Hydroelastic interaction between water waves and thin elastic plate floating on three-layer fluid

doi:10.1007/s10483-017-2185-6

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (4): 567-584.doi: https://doi.org/10.1007/s10483-017-2185-6

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Hydroelastic interaction between water waves and thin elastic plate floating on three-layer fluid

Qingrui MENG^1,2, Dongqiang LU^1,2

1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China

Received:2016-04-19 Revised:2016-06-22 Online:2017-04-01 Published:2017-04-01
Contact: Dongqiang LU E-mail:dqlu@shu.edu.cn
Supported by:
Project supported by the National Basic Research Program of China (973 Programm) (No. 2014CB046203), the National Natural Science Foundation of China (No. 11472166), and the Natural Science Foundation of Shanghai (No. 14ZR1416200)

Abstract

Abstract:

The wave-induced hydroelastic responses of a thin elastic plate floating on a three-layer fluid, under the assumption of linear potential flow, are investigated for two-dimensional cases. The effect of the lateral stretching or compressive stress is taken into account for plates of either semi-infinite or finite length. An explicit expression for the dispersion relation of the flexural-gravity wave in a three-layer fluid is analytically deduced. The equations for the velocity potential and the wave elevations are solved with the method of matched eigenfunction expansions. To simplify the calculation on the unknown expansion coefficients, a new inner product with orthogonality is proposed for the three-layer fluid, in which the vertical eigenfunctions in the open-water region are involved. The accuracy of the numerical results is checked with an energy conservation equation, representing the energy flux relation among three incident wave modes and the elastic plate. The effects of the lateral stresses on the hydroelastic responses are discussed in detail.

Key words: matched eigenfunction expansion, hydroelasticity, lateral stress, box constrained variational inequality problem (VIP), smooth gap function, integral global optimality condition, very large floating structure (VLFS), orthogonality

2010 MSC Number:

O353.4

Qingrui MENG, Dongqiang LU. Hydroelastic interaction between water waves and thin elastic plate floating on three-layer fluid. Applied Mathematics and Mechanics (English Edition), 2017, 38(4): 567-584.

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References

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Hydroelastic interaction between water waves and thin elastic plate floating on three-layer fluid

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