Abstract
The Wiener-Hopf technique was used to obtain an analytical solution of the problem of waves produced in a fluid and an ice sheet by the uniform motion of a pressure region modeling an air-cushion vessel on the free surface of the fluid in an ice channel. Ice cover is modeled by two thin semi-infinite viscoelastic plates of constant thickness, floating on the surface of an ideal incompressible fluid of finite depth and separated by the free surface of the fluid. In the moving coordinate system, the plate deflection and fluid elevation are assumed to be steady-state. The wave forces, the elevation of the free surface of the fluid, and the deflection and deformation of the plates are investigated at different vessel speeds and ice sheet thicknesses. It is shown that for some values of the speed, ice sheet thickness, and current pressure, destruction of the ice sheet near the edge is possible.
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References
L. A. Tkacheva, “Behavior of a Semi-Infinite Ice Cover under a Uniformly Moving Load,” Prikl. Mekh. Tekh. Fiz. 59(2), 82–98 (2018) [J. Appl. Mech. Tech. Phys. 59 (2), 258–272 (2018)].
L. A. Tkacheva, “Wave Motion in an Ice Sheet with Crack under Uniformly Moving Load,” Izv. Ross. Akad. Nauk. Mekh. Zhidk. Gaza, No. 1, 17–35 (2019) [Fluid Dyn. 54 (1) 14–32 (2019)].
L. A. Tkacheva, “Wave Pattern Due to a Load Moving on the Free Surface of a Fluid along the Edge of an Ice Sheet,” Prikl. Mekh. Tekh. Fiz. 60(3), 73–84 (2019) [J. Appl. Mech. Tech. Phys. 60 (3), 462–472 (2019)].
I. V. Sturova, “Motion of an External Load over a Semi-Infinite Ice Cover in the Subcritical Regime,” Izv. Ross. Akad. Nauk. Mekh. Zhidk. Gaza, No. 1, 51–60 (2018) [Fluid Dyn., No. 1, 49–58 (2018)].
Y. Li, J. Liu, M. Hu, and Z. Hu, “Numerical Smulation of Ice-Water System Response Based on Rankine Source Method and Finite Difference Method,” Ocean Eng. 138, 1–8 (2017).
A. V. Marchenko, “Resonance Interactions of Waves in the Ice Channel, Prikl. Mat. Mekh. 61(6), 963–974 (1997) [J. Appl. Math. Mech. 61 (6), 931–940 (1997).
R. Porter, “Trapping of Waves by Thin Floating Ice Sheets,” Q. J. Mech. Appl. Math. 71(4), 463–483 (2018); DOI: https://doi.org/10.1093/qjmam/hby014.
P. V. Goldstein, A. V. Marchenko, and A. Yu. Semenov, “Edge Waves in a Fluid under an Elastic Plate with a Crack,” Dokl. Akad. Nauk 339(3), 331–334 (1994).
D. V. Evans and R. Porter, “Wave Scattering by Narrow Cracks in Ice Sheets Floating on Water of Finite Depth,” J. Fluid Mech. 484, 143–165 (2003).
L. A. Tkacheva, “Edge Waves in a Fluid under Ice Cover with a Crack,” Dokl. Akad. Nauk 473(5), 545–551 (2017) [Dokl. Phys. 62 (4), 202–207 (2017)].
L. A. Tkacheva, “Action of a Local Time-Periodic Load on an Ice Sheet with a Crack,” Prikl. Mekh. Tekh. Fiz. 58(6), 133–148 (2017) [J. Appl. Mech. Tech. Phys. 58 (6), 1069–1082 (2017)].
A. D. Kerr and W. T. Palmer, “The Deformations and Stresses in Floating Ice Plates,” Acta Mech. 15, 57–72 (1972).
L. J. Doctors and S. D. Sharma, “The Wave Resistance of an Air-Cushion Vehicle in Steady and Accelerated Motion,” J. Ship Res. 16(4), 248–260 (1972).
A. M. Freudenthal and H. Geiringer, The Mathematical Theories of the Inelastic Continuum (Springer-Verlag, Berlin, 1958).
V. Squire and S. Martin, “A Subsequent Study of the Physical Properties, Response to Swell, and Subsequent Fracture of a Single Ice Floe in the Winter Bering Sea,” Tech. Report No. 18 (Univ. of Washington, 1980).
K. Shishmarev, T. Khabakhpasheva, and A. Korobkin, “The Response of Ice Cover to a Load Moving along a Frozen Channel,” Appl. Ocean Res. 59, 313–326 (2016).
B. Noble, Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations (Pergamon Press, London-New York-Paris, 1958).
I. M. Gel’fand and G. E. Shilov, Generalized Functions (Properties and Operations) (Fizmatgiz, Moscow, 1958; Academic Press, New York-London, 1963).
M. Rabaud and F. Moisy, “Ship Wakes: Kelvin or Mach Angle,” Phys. Rev. Lett. 110, 214503 (2013).
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Original Russian Text © L. A. Tkacheva.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 60, No. 5, pp. 81–97, September–October, 2019.
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Tkacheva, L.A. Edge Waves Produced by the Motion of a Vessel in an Ice Channel. J Appl Mech Tech Phy 60, 850–864 (2019). https://doi.org/10.1134/S0021894419050080
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DOI: https://doi.org/10.1134/S0021894419050080