Natural frequency statistics of waveguides with slowly changing spatially correlated material variability
Natural frequency statistics of waveguides with slowly changing spatially correlated material variability
This paper concerns wave propagation in random waveguides and, in particular, when there is spatially correlated variability in the material and/or geometric properties. The one dimensional waveguide is modelled using an analytical formulation for wave propagation and a formulation for the wavenumber is given considering slowly varying proprieties, i.e. the change given by the random field is such that there is no backscattering from a propagating wave. When propagating over a finite distance, the total phase change of a wave is given by the integral of the spatially distributed wavenumber. Spatial correlation is then seen to be important in determining the statistics of this phase (mean, variance, etc.). This information can in turn be used to calculate the natural frequencies and forced response of finite structures. Longitudinal motion in a finite length thin rod is then considered and, given a second order homogenous random field with a certain kind of autocorrelation function, an analytical solution for its Karhunen-Loeve expansion is used for deriving an expression for its natural frequencies. The slowly varying proprieties assumption is used in order to find an analytical expression the for probability density function of the natural frequencies. A FE model of the waveguide is also assembled, with the random field discretized on the FE mesh and assumed piecewise constant within the element proprieties. Monte Carlo sampling is used to evaluate statistics of the natural frequencies and the results are compared to those obtained by the wave approach.
1761-1775
Todorovic Fabro, Adriano
a184cc3b-5eb6-4e00-ab7d-2fedf8041b63
Ferguson, N.S.
8cb67e30-48e2-491c-9390-d444fa786ac8
Mace, B.R.
cfb883c3-2211-4f3a-b7f3-d5beb9baaefe
17 September 2012
Todorovic Fabro, Adriano
a184cc3b-5eb6-4e00-ab7d-2fedf8041b63
Ferguson, N.S.
8cb67e30-48e2-491c-9390-d444fa786ac8
Mace, B.R.
cfb883c3-2211-4f3a-b7f3-d5beb9baaefe
Todorovic Fabro, Adriano, Ferguson, N.S. and Mace, B.R.
(2012)
Natural frequency statistics of waveguides with slowly changing spatially correlated material variability.
International Conference on Noise and Vibration Engineering - ISMA2012, Leuven, Belgium.
17 - 19 Sep 2012.
.
Record type:
Conference or Workshop Item
(Paper)
Abstract
This paper concerns wave propagation in random waveguides and, in particular, when there is spatially correlated variability in the material and/or geometric properties. The one dimensional waveguide is modelled using an analytical formulation for wave propagation and a formulation for the wavenumber is given considering slowly varying proprieties, i.e. the change given by the random field is such that there is no backscattering from a propagating wave. When propagating over a finite distance, the total phase change of a wave is given by the integral of the spatially distributed wavenumber. Spatial correlation is then seen to be important in determining the statistics of this phase (mean, variance, etc.). This information can in turn be used to calculate the natural frequencies and forced response of finite structures. Longitudinal motion in a finite length thin rod is then considered and, given a second order homogenous random field with a certain kind of autocorrelation function, an analytical solution for its Karhunen-Loeve expansion is used for deriving an expression for its natural frequencies. The slowly varying proprieties assumption is used in order to find an analytical expression the for probability density function of the natural frequencies. A FE model of the waveguide is also assembled, with the random field discretized on the FE mesh and assumed piecewise constant within the element proprieties. Monte Carlo sampling is used to evaluate statistics of the natural frequencies and the results are compared to those obtained by the wave approach.
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Published date: 17 September 2012
Venue - Dates:
International Conference on Noise and Vibration Engineering - ISMA2012, Leuven, Belgium, 2012-09-17 - 2012-09-19
Organisations:
Dynamics Group
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Local EPrints ID: 343171
URI: http://eprints.soton.ac.uk/id/eprint/343171
PURE UUID: fed2acdc-5c6c-48fe-8e6d-0d7b4371aa25
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Date deposited: 27 Sep 2012 14:53
Last modified: 10 Jan 2023 02:32
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Author:
Adriano Todorovic Fabro
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