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Vibration analysis of a uniform pre-twisted rotating Euler–Bernoulli beam using the modified Adomian decomposition method


Adair, D and Jaeger, M, Vibration analysis of a uniform pre-twisted rotating Euler-Bernoulli beam using the modified Adomian decomposition method, Mathematics and Mechanics of Solids, 23, (9) pp. 1345-1363. ISSN 1081-2865 (2018) [Refereed Article]

Copyright Statement

The Author(s) 2017

DOI: doi:10.1177/1081286517720843


The governing equations for a pre-twisted rotating cantilever beam are derived and used for free vibration analysis of a pre-twisted rotating beam whose flexural displacements are coupled in two planes. First differential equations of motion of a rotating twisted beam, including terms due to centrifugal stiffening, are derived for an Euler–Bernoulli beam undergoing free natural vibrations. The general solutions of these equations are obtained on applying the Adomian modified decomposition method (AMDM). The AMDM allows the governing differential equations to become recursive algebraic equations and the boundary conditions to become simple algebraic frequency equations suitable for symbolic computation. With additional simple mathematical operations on the model, the natural frequencies and corresponding closed-form series solution of the mode shape can be obtained simultaneously. Two main advantages of the application of the AMDM are, for the cases considered here, its fast convergence rate to the solution with the high degree of accuracy. As the AMDM technique is systematic, it is found straight-forward to modify boundary conditions from one case to the next. Comparison of results with published data showed the present calculations to be in reasonable agreement.

Item Details

Item Type:Refereed Article
Keywords:turbine blade, modified Adomian method, rotating beam, pre-twisted beam
Research Division:Engineering
Research Group:Civil engineering
Research Field:Construction materials
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in engineering
UTAS Author:Jaeger, M (Dr Martin Jaeger)
ID Code:126925
Year Published:2018
Web of Science® Times Cited:20
Deposited By:Information and Communication Technology
Deposited On:2018-07-03
Last Modified:2019-02-26

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