformation gradient F ij = ∂x i /∂x j or the second order identity tensor I. The nature of the cloaks under review can be three-fold: some of them are neutral for a source located a couple of wavelengths away; other lead to either a mirage effect or a field confinement when the source is located inside the concealment region or within their coated region (some act as elastic concentrators squeezing the wavelength of a pressure or shear polarized incident plane wave in their core); a last category of cloaks is classified as an elastic counterpart of electromagnetic perfect cylindrical lenses. The former two categories require either rank-4 elastic tensor and rank-2 density tensor and additional rank-3 and 2 positive definite tensors (A = F) or a rank 4 elasticity tensor and a scalar density (A = I) with spatially varying positive values. However, the latter example further requires that all rank-4, 3 and 2 tensors be negative definite (A = F) or that the elasticity tensor be negative definite (and non fully symmetric) as well as a negative scalar density (A = I). We provide some illustrative numerical examples with the Finite Element package Comsol Multiphysics when A is the identity.

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Perfectly matched layers for flexural waves in Kirchhof–Love plates

Cited by 7 publications

References 18 publications

Negative index metamaterial through multi-wave interactions: numerical proof of the concept of low-frequency Lamb-wave multiplexing

Negative index metamaterial through multi-wave interactions: numerical proof of the concept of low-frequency Lamb-wave multiplexing

Comparison of Difficulty Levels of Examples in High School Mathematics Textbooks

Transformation design of in-plane elastic cylindrical cloaks, concentrators and lenses

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