Generation and Propagation of Anti-Plane Surface Waves on a Body with Depth-Dependent Properties

We discuss new type of surface waves which exist in elastic media with surface energy. Here we present the model of a coating made of polymeric brush. From the physical point of view the considered model of surface elasticity describes a highly anisotropic surface coating. Here the surface energy model could be treated as 2D reduced strain gradient continuum as surface strain energy depends on few second spatial derivatives of displacements. From the mechanical point of view the proposed model relates to 2D coating made of long fibers undergoing stretching and bending deformations. We consider here anti-plane surface waves. The dispersion relation is derived and its dependence on the material parameters is analysed.

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Propagation of plane surface waves over a rectangular step with overhang and over a partially capped rectangular trench

Journal of Applied Mechanics and Technical Physics ◽

10.1007/bf00851935 ◽

1992 ◽

Vol 32 (5) ◽

pp. 684-691

Author(s):

I. V. Sturova

Keyword(s):

Surface Waves ◽

Plane Surface

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Strongly anisotropic surface elasticity and antiplane surface waves

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2019.0100 ◽

2019 ◽

Vol 378 (2162) ◽

pp. 20190100 ◽

Cited By ~ 6

Author(s):

V. A. Eremeyev

Keyword(s):

Surface Waves ◽

Plane Surface ◽

Plane Waves ◽

Surface Elasticity ◽

Elastic Solid ◽

Point Of View ◽

Surface Strain ◽

Elastic Membrane ◽

Preferred Direction ◽

Anisotropic Surface

Within the new model of surface elasticity, the propagation of anti-plane surface waves is discussed. For the proposed model, the surface strain energy depends on surface stretching and on changing of curvature along a preferred direction. From the continuum mechanics point of view, the model describes finite deformations of an elastic solid with an elastic membrane attached on its boundary reinforced by a family of aligned elastic long flexible beams. Physically, the model was motivated by deformations of surface coatings consisting of aligned bar-like elements as in the case of hyperbolic metasurfaces. Using the least action variational principle, we derive the dynamic boundary conditions. The linearized boundary-value problem is also presented. In order to demonstrate the peculiarities of the problem, the dispersion relations for surface anti-plane waves are analysed. We have shown that the bending stiffness changes essentially the dispersion relation and conditions of anti-plane surface wave propagation. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.

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On the scattering of evanescent waves into sound

Journal of Fluid Mechanics ◽

10.1017/s0022112087002829 ◽

1987 ◽

Vol 184 ◽

pp. 101-121 ◽

Cited By ~ 5

Author(s):

J. E. Ffowcs Williams ◽

D. C. Hill

Keyword(s):

Pressure Gradient ◽

Surface Waves ◽

Axial Force ◽

Evanescent Wave ◽

Plane Surface ◽

Sound Field ◽

Incoming Wave ◽

Mean Pressure ◽

Rigid Plane ◽

Free Membrane

This paper concerns the conversion of momentum and energy from evanescent surface waves into sound. Exact results are obtained from surface waves of specified form on a confined region of an otherwise rigid plane surface. The model chosen is simple enough for exact analysis while approximating some of what we believe to be significant aspects of sound generation by vibrating surface panels.We find that the evanescent wave approaching an edge gives up all of its energy into sound, a sound which is beamed mainly parallel to the direction of the surface-wave phase velocity. The surface remains energetically inactive, but exerts a force on the fluid in the opposite direction to the incoming wave. This force is balanced by a nonlinear mean pressure gradient in the field of the evanescent wave, and by momentum in the sound field.Sound is also produced when a similar evanescent wave emerges from an edge. The surface has then to provide the necessary energy for both waves. These waves induce a mean axial force at the boundary which forces the fluid in the direction of the receding evanescent wave.A similar wave travelling across a finite panel in the otherwise rigid plane surface is observed to have some characteristics of the previous two cases, but there is no axial force arising from the mean pressure gradient.These results are applied to the problem of a semi-infinite tensioned membrane, and the energy radiation under light fluid loading is determined for the case of high and low free membrane wave speeds.

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