Abstract
The Wiener–Hopf technique is used to construct an analytical solution of the problem of vibrations of a semi‐infinite elastic floating plate under periodic external loading. The solution is obtained in explicit form ignoring draft. The dependences of the amplitudes of surface waves and ice‐plate deflection on the loading distribution and frequency, ice thickness, and liquid depth are studied numerically. It is established that for some types of acting load, no waves propagate in the plate and liquid and the plate vibrations are standing waves localized near the loading region. An example of such vibrations is given and a condition for the occurrence of localized vibrations is found.
Similar content being viewed by others
REFERENCES
D. E. Kheisin,Dynamics of an Ice Cover [in Russian] Gidrometeoizdat, Leningrad (1967).
L. V. Cherkesov,Surface and Internal Waves [in Russian], Naukova Dumka, Kiev (1973).
V. A. Squire, R. G. Hosking, A. D. Kerr, et al.,Moving Loads on Ice Plates, Kluwer Acad. Publ., Dordrecht (1996).
M. Meylan, “The forced vibrations of a thin plate floating on an infinite liquid,”J. Sound Vibr. 205, No. 5, 581-591 (1997).
J. W. Kim and R. C. Ertekin, “An eigenfunction expansion method for predicting hydroelastic behavior of a shallow-immersion VLFS,” in:Hydroelasticity in Marine Technology: Proc. of the 2nd Int. Conf. (Fukuoka, Jpn., Dec. 1-3, 1998), Res. Inst. Appl. Mech. Kyushi Univ., Fukuoka (1998), pp. 47-59.
M. Kashivagi, “Research on hydroelastic responses of VLFS: recent progress and future work,”J. Offshore Polar Eng. 10, No. 2, 17-26 (2000).
I. V. Sturova, “Effect of periodic surface pressures on a floating elastic platform,”Prikl. Mat. Mekh. 66, No. 1, 87-94 (2002).
B. Noble,Wiener-Hopf Technique for Solution of Partial Differential Equations, Pergamon Press, New York (1958).
C. Fox and V. A. Squire, “Reflection and transmission characteristics at the edge of short fast sea ice,”J. Geophys. Res. 95, No. C7, 11.629-11.639 (1990).
I. M. Gel'fand and G. E. Shilov,Generalized Functions and Operations on Them [in Russian], Fizmatgiz, Moscow (1959).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tkacheva, L.A. Plane Problem of Vibrations of an Elastic Floating Plate under Periodic External Loading. Journal of Applied Mechanics and Technical Physics 45, 420–427 (2004). https://doi.org/10.1023/B:JAMT.0000025025.38066.ab
Issue Date:
DOI: https://doi.org/10.1023/B:JAMT.0000025025.38066.ab