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Mapped spheroidal wave-envelope elements for unbounded wave problems

Mapped spheroidal wave-envelope elements for unbounded wave problems
Mapped spheroidal wave-envelope elements for unbounded wave problems
This paper describes a family of axisymmetric, spheroidal ‘wave envelope’ elements for modelling exterior wave problems. They are of variable radial order and can be used to represent steady and transient wave fields. The formulation is presented for the axisymmetric case using elements which are based on oblate and prolate spheroidal geometries. These offer the prospect of reduced dimensionality—in comparison to conventional, spherically formulated elements—when used to represent wave fields in the vicinity of slender or flat objects. Conjugated weighting functions are used to give frequency-independent acoustic ‘mass’, ‘stiffness’ and ‘damping’ matrices. This facilitates a simple extension of the method to transient problems. The effectiveness and accuracy of the method is demonstrated by a comparison of computed and analytic solutions for sound fields generated by a rigid sphere in steady harmonic oscillation, by a rigid sphere excited from rest, and by a circular plate vibrating in a plane baffle.
unbounded domain, wave equation, steady, transient, finite element, infinite element
0029-5981
1235-1254
Astley, R.J.
cb7fed9f-a96a-4b58-8939-6db1010f9893
Astley, R.J.
cb7fed9f-a96a-4b58-8939-6db1010f9893

Astley, R.J. (1998) Mapped spheroidal wave-envelope elements for unbounded wave problems. International Journal for Numerical Methods in Engineering, 41 (7), 1235-1254.

Record type: Article

Abstract

This paper describes a family of axisymmetric, spheroidal ‘wave envelope’ elements for modelling exterior wave problems. They are of variable radial order and can be used to represent steady and transient wave fields. The formulation is presented for the axisymmetric case using elements which are based on oblate and prolate spheroidal geometries. These offer the prospect of reduced dimensionality—in comparison to conventional, spherically formulated elements—when used to represent wave fields in the vicinity of slender or flat objects. Conjugated weighting functions are used to give frequency-independent acoustic ‘mass’, ‘stiffness’ and ‘damping’ matrices. This facilitates a simple extension of the method to transient problems. The effectiveness and accuracy of the method is demonstrated by a comparison of computed and analytic solutions for sound fields generated by a rigid sphere in steady harmonic oscillation, by a rigid sphere excited from rest, and by a circular plate vibrating in a plane baffle.

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More information

Published date: 15 April 1998
Keywords: unbounded domain, wave equation, steady, transient, finite element, infinite element

Identifiers

Local EPrints ID: 166557
URI: https://eprints.soton.ac.uk/id/eprint/166557
ISSN: 0029-5981
PURE UUID: 011123ff-c4d5-4135-959a-85b031b34423

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Date deposited: 29 Oct 2010 10:53
Last modified: 10 Aug 2017 22:25

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Contributors

Author: R.J. Astley

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