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

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

收稿日期:2016-04-19 修回日期:2016-06-22 出版日期:2017-04-01 发布日期:2017-04-01
通讯作者: Dongqiang LU E-mail:dqlu@shu.edu.cn
基金资助:
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)

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)

摘要/Abstract

摘要：

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.

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

Abstract:

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

中图分类号:

O353.4

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

参考文献

[1] Kashiwagi, M. Transient responses of a VLFS during landing and take-off of an airplane. Journal of Marine Science and Technology, 9, 14-23(2004)
[2] Watanabe, E., Wang, C. M., Utsunomiya, T., and Moan, T. Very Large Floating Structures:Applications, Analysis and Design, Centre for Offshore Research and Engineering, National University of Singapore, Singapore (2004)
[3] Fox, C. and Squire, V. A. Reflection and transmission characteristics at the edge of shore fast sea ice. Journal of Geophysical Research:Oceans, 95, 11629-11639(1990)
[4] Fox, C. and Squire, V. A. On the oblique reflexion and transmission of ocean waves at shore fast sea ice. Philosophical Transactions of the Royal Society of London, Series A:Physical and Engineering Sciences, 347, 185-218(1994)
[5] Kashiwagi, M. A time-domain mode-expansion method for calculating transient elastic responses of a pontoon-type VLFS. Journal of Marine Science and Technology, 5, 89-100(2000)
[6] Sahoo, T., Yip, T. L., and Chwang, A. T. Scattering of surface waves by a semi-infinite floating elastic plate. Physics of Fluids, 13, 3215-3222(2001)
[7] Teng, B., Cheng, L., Liu, S. X., and Li, F. J. Modified eigenfunction expansion methods for interaction of water waves with a semi-infinite elastic plate. Applied Ocean Research, 23, 357-368(2001)
[8] Xu, F. and Lu, D. Q. An optimization of eigenfunction expansion method for the interaction of water waves with an elastic plate. Journal of Hydrodynamics, 21, 526-530(2009)
[9] Bhattacharjee, J. and Sahoo, T. Flexural gravity wave problems in two-layer fluids. Wave Motion, 45, 133-153(2008)
[10] Xu, F. and Lu, D. Q. Wave scattering by a thin elastic plate floating on a two-layer fluid. International Journal of Engineering Science, 48, 809-819(2010)
[11] Karmakar, D., Bhattacharjee, J., and Sahoo, T. Oblique flexural gravity-wave scattering due to changes in bottom topography. Journal of Engineering Mathematics, 66, 325-341(2010)
[12] Mohapatra, S. C., Ghoshal, R., and Sahoo, T. Effect of compression on wave diffraction by a floating elastic plate. Journal of Fluids and Structures, 36, 124-135(2013)
[13] Sturova, I. V. Unsteady three-dimensional sources in deep water with an elastic cover and their applications. Journal of Fluid Mechanics, 730, 392-418(2013)
[14] Lu, D. Q. Effect of compressive stress on the dispersion relation of the flexural-gravity waves in a two-layer fluid with a uniform current. Journal of Hydrodynamics, 26, 339-341(2014)
[15] Mohanty, S. K., Mondal, R., and Sahoo, T. Time dependent flexural gravity waves in the presence of current. Journal of Fluids and Structures, 45, 28-49(2014)
[16] Mondal, R. and Sahoo, T. Wave structure interaction problems in three-layer fluid. Zeitschrift für angewandte Mathematik und Physik, 65, 349-375(2014)
[17] Maiti, P. and Mandal, B. N. Water wave scattering by an elastic plate floating in an ocean with a porous bed. Applied Ocean Research, 47, 73-84(2014)
[18] Mei, C. C. and Black, J. L. Scattering of surface waves by rectangular obstacles in waters of finite depth. Journal of Fluid Mechanics, 38, 499-511(1969)
[19] Wu, C., Watanabe, E., and Utsunomiya, T. An eigenfunction expansion-matching method for analyzing the wave-induced responses of an elastic floating plate. Applied Ocean Research, 17, 301-310(1995)

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

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

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