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

• Published in: Mathematical modelling and analysis Vol. 29; no. 2; pp. 215 - 237
• Main Authors: Kaligatla, Ramanababu, Prasad, Nagmani
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 26.03.2024
• Subjects: bending moment; Bending moments; Deflection; Density ratio; Differential equations; Eigenvectors; elastic plate; Elastic plates; Flow theory; Gravity waves; Linear algebra; Mathematical analysis; mild-slope equation; plate deflection; Potential flow; Shear forces; Specific gravity; Surface waves; Topography; two-layer liquid; variable bottom; Wave scattering; plate deflection; two-layer liquid; elastic plate; mild-slope equation; bending moment; variable bottom
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2024.17539

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.