Propagation in waveguides with slowly changing variability
Propagation in waveguides with slowly changing variability
This thesis investigates structural wave propagation in waveguides with randomly varying material and geometrical properties along the axis of propagation, specifically when the properties vary slowly enough such that there is no or negligible backscattering due to any changes in the propagation medium. This variability plays a significant role in the so called mid-frequency region, but wave-based methods are typically only applicable to homogeneous and uniform waveguides.
An analytical tool, the WKB (after Wentzel, Kramers and Brillouin) approximation, is used in order to find a suitable generalisation of the wave solutions for finite waveguides undergoing longitudinal and flexural motion. An alternative wave formulation approximation with piecewise constant properties is derived so that the internal reflections are taken into account, requiring a discretisation of the waveguide. In addition, a Finite Element approximation using an enriched hierarchical basis or Hierarchical Finite Element (HFE) is created, where the variability in the properties of the waveguide is included within the element formulation, thus not requiring a mesh discretisation as opposed to a standard FE solution.
A Fourier like series, the Karhunen-Loeve expansion, is used to represent homogeneous and spatially correlated randomness and statistics of the natural frequencies and forced response are derived. Experimental validation is carried out, using firstly a cantilever beam with small masses attached along its length according to a given random field. In the second experiment, an ensemble of glass-fibre reinforced free-free beams, whose variability is characterised by light transmissibility images, is measured. It has been found that the correlation length of the random fields or the scale of the spatial fluctuation is shown to play an important role in the dynamic response statistics. Moreover, the proposed formulations show good agreement with the standard approaches but at a fraction of the computational cost, providing a good framework for uncertainty quantification.
Todorovic Fabro, Adriano
a184cc3b-5eb6-4e00-ab7d-2fedf8041b63
February 2014
Todorovic Fabro, Adriano
a184cc3b-5eb6-4e00-ab7d-2fedf8041b63
Ferguson, N.S.
8cb67e30-48e2-491c-9390-d444fa786ac8
Todorovic Fabro, Adriano
(2014)
Propagation in waveguides with slowly changing variability.
University of Southampton, Engineering and the Environment, Doctoral Thesis, 225pp.
Record type:
Thesis
(Doctoral)
Abstract
This thesis investigates structural wave propagation in waveguides with randomly varying material and geometrical properties along the axis of propagation, specifically when the properties vary slowly enough such that there is no or negligible backscattering due to any changes in the propagation medium. This variability plays a significant role in the so called mid-frequency region, but wave-based methods are typically only applicable to homogeneous and uniform waveguides.
An analytical tool, the WKB (after Wentzel, Kramers and Brillouin) approximation, is used in order to find a suitable generalisation of the wave solutions for finite waveguides undergoing longitudinal and flexural motion. An alternative wave formulation approximation with piecewise constant properties is derived so that the internal reflections are taken into account, requiring a discretisation of the waveguide. In addition, a Finite Element approximation using an enriched hierarchical basis or Hierarchical Finite Element (HFE) is created, where the variability in the properties of the waveguide is included within the element formulation, thus not requiring a mesh discretisation as opposed to a standard FE solution.
A Fourier like series, the Karhunen-Loeve expansion, is used to represent homogeneous and spatially correlated randomness and statistics of the natural frequencies and forced response are derived. Experimental validation is carried out, using firstly a cantilever beam with small masses attached along its length according to a given random field. In the second experiment, an ensemble of glass-fibre reinforced free-free beams, whose variability is characterised by light transmissibility images, is measured. It has been found that the correlation length of the random fields or the scale of the spatial fluctuation is shown to play an important role in the dynamic response statistics. Moreover, the proposed formulations show good agreement with the standard approaches but at a fraction of the computational cost, providing a good framework for uncertainty quantification.
Text
Fabro_PhDThesis_Final.pdf
- Other
More information
Published date: February 2014
Organisations:
University of Southampton, Inst. Sound & Vibration Research
Identifiers
Local EPrints ID: 363111
URI: http://eprints.soton.ac.uk/id/eprint/363111
PURE UUID: 9e20a356-d8a0-4b7a-9297-8c0dbb53b9d6
Catalogue record
Date deposited: 25 Mar 2014 15:12
Last modified: 15 Mar 2024 02:34
Export record
Contributors
Author:
Adriano Todorovic Fabro
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
