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

journal contribution
posted on 2023-05-19, 19:12 authored by Adair, D, Jaeger, M
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.


Publication title

Mathematics and Mechanics of Solids










School of Engineering


Sage Publications Ltd

Place of publication

6 Bonhill Street, London, England, Ec2A 4Pu

Rights statement

The Author(s) 2017

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in engineering

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    University Of Tasmania