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On the forced response of waveguides using the wave and finite element method

On the forced response of waveguides using the wave and finite element method
On the forced response of waveguides using the wave and finite element method
The forced response of waveguides subjected to time harmonic loading is treated. The approach starts with the wave and finite element (WFE) method where a segment of the waveguide is modeled using traditional finite element methods. The mass and stiffness matrices of the segment are used to formulate an eigenvalue problem whose solution yields the wave properties of the waveguide. The WFE formulation is used to obtain the response of the waveguide to a convected harmonic pressure (CHP). Since the Fourier transform of the response to a general excitation is a linear combination of the responses to CHPs, the response to a general excitation can be obtained via an inverse Fourier transform process. This is evaluated analytically using contour integration and the residue theorem. Hence, the approach presented herein enables the response of a waveguide to general loading to be found by: (a) modeling a segment of the waveguide using finite element methods and post-processing it to obtain the wave characteristics, (b) using Fourier transform and contour integration to obtain the wave amplitudes and (c) using the wave amplitudes to find the response at any point in the waveguide. Numerical examples are presented
0022-460X
5474 - 5488
Renno, Jamil M.
132f3c49-a612-4ccc-8772-293c8e015d1c
Mace, Brian R.
cfb883c3-2211-4f3a-b7f3-d5beb9baaefe
Renno, Jamil M.
132f3c49-a612-4ccc-8772-293c8e015d1c
Mace, Brian R.
cfb883c3-2211-4f3a-b7f3-d5beb9baaefe

Renno, Jamil M. and Mace, Brian R. (2010) On the forced response of waveguides using the wave and finite element method. Journal of Sound and Vibration, 329 (26), 5474 - 5488. (doi:10.1016/j.jsv.2010.07.009).

Record type: Article

Abstract

The forced response of waveguides subjected to time harmonic loading is treated. The approach starts with the wave and finite element (WFE) method where a segment of the waveguide is modeled using traditional finite element methods. The mass and stiffness matrices of the segment are used to formulate an eigenvalue problem whose solution yields the wave properties of the waveguide. The WFE formulation is used to obtain the response of the waveguide to a convected harmonic pressure (CHP). Since the Fourier transform of the response to a general excitation is a linear combination of the responses to CHPs, the response to a general excitation can be obtained via an inverse Fourier transform process. This is evaluated analytically using contour integration and the residue theorem. Hence, the approach presented herein enables the response of a waveguide to general loading to be found by: (a) modeling a segment of the waveguide using finite element methods and post-processing it to obtain the wave characteristics, (b) using Fourier transform and contour integration to obtain the wave amplitudes and (c) using the wave amplitudes to find the response at any point in the waveguide. Numerical examples are presented

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e-pub ahead of print date: 10 August 2010
Published date: 20 December 2010
Organisations: Dynamics Group

Identifiers

Local EPrints ID: 300880
URI: http://eprints.soton.ac.uk/id/eprint/300880
ISSN: 0022-460X
PURE UUID: 35487fba-f5ee-4d60-a5c4-ee9beb640641
ORCID for Brian R. Mace: ORCID iD orcid.org/0000-0003-3312-4918

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Date deposited: 01 Mar 2012 11:20
Last modified: 28 Apr 2022 01:48

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Contributors

Author: Jamil M. Renno
Author: Brian R. Mace ORCID iD

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