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- W124221427 abstract "This thesis considers issues concerning the application of the wave finite element (WFE) method tothe free and forced vibrations of one-dimensional waveguides. A short section of the waveguide ismodelled using conventional finite element (FE) methods. A periodicity condition is applied and theresulting mass and stiffness matrices are post-processed to yield the dispersion relations and so on.First, numerical issues are discussed and methods to reduce the errors are proposed. FEdiscretisation errors and errors due to round-off of inertia terms are described. A method usingconcatenated elements is proposed to reduce those round-off errors. Conditioning of the eigenvalueproblem is discussed. An application of singular value decomposition is proposed to reduce errors innumerically determining eigenvectors together with Zhong’s formulation of the eigenvalue problem.Effects of the modelling of the cross-section on conditioning are shown. Three methods fornumerically determining the group velocity are compared and the power and energy relationship isseen to be reliable.The WFE method is then applied to complicated structures and its accuracy evaluated. Dispersioncurves are shown including purely real, purely imaginary and complex wavenumbers. Free wavepropagation in a plate strip with free edges, a ring and a cylindrical strip is predicted and the resultscompared with analytical or numerical solutions to the analytical dispersion equations. In particular,dispersion curves for freely propagating flexural waves, including attenuating waves, are presented.Complicated phenomena such as curve veering, non-zero cut-on phenomena and bifurcations areobserved as results of wave coupling in the wave domain. A method of decomposition of the poweris proposed to reduce the size of the system matrices and to investigate the wave characteristics ofeach wave mode.The wave approach is then used to predict the forced response. A well-conditioned formulation fordetermining the amplitudes of directly excited waves is proposed. The forced response is determinedby considering wave propagation and subsequent reflection at boundaries. Numerical examples of abeam, a plate and a cylinder are shown. Inclusion of rapidly decaying waves is discussed.As a practical application, free and forced vibrations of a tyre are analysed. The complicatedcross-section of a tyre is modelled using a commercial FE package. Frequency dependent materialproperties of rubber are included. Free wave propagation is shown including attenuating waves andpredicted responses are compared with experiment. Effects of the size of the excited region arediscussed." @default.
- W124221427 created "2016-06-24" @default.
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- W124221427 date "2007-12-01" @default.
- W124221427 modified "2023-09-24" @default.
- W124221427 title "On the application of finite element analysis to wave motion in one-dimensional waveguides" @default.
- W124221427 hasPublicationYear "2007" @default.
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