Revisiting imperfect interface laws for two-dimensional elastodynamics

We study the interaction of in-plane elastic waves with imperfect interfaces composed of a periodic array of voids or cracks. An effective model is derived from high-order asymptotic analysis based on two-scale homogenization and matched asymptotic technique. In two-dimensional elasticity, we obtain jump conditions set on the in-plane displacements and normal stresses; the jumps involve in addition effective parameters provided by static, elementary problems being the equivalents of the cell problems in classical two-scale homogenization. The derivation of the model is conducted in the transient regime and its stability is guarantied by the positiveness of the effective interfacial energy. Spring models are envisioned as particular cases. It is shown that massless-spring models are recovered in the limit of small void thicknesses and collinear cracks. By contrast, the use of mass-spring model is justified at normal incidence, otherwise unjustified. We provide quantitative validations of our model and comparison with spring models by means of comparison with direct numerical calculations in the harmonic regime.

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Abnormal wave propagation behaviors in two-dimensional mass–spring structures with nonlocal effect

Mathematics and Mechanics of Solids ◽

10.1177/1081286519853606 ◽

2019 ◽

Vol 24 (11) ◽

pp. 3632-3643 ◽

Cited By ~ 2

Author(s):

Jiao Wang ◽

Yang Huang ◽

Weiqiu Chen ◽

Weiqiu Zhu

Keyword(s):

Wave Propagation ◽

Group Velocity ◽

Elastic Waves ◽

Negative Refraction ◽

Nonlocal Effect ◽

Two Dimensional ◽

Spring Stiffness ◽

Negative Group ◽

Mass Spring ◽

Negative Group Velocity

This paper considers the propagation of elastic waves in periodic two-dimensional mass–spring structures with diagonal springs. The second-neighbor interactions in non-diagonal directions are included to account for the nonlocal effect. The influences of the spring stiffness in the diagonal directions and the nonlocal effect on the propagation characteristics of elastic waves are then scrutinized. Through the dispersion relation curve and the equi-frequency contours, it is seen that when the diagonal spring stiffness increases, the slope of the second curve in the [Formula: see text]–M direction will not always be positive, meaning that the negative group velocity occurs. Therefore, an incident wavevector with a chosen angle to the negative group velocity can lead to the negative refraction phenomenon in the two-dimensional mass–spring structure. Another interesting phenomenon called directional radiation of elastic waves can also be achieved by adjusting the nonlocal effect. Within a certain range, the stronger the nonlocal effect in a specific direction is, the more obviously the elastic waves propagate along this direction. In this paper, we theoretically analyze and numerically simulate the phenomena of negative refraction and directional wave propagation by choosing a proper set of parameters of the two-dimensional mass–spring structure.

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Scattering and Transmission of Elastic Waves from an Interface Between Two Planar Waveguides

Surface Review and Letters ◽

10.1142/s0218625x0300558x ◽

2003 ◽

Vol 10 (05) ◽

pp. 727-736

Author(s):

M. Tamine

Keyword(s):

Elastic Waves ◽

Strain Field ◽

Phonon Scattering ◽

Domain Boundary ◽

Normal Incidence ◽

Planar Waveguides ◽

Two Dimensional ◽

Reflection And Transmission ◽

Coherent Coupling ◽

Matching Procedure

The scattering and transmission properties of elastic waves in a two-dimensional waveguide constructed from two dissimilar square lattices which exhibit a strain field at the interface, have been theoretically studied. The strain field is described by the existence of the local forces at an interface different to those occurring outside the surrounding interface. The theoretical approach using the matching procedure for calculating phonon scattering at the interface domain boundary is also presented. The reflection and transmission probabilities in the scattering region are calculated and illustrated for the longitudinal and transversal propagating modes in the normal incidence of the elastic wave. The conductance properties in full accordance with the Landauer–Büttiker description of electron transport are also calculated. The asymmetric Fano resonance type may appear in the phonon transmission spectra due to the coherent coupling between the two-dimensional crystal phonons and the localized vibration modes on the interface boundary. A discussion on the vibrational waves in the scattering region is given. We also show how even a simple interface in a two-dimensional situation can be used as a phonon filter, and how phonons can be used to probe an interface.

