Generation and Reception of Elastic Waves via a Plane Boundary

A. Lutsch; G. J. Kühn

doi:10.1121/1.1918974

Reflection of high-frequency elastic waves from a non-plane boundary surface of the elastic medium

Journal of Sound and Vibration ◽

10.1016/j.jsv.2006.12.018 ◽

2007 ◽

Vol 302 (4-5) ◽

pp. 925-935 ◽

Cited By ~ 2

Author(s):

A. Pompei ◽

M.A. Sumbatyan ◽

N.V. Boyev

Keyword(s):

Elastic Medium ◽

Elastic Waves ◽

High Frequency ◽

Boundary Surface ◽

Plane Boundary

Download Full-text

Reflection and Transmission of Circularly Polarized Elastic Waves of Finite Amplitude

Journal of Applied Mechanics ◽

10.1115/1.3424669 ◽

1979 ◽

Vol 46 (4) ◽

pp. 867-872 ◽

Cited By ~ 8

Author(s):

M. M. Carroll

Keyword(s):

Elastic Waves ◽

Finite Elasticity ◽

Elliptic Functions ◽

Finite Amplitude ◽

Plane Boundary ◽

Elastic Solids ◽

Jacobian Elliptic Functions ◽

Reflection And Transmission ◽

The Third ◽

Fixed Boundaries

Finite amplitude standing wave solutions, obtained previously, are specialized to the case of incompressible isotropic elastic solids with cubic or quintic shear response. This allows closed-form expressions for the motion and stress field, in terms of Jacobian elliptic functions and elliptic integrals and furnishes solutions for approximate finite elasticity theories in which terms up to sixth degree in the stress and strains are retained. The solutions for reflection from free or fixed boundaries, for resonant standing waves in a plate, and for reflection and transmission at a plane boundary are examined in the context of the third and fourth-order approximations.

Download Full-text

Reflexion and Refraction of Plane Elastic Waves at a Plane Boundary between Aeolotropic Media

Geophysical Journal International ◽

10.1111/j.1365-246x.1960.tb01714.x ◽

1960 ◽

Vol 3 (4) ◽

pp. 406-418 ◽

Cited By ~ 47

Author(s):

M. J. P. Musgrave

Keyword(s):

Elastic Waves ◽

Plane Boundary

Download Full-text

High Resolution Electron Microscopy of internal interfaces in layered materials

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100174734 ◽

1990 ◽

Vol 48 (4) ◽

pp. 320-321

Author(s):

Yoichi Ishida ◽

Hideki Ichinose ◽

Yutaka Takahashi ◽

Jin-yeh Wang

Keyword(s):

Grain Boundaries ◽

Mirror Symmetry ◽

Functional Materials ◽

High Resolution Electron Microscopy ◽

Layered Materials ◽

Plane Boundary ◽

Chemical Information ◽

Layer Plane ◽

High Tc ◽

Cubic Metals

Layered materials draw attention in recent years in response to the world-wide drive to discover new functional materials. High-Tc superconducting oxide is one example. Internal interfaces in such layered materials differ significantly from those of cubic metals. They are often parallel to the layer of the neighboring crystals in sintered samples(layer plane boundary), while periodically ordered interfaces with the two neighboring crystals in mirror symmetry to each other are relatively rare. Consequently, the atomistic features of the interface differ significantly from those of cubic metals. In this paper grain boundaries in sintered high-Tc superconducting oxides, joined interfaces between engineering ceramics with metals, and polytype interfaces in vapor-deposited bicrystal are examined to collect atomic information of the interfaces in layered materials. The analysis proved that they are not neccessarily more complicated than that of simple grain boundaries in cubic metals. The interfaces are majorly layer plane type which is parallel to the compound layer. Secondly, chemical information is often available, which helps the interpretation of the interface atomic structure.

Download Full-text

Remarks on nonlinear elastic waves with null conditions

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2020039 ◽

2020 ◽

Vol 26 ◽

pp. 121

Author(s):

Dongbing Zha ◽

Weimin Peng

Keyword(s):

Initial Data ◽

Global Existence ◽

Elastic Waves ◽

Wave Equations ◽

Alternative Proof ◽

Classical Solutions ◽

Small Initial Data ◽

Hyperelastic Materials ◽

Variational Structure ◽

Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

Download Full-text