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

¹ 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
² Glaizer Group, Agence en Innovation, 15 bis rue Jean Jaurès, 92260 Fontenay-aux-Roses, France. Francois.Loret@glaizer.com

Received: 19 November 2006
Revised: 22 May 2007

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.