Variability in the dynamic response of connected structures possessing spatially slowly varying properties

Abstract

This thesis covers the modelling and analysis of the dynamic behaviour of coupled structures possessing slowly varying properties. A mobility method is used to dynamically couple beams to a plate through a series of point connections comprising rigid links or flexible ones, the latter in the form of elastic springs. This is a relevant problem for cable bundles providing electrical power or for communications in cars, satellites and airplanes. In the case of rigid links, the response of the coupled system will generally be governed by the response of the least mobile structure, but with additional modes. For flexible links, there is a frequency at which the response of the combined system uncouples. The flexible links can also be used to reduce the uncertainties due to one of the substructures. Uncertainties in the positioning of the connection points were also considered and they can be as important as uncertainties in the mechanical properties of the structures in terms of the coupled system response variability.

The slowly varying properties are then introduced using a description given by a random field using the Karhunen–Loève expansion. For the slowly varying beams, the Wentzel–Kramers– Brillouin approximation is used to find analytical solutions of the flexural wave equation and subsequently expressions for the input and transfer mobilities. The slowly varying plate is solved combining Finite Element Analysis and a Perturbation Method in order to find the required mode shapes, natural frequencies and mobilities. Infinite and finite coupled structures were considered. The work presented here thus proposes an alternative to the standard technique used in the industry of considering the cable bundles as lumped mass at the connection points. This approximation is valid at lower frequencies, where they indeed behave as an additional mass. However, at higher frequencies they can contribute to adding some stiffness and apparent damping, as the response of the coupled system is now shared into more modal resonances, from the modes of the host structure and the attached cables.

Experimental validation is presented showing the effects of randomly spaced connections and are in good agreement with numerical simulations. In order to capture the varying properties, a novel technique is proposed that combines a wavenumber correlation technique within a Bayesian framework in order to estimate the values of the bending stiffness of the particular cable bundles. The Bayes’ technique was also used to reconstruct random fields from synthetic data. It could subsequently be applied experimentally and provide the required input for models possessing slowly varying properties.

More information

Identifiers

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

Catalogue record

Export record