Spectral Theory for a Floating Massless Thin Plate on Water of Arbitrary Depth

Michael H. Meylan; Christophe Hazard

Spectral Theory for a Floating Massless Thin Plate on Water of Arbitrary Depth

Michael H. Meylan
, Christophe Hazard

Massey University Auckland

Résultats de recherche: Contribution à une conférence › Papier › Revue par des pairs

Résumé

We develop the spectral theory for a floating massless thin plate on water of arbitrary depth. Using this theory we calculate the time dependent motion by a generalised Fourier expansion. The spectral theory depends on finding an inner product in which the operator which determines the time dependent motion is self-adjoint. It is shown that the time harmonic solutions for an incoming wave are the eigenfunctions of this self adjoint operator. If the plate motion is expanded in these eigenfunction the time dependent motion can be calculated straight-forwardly. Results are presented concentrating on establishing that we can repeat the calculations of Meylan (2002) where the equivalent theory for shallow water was developed.

langue originale	Anglais
Pages	365-370
Nombre de pages	6
état	Publié - 1 déc. 2002
Evénement	Proceedings of the Twelfth (2002) International Offshore and Polar Engineering Conference - Kitakyushu, Japon Durée: 26 mai 2002 → 31 mai 2002

Une conférence

Une conférence	Proceedings of the Twelfth (2002) International Offshore and Polar Engineering Conference
Pays/Territoire	Japon
La ville	Kitakyushu
période	26/05/02 → 31/05/02

Contient cette citation

@conference{139f78e2ef2042c78a46c133d8bb63a9,

title = "Spectral Theory for a Floating Massless Thin Plate on Water of Arbitrary Depth",

abstract = "We develop the spectral theory for a floating massless thin plate on water of arbitrary depth. Using this theory we calculate the time dependent motion by a generalised Fourier expansion. The spectral theory depends on finding an inner product in which the operator which determines the time dependent motion is self-adjoint. It is shown that the time harmonic solutions for an incoming wave are the eigenfunctions of this self adjoint operator. If the plate motion is expanded in these eigenfunction the time dependent motion can be calculated straight-forwardly. Results are presented concentrating on establishing that we can repeat the calculations of Meylan (2002) where the equivalent theory for shallow water was developed.",

keywords = "Hydroelastic, Spectral theory, Wave forcing",

author = "Meylan, \{Michael H.\} and Christophe Hazard",

year = "2002",

month = dec,

day = "1",

language = "English",

pages = "365--370",

note = "Proceedings of the Twelfth (2002) International Offshore and Polar Engineering Conference ; Conference date: 26-05-2002 Through 31-05-2002",

}

TY - CONF

T1 - Spectral Theory for a Floating Massless Thin Plate on Water of Arbitrary Depth

AU - Meylan, Michael H.

AU - Hazard, Christophe

PY - 2002/12/1

Y1 - 2002/12/1

N2 - We develop the spectral theory for a floating massless thin plate on water of arbitrary depth. Using this theory we calculate the time dependent motion by a generalised Fourier expansion. The spectral theory depends on finding an inner product in which the operator which determines the time dependent motion is self-adjoint. It is shown that the time harmonic solutions for an incoming wave are the eigenfunctions of this self adjoint operator. If the plate motion is expanded in these eigenfunction the time dependent motion can be calculated straight-forwardly. Results are presented concentrating on establishing that we can repeat the calculations of Meylan (2002) where the equivalent theory for shallow water was developed.

AB - We develop the spectral theory for a floating massless thin plate on water of arbitrary depth. Using this theory we calculate the time dependent motion by a generalised Fourier expansion. The spectral theory depends on finding an inner product in which the operator which determines the time dependent motion is self-adjoint. It is shown that the time harmonic solutions for an incoming wave are the eigenfunctions of this self adjoint operator. If the plate motion is expanded in these eigenfunction the time dependent motion can be calculated straight-forwardly. Results are presented concentrating on establishing that we can repeat the calculations of Meylan (2002) where the equivalent theory for shallow water was developed.

KW - Hydroelastic

KW - Spectral theory

KW - Wave forcing

M3 - Paper

AN - SCOPUS:1842609501

SP - 365

EP - 370

T2 - Proceedings of the Twelfth (2002) International Offshore and Polar Engineering Conference

Y2 - 26 May 2002 through 31 May 2002

ER -

Spectral Theory for a Floating Massless Thin Plate on Water of Arbitrary Depth

Résumé

Une conférence

Empreinte digitale

Contient cette citation