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Exact eigensolution of a class of multi-level elastically connected members

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posted on 2017-05-04, 13:20 authored by W.P. Howson, Andrew WatsonAndrew Watson
Attention is given to determining the exact natural frequencies and modes of vibration of a class of structures comprising any number of related parallel members that are connected to each other, and possibly also to foundations, by uniformly distributed elastic interfaces of unequal stiffness. The members themselves are considered to have a uniform distribution of mass and stiffness and account can be taken of additional point masses and spring supports. The formulation is general and applies to any structure in which the motion of the component members is governed by a second order Sturm-Liouville equation. Closed form solution of the governing differential equations leads either, to a series of exact substitute systems that are easy to solve through a stiffness approach and which together yield the complete spectrum of natural frequencies and corresponding mode shapes of the original structure, or to simple exact relationships between the natural frequencies corresponding to coupled and uncoupled motion that enable hand solution of the more standard problems to be achieved. An appropriate form of the Wittrick-Williams algorithm is presented for converging on the required natural frequencies to any desired accuracy with the certain knowledge that none have been missed. Examples are given to confirm the accuracy of the approach and to indicate its range of application.

History

School

  • Aeronautical, Automotive, Chemical and Materials Engineering

Department

  • Aeronautical and Automotive Engineering

Published in

Engineering Structures

Citation

HOWSON, W.P. and WATSON, A., 2017. Exact eigensolution of a class of multi-level elastically connected members. Engineering Structures, 143, pp. 375–383.

Publisher

© Elsevier

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

2017-03-27

Publication date

2017

Notes

This paper was accepted for publication in the journal Engineering Structures and the definitive published version is available at http://dx.doi.org/10.1016/j.engstruct.2017.03.059

ISSN

0141-0296

Language

  • en

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