Effect of compression on wave diffraction by a floating elastic plate

Mohapatra, Soudamini; Ghoshal, Ritwik; Sahoo, T.

doi:10.1016/j.jfluidstructs.2012.07.005

Cited by 31 publications

(8 citation statements)

References 25 publications

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“…Moreover, for Q < Q cg , two of the positive real roots disperse into a complex plane to provide four complex roots and one real root. In the earlier study of [18,49,54], although the critical value of compressive force for which group and phase velocities vanish was determined, a detailed analysis of wave blocking in this trapped energy zone was missing. Further, in this trapped energy zone, the occurrence of three real positive roots and their coalescence is contrary to the earlier assumption that the dispersion relation in equation (3.5) has a single positive real root (as in [18,49]).…”

Section: Wave Blocking In the Absence Of Currentmentioning

confidence: 99%

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Dynamics of flexural gravity waves: from sea ice to Hawking radiation and analogue gravity

2018

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The propagation of flexural gravity waves, routinely used to model wave interaction with sea ice, is studied, including the effect of compression and current. A number of significant and surprising properties are shown to exist. The occurrence of blocking above a critical value of compression is illustrated. This is analogous to propagation of surface gravity waves in the presence of opposing current and light wave propagation in the curved space-time near a black hole, therefore providing a novel system for studying analogue gravity. Between the blocking and buckling limit of the compressive force, the dispersion relation possesses three positive real roots, contrary to an earlier observation of having a single positive real root. Negative energy waves, in which the phase and group velocity point in opposite directions, are also shown to exist. In the presence of an opposing current and certain critical ranges of compressive force, the second blocking point shifts from the positive to the negative branch of the dispersion relation. Such a shift is known as the Hawking effect from the analogous behaviour in the theory of relativity which leads to Hawking radiation. The theory we develop is illustrated with simulations of linear waves in the time domain.

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Section: Wave Blocking In the Absence Of Currentmentioning

confidence: 99%

“…From equation ( 4.3), it is clear that phase velocity will never vanish for Q < 2 Dg. On the other hand, the phase velocity attains zero minimum for Q = 2 Dg (the point P in figure 1a) which is referred to as the critical compressive force Q c and the associated wavenumber is given by k c = (g/D) 1/4 (see [49]).…”

Section: Wave Blocking In the Absence Of Currentmentioning

confidence: 99%

Dynamics of flexural gravity waves: from sea ice to Hawking radiation and analogue gravity

2018

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“…where q j is the stiffness of the mooring lines for j = 1, 2. It may be mentioned that if one set q j = 0 in Equation (37a,b), then the reduced boundary condition will be a flexible plate with a free edge [27]. Also, the following continuity conditions at x = 0 and y = h are necessary to solve the BVP…”

Section: Governing Equation and Boundary Conditionsmentioning

confidence: 99%

Hydroelastic Response of a Flexible Submerged Porous Plate for Wave Energy Absorption

Mohapatra

Soares

2020

JMSE

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The application of flexible horizontal porous structure has a significant impact on the design of breakwaters and wave energy absorption devices for coastal protection and wave energy extraction, respectively. This type of structure is more economical compared to a rigid type structure. Therefore, the hydroelastic response of the flexible porous structure can be investigated to widen the influence of structural deformations in design parameters. This paper presents a generalized expansion formula for the said problem based on Green’s function in the water of finite depth (FD) and infinite depth (ID). The series form of the velocity potentials for the wave-maker problem is also derived using Green’s second identity. The derived expansion formula is applied to a real physical problem and the analytical solution is obtained utilizing a matched eigenfunction expansion method under velocity potential decompositions. The convergence study of the series solution is checked. The present results and the published experimental datasets, as well as analysis, are compared. The effect of design parameters on the hydroelastic response of the submerged flexible porous plate is analyzed. It is observed that the analysis of the results will be useful for gaining insight into how to design a wave energy absorption device.

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“…Williams and Porter (2009) studied the problem of wave propagation through the ice sheets with non uniform draught. Mohapatra et al (2013) analyzed the effects of compressive force on the wave/elastic sheet interactions. The Wiener-Hopf method was also widely used to solve this type of problem.…”

Section: Introductionmentioning

confidence: 99%

Interaction of waves with a body floating on polynya between two semi-infinite ice sheets

Shi

2018

Journal of Fluids and Structures

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The interaction of waves with a two-dimensional body floating on polynya between two semi-infinite ice sheets is investigated, based on a hybrid method utilizing a simple source function and eigenfunction matching. The ice sheet is modelled as a continuous thin elastic plate with uniform properties, while the fluid flow is described by the velocity potential. In the polynya, an integral equation is established by using the simple source function. In the two exterior ice covered regions, the potential is expanded in terms of eigenfunctions which satisfy the governing equation and all boundary conditions apart from that on the interface with the inner region. The unknown coefficients in the expansion and the boundary integral equation in the inner region are solved together by enforcing the continuity conditions of the pressure and normal velocity on the interface. The effectiveness and accuracy of the hybrid method is demonstrated through comparison with published results for a submerged cylinder and a floating rectangular body. Simulations are then carried out for a floating elliptical cylinder. Extensive results for the hydrodynamic force and motion response are provided, and the effects of ice draught as well as the body shape are investigated.

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Effect of compression on wave diffraction by a floating elastic plate

Cited by 31 publications

References 25 publications

Dynamics of flexural gravity waves: from sea ice to Hawking radiation and analogue gravity

Dynamics of flexural gravity waves: from sea ice to Hawking radiation and analogue gravity

Hydroelastic Response of a Flexible Submerged Porous Plate for Wave Energy Absorption

Interaction of waves with a body floating on polynya between two semi-infinite ice sheets

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