Abstract
The method of many scales was used to construct an asymptotic expansion up to thirdorder terms for the velocity potential of a fluid of finite depth and the flexural deformations of a floating elastic plate arising from the interaction of harmonics of finite-amplitude progressive surface waves. An expression for the second-harmonic amplitude was obtained, and critical values of the wavenumber were determined. Vibrations of plates with different thicknesses and elastic modulus were analyzed. Vertical displacements of the plate under flexural deformation were studied.
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D. E. Khesin, “Nonstationary Problem of Vibrations of an Infinite Plate Floating on the Surface of an Ideal Fluid,” Izv. Akad. Nauk SSSR, Mekh. Mashinostr., No. 1, 163–167 (1962).
A. E. Bukatov and L. V. Cherkesov, “Unsteady Vibrations of an Elastic Plate Floating on a Fluid Surface,” Prikl. Mekh. 6 (8), 89–96 (1970).
V. A. Tkachenko and V. V. Yakovlev, “Unsteady Flexural-Gravity Waves in the Fluid–Plate System,” Prikl. Mekh. 20 (3), 70–75 (1984).
V. A. Squire, “A Theoretical, Laboratory and Field Study of Ice Coupled Waves,” J. Geophys. Res. 89 (C5), 1079–1089 (1984).
R. M. S. M. Schulkes, A. D. Sneyd, “Time-Dependent Response of Floating Ice to a Steadily Moving Load,” J. Fluid Mech. 186, 25–46 (1988.)
D. G. Daffy, “The Response of Floating Ice to a Moving, Vibrating Load,” Cold Red. Sci. Tech. 20, 51–64 (1991).
V. A. Squire, R. J. Hosking, A. D. Kerr, and P. J. Langhorne, Moving Loads on Ice Plates (Kluwer, Dordrecht, 1996).
A. V. Pogorelova and V. M. Kozin, “Flexural-Gravity Waves due to Unsteady Motion of Point Source under a Floating Plate in Fluid of Finiate Depth,” J. Hydrodyn. 22 (5), 71–76 (2010); DOI: 10.1016/S1001-6058(09)60172-4.
I. B. Sturova, “Wave Generation by an Oscillating Submerged Cylinder in the Presence of a Floating Semi-Infinite Elastic Plate,” Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 4. 98–108 (2014).
A. E. Bukatov and A. A. Bukatov, “Propagation of Surface Wave of Finite Amplitude in a Basin with Floating Broken Ice,” Int. J. Offshore Polar Eng. 9 (3), 161–166 (1999).
R. V. Gol’dstein and A. V. Marchenko, “Long Waves in the Ice Cover–Fluid System in the Presence of Ice Compression,” in Electrophysical and Physicomechanical Properties of Ice (Gidrometeoizdat, Leningrad, 1989), pp. 188–205 [in Russian].
O. M. Gladun and V. S. Fedosenko, “Nonlinear Steady-State Vibrations of an Elastic Plate Floating on the Surface of a Fluid of Finite Depth,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 146–154 (1989).
A. T. Il’ichev, “Soliton-Like Structures at the Water–Ice Interface,” Usp. Mat. Nauk 70 (6), 85–138 (2015).
A. E. Bukatov and A. A. Bukatov, “Finite-Amplitude Waves in a Homogeneous Fluid with a Floating Elastic Plate,” Prikl. Mekh. Tekh. Fiz. 50 (5), 67–74 (2009) [J. Appl. Mech. Tech. Phys. 50 (5), 67–74 (2009)].
A. E. Bukatov and A. A. Bukatov, “Interaction of Surface Waves in a Basin with Floating Broken Ice,” Mor. Gidrofiz. Zh., No. 6, 3–22 (2003).
A. H. Nayfen, Perturbation Methods (John Wiley and Sons, 1973).
D. Ye. Kheysin, Dynamics of the Ice Cover (Gidrometeoizdat, Leningrad, 1967; U.S. Army Foreign Science and Technology Center, Technical translation FSTC-HT-23-485-69, 1969).
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Original Russian Text © A.E. Bukatov, A.A. Bukatov.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 4, pp. 99–109, July–August, 2018.
† Deceased.
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Bukatov, A.E., Bukatov, A.A. Vibrations of a Floating Elastic Plate Upon Nonlinear Interaction of Flexural-Gravity Waves. J Appl Mech Tech Phy 59, 662–672 (2018). https://doi.org/10.1134/S0021894418040120
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DOI: https://doi.org/10.1134/S0021894418040120