Topographical effects on wave scattering by an elastic plate floating on two-layer fluid

    Ramanababu Kaligatla   Affiliation
    ; Nagmani Prasad   Affiliation


This article illustrates the hydroelastic interactions between surface gravity waves and a floating elastic plate in a two-layer liquid with variable bottom topography under the assumptions of small amplitude waves and potential flow theory. In this study, semi-infinite and finite-length plates are considered. The eigenfunction expansion method is applied in the fluid region with uniform bottom topography. A system of differential equations (mild-slope equations) is solved in the fluid region with variable bottom topography. From the matching and jump conditions, the solution is expressed as a linear algebraic system from which all the unknown constants are computed. We explored the effects of density ratio, depth ratio, and bottom topography on the bending moment, shear force, and the deflection of the elastic plate. Results show that when the density ratio becomes closer to one, the occurred bending moment and shear forces to the elastic plates tend to diminish. The bending  moment and shear forces to the pates are higher and lower at a smaller depth ratiofor the incident surface wave and interfacial waves, respectively. The variations in the bending moment, shear force, and plate deflection, caused by surface and interfacial waves, are observed to be in opposite trends, respectively. Bottom profiles similarly affect semi-infinite and finite-length plates when they undergo free-edge conditions. These effects, however, are substantial when the plate is simply supported at the edges. Elastic plate with free edges experiences lower deflection for concave-up and plane-sloping bottoms for incident surface and interfacial waves, respectively.

Keyword : two-layer liquid, elastic plate, variable bottom, mild-slope equation, bending moment, plate deflection

How to Cite
Kaligatla, R., & Prasad, N. (2024). Topographical effects on wave scattering by an elastic plate floating on two-layer fluid. Mathematical Modelling and Analysis, 29(2), 215–237.
Published in Issue
Mar 26, 2024
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K.A. Belibassakis. A boundary element method for the hydrodynamic analysis of floating bodies in variable bathymetry regions. Engineering Analysis with Boundary Elements, 32(10):796–810, 2008.

L.G. Bennetts, N.R.T Biggs and D. Porter. A multi-mode approximation to wave scattering by ice sheets of varying thickness. Journal of Fluid Mechanics, 579:413–443, 2007.

P.G. Chamberlain and D. Porter. Wave scattering in a two-layer fluid of varying depth. Journal of Fluid Mechanics, 524:207–228, 2005.

D. Das and B.N. Mandal. Wave scattering by a horizontal circular cylinder in a two-layer fluid with an ice-cover. International Journal of Engineering Science, 45(10):842–872, 2007.

D. Karmakar, J. Bhattacharjee and T. Sahoo. Oblique flexural gravity-wave scattering due to changes in bottom topography. Journal of Engineering Mathematics, 66(4):325–341, 2010.

A. Kaur and S.C. Martha. Interaction of surface water waves with an elastic plate over an arbitrary bottom topography. Archive of Applied Mechanics, 92(11):3361–3379, 2022.

S. Kundu and R. Gayen. Surface wave scattering by an elastic plate submerged in water with uneven bottom. Mathematical Modelling and Analysis, 25(3):323–337, 2020.

J.H. Kyoung, S.Y. Hong, B.W. Kim and S.K. Cho. Hydroelastic response of a very large floating structure over a variable bottom topography. Ocean Engineering, 32(17):2040–2052, 2005.

Y. Liu and H.-J. Li. Oblique flexural-gravity wave scattering by a submerged semi-circular ridge. Geophysical & Astrophysical Fluid Dynamics, 110(3):259–273, 2016.

S.R. Manam and R.B. Kaligatla. A mild-slope model for membranecoupled gravity waves. Journal of Fluids and Structures, 30:173–187, 2012.

Manisha, R.B. Kaligatla and T. Sahoo. Effect of bottom undulation for mitigating wave-induced forces on a floating bridge. Wave Motion, 89:166–184, 2019.

Q. Meng and D. Lu. Hydroelastic interaction between water waves and thin elastic plate floating on three-layer fluid. Applied Mathematics and Mechanics, 38(4):567–584, 2017.

S. Mohapatra and S.N. Bora. Propagation of oblique waves over small bottom undulation in an ice-covered two-layer fluid. Geophysical & Astrophysical Fluid Dynamics, 103(3):347–374, 2009.

S. Naskar, S. Gupta and R. Gayen. Surface wave propagation over small bottom undulations in the presence of a submerged flexible porous barrier. Ocean Engineering, 241:109996, 2021.

R. Porter and D. Porter. Water wave scattering by a step of arbitrary profile. Journal of Fluid Mechanics, 441:131–164, 2000.

S. Singla, S.C. Martha and T. Sahoo. Mitigation of structural responses of a very large floating structure in the presence of vertical porous barrier. Ocean Engineering, 165:505–527, 2018.

V.A. Squire. Synergies between VLFS hydroelasticity and sea ice research. International Journal of Offshore and Polar Engineering, 18(04), 2008.

Saista Tabssum and Balaji Ramakrishnan. Effect of sloping bottom on wave interaction with multiple flexible moored breakwaters. Journal of Offshore Mechanics and Arctic Engineering, 146(4), 2024.

C. M. Wang, E. Watanabe and T. Utsunomiya. Very large floating structures. CRC Press, 2006.

C.D. Wang and M.H. Meylan. The linear wave response of a floating thin plate on water of variable depth. Applied Ocean Research, 24(3):163–174, 2002.

C.M. Wang and Z.Y. Tay. Very large floating structures: applications, research and development. Procedia Engineering, 14:62–72, 2011.

F. Xu and D.Q. Lu. Wave scattering by a thin elastic plate floating on a twolayer fluid. International Journal of Engineering Science, 48(9):809–819, 2010.