title: Conformal Fourier wavenumber decompositions on continuous differentiable surfaces.
abstract: In this manuscript, a method is introduced for the evaluation of Fourier wavenumber decompositions on C(1) vibrating surfaces for spatial-spectral analysis. Whereas typical Fourier analysis is restricted to geometries that are separable for meaningful interpretations of the corresponding wave motion, this approach allows for conformal spectral analysis along curved surfaces. This is accomplished by restricting the wavevectors to lie within the local tangent to the surface and to be spatially dependent. The theoretical development is presented and it is demonstrated that commonly utilized kernels appropriate for some simple geometries can be recovered. Additionally, this approach is applied in the analysis of the vibration and radiation of a point driven, fluid loaded cone, where the displacements and pressures have been obtained using the finite element method.
authors.affiliation: Naval Research Laboratory, Physics Acoustics Branch, Washington, DC 20375-0001, USA. anthony.romano@nrl.navy.mil
authors.forename: Anthony J
authors.initials: AJ
authors.lastname: Romano
authors.forename: P B
authors.initials: PB
authors.lastname: Abraham
authors.forename: N P
authors.initials: NP
authors.lastname: Valdivia
authors.forename: B H
authors.initials: BH
authors.lastname: Houston
authors.forename: J A
authors.initials: JA
authors.lastname: Bucaro
authors.forename: S
authors.initials: S
authors.lastname: Dey
mesh_terms: D005583:Fourier Analysis; D008962:Models, Theoretical; D011312:Pressure; D013016:Sound; D014732:Vibration