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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/28344

Title: On the provenance of hinged-hinged frequencies in Timoshenko beam theory
Authors: Howson, W.P.
Watson, Andrew
Issue Date: 2018
Publisher: © Elsevier
Citation: HOWSON, W.P. and WATSON, A., 2018. On the provenance of hinged-hinged frequencies in Timoshenko beam theory. Computers and Structures, 197, pp.71-81.
Abstract: An exact differential equation governing the motion of an axially loaded Timoshenko beam supported on a two parameter, distributed foundation is presented. Attention is initially focused on establishing the provenance of those Timoshenko frequencies generated from the hinged-hinged case, both with and without the foundation being present. The latter option then enables an exact, neo-classical assessment of the ‘so called’ two frequency spectra, together with their corresponding modal vectors, to be undertaken when zero, tensile or compressive static axial loads are present in the member. An alternative, ‘precise’ approach, that models Timoshenko theory efficiently, but eliminates the possibility of a second spectrum, is then described and used to confirm the original eigenvalues. This leads to a definitive conclusion regarding the structure of the Timoshenko spectrum. The ‘precise’ technique is subsequently extended to allow, either the full foundation to be incorporated, or either of its component parts individually. An illustrative example from the literature is solved to confirm the accuracy of the approach, the nature of the Timoshenko spectrum and a wider indication of the effects that a distributed foundation can have.
Description: This paper is closed access until 5 February 2019.
Version: Accepted for publication
DOI: 10.1016/j.compstruc.2017.11.017
URI: https://dspace.lboro.ac.uk/2134/28344
Publisher Link: https://doi.org/10.1016/j.compstruc.2017.11.017
ISSN: 0045-7949
Appears in Collections:Closed Access (Aeronautical and Automotive Engineering)

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