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Propagation in waveguides with slowly changing variability

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
Todorovic Fabro, Adriano
a184cc3b-5eb6-4e00-ab7d-2fedf8041b63
Ferguson, Neil
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.

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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
ORCID for Neil Ferguson: ORCID iD orcid.org/0000-0001-5955-7477

Catalogue record

Date deposited: 25 Mar 2014 15:12
Last modified: 06 Jun 2018 13:18

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Contributors

Author: Adriano Todorovic Fabro
Thesis advisor: Neil Ferguson ORCID iD

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