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The Singularity Expansion Method applied to the transient motions of a floating elastic plate

Published online by Cambridge University Press:  23 October 2007

Christophe Hazard  and
François Loret
Christophe Hazard
Affiliation:
Laboratoire POEMS, UMR 2706 CNRS/ENSTRA/INRIA, École Nationale Supérieure de Techniques Avancées, 32 boulevard Victor, 75739 Paris Cedex 15, France. Christophe.Hazard@ensta.fr
François Loret
Affiliation:
Glaizer Group, Agence en Innovation, 15 bis rue Jean Jaurès, 92260 Fontenay-aux-Roses, France. Francois.Loret@glaizer.com
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Abstract

In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles of the analytic continuation called resonances of the system, and a low frequency component associated to a branch point at frequency zero. We present the mathematical analysis of this method for the two-dimensional sea-keeping problem of a thin elastic plate (ice floe, floating runway, ...) and provide some numerical results to illustrate and discuss its efficiency.

Keywords

Laplace transformresonancemeromorphic family of operatorsintegral representation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 5 , September 2007 , pp. 925 - 943
Copyright
© EDP Sciences, SMAI, 2007

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