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Time-dependent response of a heterogeneous elastic plate floating on shallow water of variable depth

Published online by Cambridge University Press:  18 September 2009

IZOLDA V. STUROVA
IZOLDA V. STUROVA*
Affiliation:
Lavrentyev Institute of Hydrodynamics, Lavrentyev Prospect 15, 630090 Novosibirsk, Russia
*
†Email address for correspondence: [email protected]
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Abstract

The problem of unsteady behaviour of a floating thin plate is solved. The simultaneous motion of the plate and the fluid is considered within the framework of linear shallow-water theory. It is assumed that the bottom is not uniform in depth under the heterogeneous plate represented by an infinitely extended strip of finite width. The elastic deflection of the plate is expressed by a superposition of modal functions of a homogeneous beam with free edge conditions. The time-dependent unknown amplitudes are determined from the solution of a linear set of ordinary differential equations with constant coefficients. The eigenvalues of this set are determined numerically. Proposed method is used for the solution of three unsteady problems: the scattering of localized surface wave by an elastic plate, decay of the initial deformation of the plate in the fluid at rest and the action of a periodic load on a plate. Numerical calculations are performed for the ice sheet with the variable thickness and various bottom topographies.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 637 , 25 October 2009 , pp. 305 - 325
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Bennetts, L. G., Biggs, N. R. T. & Porter, D. 2007 A multi-mode approximation to wave scattering by ice sheets of varying thickness. J. Fluid Mech. 579, 413–443.Google Scholar
Chen, X.-J., Wu, Y.-S., Cui, W.-C. & Jensen, J. J. 2006 Review of hydroelasticity theories for global response of marine structures. Ocean Engng 33, 439–457.Google Scholar
Endo, H. & Yago, K. 1999 Time history response of a large floating structure subjected to dynamic load. J. Soc. Nav. Archit. Japan 186, 369–376.Google Scholar
Godunov, S. K. 1997 Ordinary Differential Equations with Constant Coefficient. Translations of Mathematical Monographs, vol. 169. American Mathematical Society, Providence, RI.CrossRefGoogle Scholar
Hazard, C. & Meylan, M. H. 2007 Spectral theory for an elastic thin plate floating on water of finite depth. SIAM J. Appl. Math. 68, 629–647.Google Scholar
Kashiwagi, M. 2000 A time-domain mode-expansion method for calculating transient elastic responses of a pontoon-type VLFS. J. Mar. Sci. Technol. 5, 89–100.CrossRefGoogle Scholar
Kashiwagi, M. 2004 Transient responses of a VLFS during landing and take-off of an airplane. J. Mar. Sci. Technol. 9, 14–23.CrossRefGoogle Scholar
Lee, D. H. & Choi, H. S. 2003 Transient hydroelastic response of very large floating structures by FE-BE hybrid method. In Proceedings of the Thirteenth International Society of Offshore and Polar Engineering, Honolulu, Hawaii, USA, May 2003, pp. 100–105.Google Scholar
Meylan, M. H. 1997 The forced vibration of a thin plate floating on an infinite liquid. J. Sound Vib. 205, 581–591.CrossRefGoogle Scholar
Meylan, M. H. 2001 An application of scattering frequencies to hydroelasticity. In Proceedings of the Eleventh International Society of Offshore and Polar Engineering, Stavanger, Norway, June 2001. Intern. Society of Offshore and Polar Engineers, Cupertino, California, vol. 3, pp. 385–391.Google Scholar
