# Influence of Support Conditions on the Hydroelastic Behaviour of Floating Thick Elastic Plate

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## Abstract

The hydroelastic response of very large floating structures (VLFS) under the action of ocean waves is analysed considering the small amplitude wave theory. The very large floating structure is modelled as a floating thick elastic plate based on Timoshenko-Mindlin plate theory, and the analysis for the hydroelastic response is performed considering different edge boundary conditions. The numerical study is performed to analyse the wave reflection and transmission characteristics of the floating plate under the influence of different support conditions using eigenfunction expansion method along with the orthogonal mode-coupling relation in the case of finite water depth. Further, the analysis is extended for shallow water depth, and the continuity of energy and mass flux is applied along the edges of the plate to obtain the solution for the problem. The hydroelastic behaviour in terms of reflection and transmission coefficients, plate deflection, strain, bending moment and shear force of the floating thick elastic plate with support conditions is analysed and compared for finite and shallow water depth. The study reveals an interesting aspect in the analysis of thick floating elastic plate with support condition due to the presence of the rotary inertia and transverse shear deformation. The present study will be helpful for the design and analysis of the VLFS in the case of finite and shallow water depth.

## Keywords

Timoshenko-Mindlin plate theory Very large floating structure Support condition Rotary inertia Transverse shear deformation## Notes

### Funding

The authors are thankful to NITK Surathkal and MHRD for providing financial and necessary support to perform the research work. The authors also acknowledge the Science and Engineering Research Board (SERB), Department of Science & Technology (DST), Government of India, for supporting financially under the Young Scientist research grant No. YSS/2014/000812.

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