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A power series solution for rotating nonuniform Euler-Bernoulli cantilever beams


Adair, D and Jaeger, M, A power series solution for rotating nonuniform Euler-Bernoulli cantilever beams, Journal of Vibration and Control, 24, (17) pp. 3855-3864. ISSN 1077-5463 (2017) [Refereed Article]

Copyright Statement

Copyright The Author(s) 2017

DOI: doi:10.1177/1077546317714183


A systematic procedure is developed for studying the dynamic response of a rotating nonuniform Euler–Bernoulli beam with an elastically restrained root. To find the solution, a novel approach is used in that the fourth-order differential equation describing the vibration problem is first written as a first-order matrix differential equation, which is then solved using the power series method. The method can be used to obtain an approximate solution of vibration problems for nonuniform Euler–Bernoulli beams. Specifically, numerical examples are presented here to demonstrate the usefulness of the method in frequency analysis of nonuniform Euler–Bernoulli clamped-free cantilever beams. Results for mode shapes and frequency parameters were found to be in satisfactory agreement with previously published results. The effects of tapering, both equal and unequal, were investigated for both a cantilever wedge and cantilever cone.

Item Details

Item Type:Refereed Article
Keywords:power series method, rotating beam, nonuniform Euler–Bernoulli beam, cantilever
Research Division:Engineering
Research Group:Mechanical engineering
Research Field:Numerical modelling and mechanical characterisation
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in engineering
UTAS Author:Adair, D (Dr Desmond Adair)
UTAS Author:Jaeger, M (Dr Martin Jaeger)
ID Code:122579
Year Published:2017
Web of Science® Times Cited:17
Deposited By:Engineering
Deposited On:2017-11-19
Last Modified:2021-07-05

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