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Title: Propagation in waveguides with slowly changing variability
Author: Todorovic Fabro, Adriano
ISNI:       0000 0004 5349 1384
Awarding Body: University of Southampton
Current Institution: University of Southampton
Date of Award: 2014
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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.
Supervisor: Ferguson, Neil Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QC Physics