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 modelled 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) modelling a segment of the waveguide using finite element methods and post-processing it to obtain the wave characteristics, b) using a 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.
forced response, finite element, wave basis, periodic structures
9780854329106
University of Southampton
Renno, J.M.
132f3c49-a612-4ccc-8772-293c8e015d1c
Mace, B.R.
cfb883c3-2211-4f3a-b7f3-d5beb9baaefe
2010
Renno, J.M.
132f3c49-a612-4ccc-8772-293c8e015d1c
Mace, B.R.
cfb883c3-2211-4f3a-b7f3-d5beb9baaefe
Renno, J.M. and Mace, B.R.
(2010)
On the forced response of waveguides using the wave and finite element method.
Brennan, M.J., Kovacic, Ivana, Lopes Jr, V., Murphy, K., Petersson, B., Rizzi, S. and Yang, T.
(eds.)
In Proceedings of the Tenth International Conference on Recent Advances in Structural Dynamics (RASD2010).
University of Southampton..
Record type:
Conference or Workshop Item
(Paper)
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 modelled 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) modelling a segment of the waveguide using finite element methods and post-processing it to obtain the wave characteristics, b) using a 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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Published date: 2010
Additional Information:
Paper No. 137,17pp(Format - USB Pen Drive)
Keywords:
forced response, finite element, wave basis, periodic structures
Identifiers
Local EPrints ID: 160739
URI: http://eprints.soton.ac.uk/id/eprint/160739
ISBN: 9780854329106
PURE UUID: 785707ac-e761-463a-9d50-847aee90af95
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Date deposited: 21 Jul 2010 07:55
Last modified: 28 Apr 2022 01:48
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Contributors
Author:
J.M. Renno
Editor:
M.J. Brennan
Editor:
Ivana Kovacic
Editor:
V. Lopes Jr
Editor:
K. Murphy
Editor:
B. Petersson
Editor:
S. Rizzi
Editor:
T. Yang
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