An approximate theory for waves in a slender elastic wedge immersed in liquid

Shanin, A. V.; Krylov, Victor V.

doi:10.1098/rspa.2000.0608

Cited by 4 publications

(4 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The analytical structure of such waves is, usually, different from the waves discussed in this paper, even though certain types of edge waves can also be successfully described using an asymptotic plate theory, e.g. waves localized in the vicinity of a thin wedge with linearly varying thickness, see [18][19][20] and references therein.…”

Section: Introductionmentioning

confidence: 91%

Extensional edge waves in pre-stressed incompressible plates

Pichugin

Rogerson

2011

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

Consider a semi-infinite layer of an incompressible elastic material subjected to a finite static homogeneous pre-deformation. This paper describes the long-wave low-frequency limiting behaviour of extensional edge waves that may propagate along the free edge of such a layer. The analysis is done by constructing an asymptotic plate theory that describes the extensional motion of thin pre-stressed incompressible plates. The secular equation for edge waves propagating along one of the principal axes of the pre-stress is studied for bi-axial deformations and several specific material models. We show that certain combinations of material models and configurations of pre-stresses do not support the propagation of edge waves, which mirrors the situation with surface waves in pre-stressed media. More unusually, we present a seemingly first explicit example of the non-unique edge wave solutions existing in thin pre-stressed plates.

show abstract

Section: Introductionmentioning

confidence: 91%

Extensional edge waves in pre-stressed incompressible plates

Pichugin

Rogerson

2011

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

show abstract

“…As a result, one can obtain relatively simple and physically explicit solutions for localised waves propagating in wedges in contact with water (Krylov, 1994(Krylov, , 1998Shuvalov et al, 2000). Other known approaches to analysing wedge elastic waves in contact with water include Wiener-Hopf techniques (Shanin et al, 2000) and finite element calculations (Hladky-Hennion et al, 1997). It should be noted that wedge elastic waves in contact with water that should be used for propulsion are waves propagating in the subsonic regime of wave propagation (in comparison with the speed of sound in water).…”

Section: Introductionmentioning

confidence: 99%

On the role of nonlinear distortion in the theory of wave-like aquatic propulsion

Krylov

2017

Ocean Engineering

View full text Add to dashboard Cite

Recent experimental investigations of small model boats propelled by propagating flexural waves carried out by the present author and his co-workers demonstrated viability of this type of propulsion as an alternative to a well-known screw propeller. Since the amplitudes of propagating flexural waves propelling the model boats are large enough, it is natural to consider the effect of nonlinear distortion of propagating localised flexural waves on generated thrust. This problem is explored in the present work by adding nonlinear harmonics of propulsive flexural waves to the well-known Lighthill's formula for generated thrust, which predicts a zero value of thrust in the case of linear flexural wave of constant amplitude. For simplicity, only the lowest (third) harmonic growing linearly with the distance of propagation is used. The resulting formula for the averaged thrust shows that, due to the effect of the third harmonic, the thrust is no longer zero, thereby demonstrating that nonlinear distortion of the propulsive flexural waves contributes positively to the generated thrust.

show abstract

“…As a result, one can obtain relatively simple and physically explicit solutions for localised waves propagating in wedges in contact with vacuum (Krylov, 1989(Krylov, , 1990a(Krylov, , 1990b as well as in wedges immersed in water (Krylov, 1994(Krylov, , 1998Krylov and Shuvalov, 2000;Shuvalov and Krylov, 2000). Other known approaches to analysing wedge elastic waves in contact with water include Wiener-Hopf techniques (Shanin and Krylov, 2000) and finite element calculations (Hladky-Hennion et al, 1997).…”

Section: Guided Elastic Waves In Contact With Watermentioning

confidence: 99%

Experimental confirmation of the propulsion of marine vessels employing guided flexural waves in attached elastic fins

Krylov

Pritchard

2007

Journal of Fluids and Structures

View full text Add to dashboard Cite

• This is the author's version of a work that was accepted for publication in AbstractThis paper describes the results of the first experimental verification of the idea of wavelike aquatic propulsion of manned marine vessels first published by one of the present authors (V.V.K.) in 1994. The idea is based on employing the unique type of guided flexural elastic waves propagating along edges of immersed wedge-like structures attached to a body of a small ship or a submarine as keels or wings and used for the propulsion. The principle of employing such guided flexural waves as a source of aquatic propulsion is similar to that used in nature by stingrays. It is vitally important for the application of this idea to manned vessels that, in spite of vibration of the fins, the main body of the craft remains undisturbed as the energy of guided elastic waves is concentrated away from it. The main expected advantages of this new propulsion method over the existing ones, e.g. jets and propellers, are the following: it is quiet, and it is environmentally friendly and safe for people and wildlife. To * Corresponding author: Tel.: +44 1509 227216, E-mail address: V.V.Krylov@lboro.ac.uk 2 verify the idea experimentally, the first working prototype of a small catamaran using the above-mentioned wave-like propulsion via the attached rubber keel has been build and tested.The test results have shown that the catamaran was propelled efficiently and could achieve the speed of 36 cm/s, thus demonstrating that the idea of wave-like propulsion of manned craft is viable. The reported proof of the viability of this idea may open new opportunities for marine craft propulsion, which can have far reaching implications.

show abstract

An approximate theory for waves in a slender elastic wedge immersed in liquid

Cited by 4 publications

References 8 publications

Extensional edge waves in pre-stressed incompressible plates

Extensional edge waves in pre-stressed incompressible plates

On the role of nonlinear distortion in the theory of wave-like aquatic propulsion

Experimental confirmation of the propulsion of marine vessels employing guided flexural waves in attached elastic fins

Contact Info

Product

Resources

About