Meylan, M. H. 2002 Spectral solution of time-dependent shallow water hydroelasticity. J. Fluid Mech. 454, 387–402.CrossRefGoogle Scholar
Müller, P. C. & Schiehlen, W. O. 1985 Linear Vibrations. Martinus Nijhoff Publishers.Google Scholar
Ohmatsu, S. 1998 Numerical calculation of hydroelastic behaviour of VLFS in time domain. In Proceedings of the Second International Conference on Hydroelasticity in Marine Technology, Fukuoka, Japan, December 1998, pp. 89–97.Google Scholar
Ohmatsu, S. 2005 Overview: research on wave loading and responses of VLFS. Mar. Struct. 18, 149–168.Google Scholar
Porter, D. & Porter, R. 2004 Approximations to wave scattering by an ice sheet of variable thickness over undulating bed topography. J. Fluid Mech. 509, 145–179.CrossRefGoogle Scholar
Qiu, L.-C. 2007 Numerical simulation of transient hydroelastic response of a floating beam induced by landing loads. Appl. Ocean Res. 29, 91–98.CrossRefGoogle Scholar
Qui, L.-C. & Liu, H. 2005 Transient hydroelastic response of VLFS by FEM with impedance boundary conditions in time domain. China Ocean Engng 19, 1–9.Google Scholar
Squire, V. A. 2007 Of ocean waves and sea-ice revisited. Cold Reg. Sci. Technol. 49, 110–133.Google Scholar
Stoker, J. J. 1957 Water Waves: The Mathematical Theory with Applications. Interscience.Google Scholar
Sturova, I. V. 2002 a The action of periodic surface pressures on a floating elastic platform. J. Appl. Math. Mech. 66, 71–81.CrossRefGoogle Scholar
Sturova, I. V. 2002 b Unsteady behaviour of an elastic beam floating on shallow water under external loading. J. Appl. Mech. Tech. Phys. 43, 415–423.Google Scholar
Sturova, I. V. 2003 The action of an unsteady external load on a circular elastic plate floating on shallow water. J. Appl. Math. Mech. 67, 407–416.CrossRefGoogle Scholar
Sturova, I. V. 2006 a The effect of periodic surface pressure on a rectangular elastic plate floating on shallow water. J. Appl. Math. Mech. 70, 378–386.Google Scholar
Sturova, I. V. 2006 b Unsteady behaviour of an elastic beam floating on the surface of an infinitely deep fluid. J. Appl. Mech. Tech. Phys. 47, 71–78.Google Scholar
Sturova, I. V. 2008 a Effect of bottom topography on the unsteady behaviour of an elastic plate floating on shallow water. J. Appl. Math. Mech. 72, 417–426.CrossRefGoogle Scholar
Sturova, I. V. 2008 b Unsteady behaviour of a heterogeneous elastic beam floating on shallow water. J. Appl. Math. Mech. 72, 704–714.CrossRefGoogle Scholar
Sturova, I. V. & Korobkin, A. A. 2005 Two-dimensional problem of periodic loading of an elastic plate floating on the surface of an infinitely deep fluid. J. Appl. Mech. Tech. Phys. 46, 355–364.CrossRefGoogle Scholar
Timoshenko, S. 1959 Vibration Problems in Engineering, 3rd ed. (In collaboration with D. H. Young), Van Nostrand.Google Scholar
Tkacheva, L. A. 2000 Eigenvibrations of a flexible platform floating on shallow water. J. Appl. Mech. Tech. Phys. 41, 159–166.CrossRefGoogle Scholar
Tkacheva, L. A. 2005 a Action of a periodic load on an elastic floating plate. Fluid Dyn. 40, 282–296.CrossRefGoogle Scholar
Tkacheva, L. A. 2005 b Vibrations of a floating elastic plate due to periodic displacements of a bottom segment. J. Appl. Mech. Tech. Phys. 46, 754–765.Google Scholar
Watanabe, E. & Utsunomiya, T. 1996 Transient response analysis of a VLFS at airplane landing. In Proceedings of the International Workshop on Very Large Floating Structures, Hayama, Japan, November 1996, pp. 243–247.Google Scholar
Watanabe, E. & Utsunomiya, T. & Wang, C. M. 2004 Hydroelastic analysis of pontoon-type VLFS: a literature survey. Engng Struct. 26, 245–256.Google Scholar