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

Christophe Hazard; François Loret

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 5, page 925-943
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Hazard, Christophe, and Loret, François. "The Singularity Expansion Method applied to the transient motions of a floating elastic plate." ESAIM: Mathematical Modelling and Numerical Analysis 41.5 (2007): 925-943. <http://eudml.org/doc/250021>.

@article{Hazard2007,
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. },
author = {Hazard, Christophe, Loret, François},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Laplace transform; resonance; meromorphic family of operators; integral representation.; analytic continuation; sea-keeping problem},
language = {eng},
month = {10},
number = {5},
pages = {925-943},
publisher = {EDP Sciences},
title = {The Singularity Expansion Method applied to the transient motions of a floating elastic plate},
url = {http://eudml.org/doc/250021},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Hazard, Christophe
AU - Loret, François
TI - The Singularity Expansion Method applied to the transient motions of a floating elastic plate
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/10//
PB - EDP Sciences
VL - 41
IS - 5
SP - 925
EP - 943
AB - 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.
LA - eng
KW - Laplace transform; resonance; meromorphic family of operators; integral representation.; analytic continuation; sea-keeping problem
UR - http://eudml.org/doc/250021
ER -

References

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