Wave Propagation through a Submerged Horizontal Plate at the Bottom of a Water Channel

Document Type : Original Article

Authors

1 Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

2 Department of Mechanical Engineering, Faculty of Engineering and Technology, University of Mazandaran, Babolsar, Iran

3 Department of Civil, Environmental and Mining Engineering, University of Western Australia, Perth, Australia

Abstract

Vibrational study of fluid-structure interaction is one of the most widely used cases in engineering. In various industries, the effect of fluid on the structure and vice versa is necessary to investigate such as shipbuilding, ocean energy sources, offshore structures, etc. In this paper, the dynamic behavior of a long rectangular plate located on a viscoelastic bed at the bottom of a narrow channel has been studied in detail. According to earlier studies, the muddy seabed of coasts attenuate the waves. Here we investigate the interaction between the gravity sea waves and the muddy seabed by modeling the seabed as a rectangular plate that located on a viscoelastic foundation which contains springs and dampers. The springs and dampers are attached at the bottom of plate to model the behavior of the muddy seabed. The governing equations of motion have been obtained and a new semi-analytical solution has been presented to solve them. The proposed model is validated against available literatures. Then, the influence of different parameters such as boundary conditions, plate's rigidity and mass, damping ratio, restoring force and different transverse modes on the vibrational behavior of the system has been investigated in detail. The effects of various parameters on the frequency response of the system have been studied in detail.

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[1]     Creel L. Ripple effects: population and coastal regions. Population Reference Bureau Washington, DC; 2003.
[2]     Gade HG. Effects of a nonrigid, impermeable bottom on plane surface waves in shallow water. J Mar Res 1958;16:61–81.
[3]     Holland KT, Vinzon SB, Calliari LJ. A field study of coastal dynamics on a muddy coast offshore of Cassino beach, Brazil. Cont Shelf Res 2009;29:503–14. doi:10.1016/j.csr.2008.09.023.
[4]     Elgar S, Raubenheimer B. Wave dissipation by muddy seafloors. Geophys Res Lett 2008;35:n/a-n/a. doi:10.1029/2008GL033245.
[5]     Silvester R. Headland defense of coasts, Coastal Engineering Proceedings 1976;1.
[6]     Mac Pherson H, Kurup PG. Wave damping at the Kerala mudbanks 1981.
[7]     Sheremet A, Stone GW. Observations of nearshore wave dissipation over muddy sea beds. J Geophys Res Ocean 2003;108.
[8]     Macpherson H. The attenuation of water waves over a non-rigid bed. J Fluid Mech 1980;97:721. doi:10.1017/S0022112080002777.
[9]     Dalrymple RA, Liu PLF. Waves over soft muds: a two-layer fluid model. J Phys Oceanogr 1978;8:1121–31.
[10]   Alam M-R, Liu Y, Yue DKP. Waves due to an oscillating and translating disturbance in a two-layer density-stratified fluid. J Eng Math 2009;65:179–200.
[11]   Ko-Fei L, Mei CC. Long waves in shallow water over a layer of bingham-plastic fluid-mud—I. Physical aspects. Int J Eng Sci 1993;31:125–44. doi:10.1016/0020-7225(93)90070-B.
[12]   Alam M-R. A Flexible Seafloor Carpet for High-Performance Wave Energy Extraction. Vol. 4 Offshore Geotech. Ronald W. Yeung Honor. Symp. Offshore Sh. Hydrodyn., American Society of Mechanical Engineers; 2012, p. 839–46. doi:10.1115/OMAE2012-84034.
[13]   Alam M-R. Nonlinear analysis of an actuated seafloor-mounted carpet for a high-performance wave energy extraction. Proc R Soc A Math Phys Eng Sci 2012;468:3153–71. doi:10.1098/rspa.2012.0193.
[14]   Asaeian A, Jafari-Talookolaei R-A, Attar M. Dynamic investigation of wave energy absorber plate located on the bottom of a channel. Modares Mech Eng 2018;18:361–9.
[15]   Sahoo T, Yip TL, Chwang AT. Scattering of surface waves by a semi-infinite floating elastic plate. Phys Fluids 2001;13:3215–22. doi:10.1063/1.1408294.
[16]   Mondal R, Sahoo T. Wave structure interaction problems for two-layer fluids in three dimensions. Wave Motion 2012;49:501–24. doi:10.1016/j.wavemoti.2012.02.002.
[17]   Havelock TH. LIX. Forced surface-waves on water. London, Edinburgh, Dublin Philos Mag J Sci 1929;8:569–76. doi:10.1080/14786441008564913.
[18]   Evans D V, Porter R. Wave scattering by narrow cracks in ice sheets floating on water of finite depth. J Fluid Mech 2003;484:143.
[19]   Rao SS. Vibration of continuous systems. vol. 464. Wiley Online Library; 2007.
[20]   Ball FK. Energy transfer between external and internal gravity waves. J Fluid Mech 1964;19:465.