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Radiative transfer of elastic waves versus finite difference simulations in two-dimensional random media

Journal of Geophysical Research Atmospheres ◽

10.1029/2005jb003952 ◽

2006 ◽

Vol 111 (B4) ◽

Cited By ~ 49

Author(s):

J. Przybilla ◽

M. Korn ◽

U. Wegler

Keyword(s):

Radiative Transfer ◽

Finite Difference ◽

Elastic Waves ◽

Random Media ◽

Two Dimensional

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Dynamic Analysis Of Elastic Waves In A Elliptic Cavity In An Inhomogeneous Medium With Two-Dimensional Density Variation

2020 15th Symposium on Piezoelectrcity, Acoustic Waves and Device Applications (SPAWDA) ◽

10.1109/spawda51471.2021.9445549 ◽

2021 ◽

Author(s):

Chen-xi Sun ◽

Zai-lin Yang ◽

Yong Yang

Keyword(s):

Dynamic Analysis ◽

Inhomogeneous Medium ◽

Elastic Waves ◽

Density Variation ◽

Two Dimensional ◽

Elliptic Cavity

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Multiple-scattering theory for out-of-plane propagation of elastic waves in two-dimensional phononic crystals

Journal of Physics Condensed Matter ◽

10.1088/0953-8984/17/25/003 ◽

2005 ◽

Vol 17 (25) ◽

pp. 3735-3757 ◽

Cited By ~ 26

Author(s):

Jun Mei ◽

Zhengyou Liu ◽

Chunyin Qiu

Keyword(s):

Multiple Scattering ◽

Elastic Waves ◽

Scattering Theory ◽

Phononic Crystals ◽

Two Dimensional ◽

Multiple Scattering Theory ◽

Out Of Plane ◽

Propagation Of Elastic Waves

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Diffraction of a pulse by a resistive half-plane. I. Normal incidence

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1960.0085 ◽

1960 ◽

Vol 255 (1283) ◽

pp. 538-549 ◽

Cited By ~ 6

Keyword(s):

Time Dependence ◽

Half Plane ◽

Wave Diffraction ◽

Diffraction Problem ◽

Normal Incidence ◽

Step Function ◽

Two Dimensional ◽

Dynamic Similarity ◽

Function Time ◽

Dimensional Wave

The two-dimensional wave diffraction problem, acoustic or electromagnetic, in which a pulse of step-function time dependence is diffracted by a resistive half-plane is solved by assuming dynamic similarity in the solution.

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A CALIBRATED MODEL SEISMIC SYSTEM

Geophysics ◽

10.1190/1.1440270 ◽

1972 ◽

Vol 37 (3) ◽

pp. 445-455 ◽

Cited By ~ 1

Author(s):

C. N. G. Dampney ◽

B. B. Mohanty ◽

G. F. West

Keyword(s):

Wave Propagation ◽

Elastic Wave ◽

Elastic Waves ◽

Critical Examination ◽

Two Dimensional ◽

Linear Filtering ◽

Analog Model ◽

Basic Assumptions ◽

Electronic Circuitry ◽

Seismic System

Simple electronic circuitry and axially polarized ceramic transducers are employed to generate and detect elastic waves in a two‐dimensional analog model. The absence of reverberation and the basic simplicity. of construction underlie the advantages of this system. If the form of the fundamental wavelet in the model itself, as modified by the linear filtering effects of the remainder of the system, can be found, then calibration is achieved. This permits direct comparison of theoretical and experimental seismograms for a given model if its impulse response is known. A technique is developed for calibration and verified by comparing Lamb’s theoretical and experimental seismograms for elastic wave propagation over the edge of a half plate. This comparison also allows a critical examination of the basic assumptions inherent in a model seismic system.

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An obstacle problem for elliptic membrane shells

Mathematics and Mechanics of Solids ◽

10.1177/1081286518800164 ◽

2018 ◽

Vol 24 (5) ◽

pp. 1503-1529 ◽

Cited By ~ 5

Author(s):

Philippe G. Ciarlet ◽

Cristinel Mardare ◽

Paolo Piersanti

Keyword(s):

Vector Field ◽

Asymptotic Analysis ◽

Obstacle Problem ◽

Displacement Vector ◽

Middle Surface ◽

Two Dimensional ◽

Displacement Vector Field ◽

Membrane Shells ◽

Signorini Condition ◽

Confinement Condition

Our objective is to identify two-dimensional equations that model an obstacle problem for a linearly elastic elliptic membrane shell subjected to a confinement condition expressing that all the points of the admissible deformed configurations remain in a given half-space. To this end, we embed the shell into a family of linearly elastic elliptic membrane shells, all sharing the same middle surface [Formula: see text], where [Formula: see text] is a domain in [Formula: see text] and [Formula: see text] is a smooth enough immersion, all subjected to this confinement condition, and whose thickness [Formula: see text] is considered as a “small” parameter approaching zero. We then identify, and justify by means of a rigorous asymptotic analysis as [Formula: see text] approaches zero, the corresponding “limit” two-dimensional variational problem. This problem takes the form of a set of variational inequalities posed over a convex subset of the space [Formula: see text]. The confinement condition considered here considerably departs from the Signorini condition usually considered in the existing literature, where only the “lower face” of the shell is required to remain above the “horizontal” plane. Such a confinement condition renders the asymptotic analysis substantially more difficult, however, as the constraint now bears on a vector field, the displacement vector field of the reference configuration, instead of on only a single component of this field.

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