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Simulation of the vibrations of a non-uniform beam loaded with both a transversely and axially eccentric tip mass

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Adair, D and Jaeger, M 2018 , 'Simulation of the vibrations of a non-uniform beam loaded with both a transversely and axially eccentric tip mass' , International Journal of Computational Methods and Experimental Measurements, vol. 6, no. 4 , pp. 679-690 , doi: 10.2495/CMEM-V6-N4-679-690.

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Abstract

The main purpose of this work is to employ the Adomian modified decomposition method (AMDM) tocalculate free transverse vibrations of non-uniform cantilever beams carrying a transversely and axiallyeccentric tip mass. The effects of the variable axial force are taken into account here, and Hamilton’sprinciple and Timoshenko beam theory are used to obtain a single governing non-linear partial differentialequation of the system as well as the appropriate boundary conditions. Two product non-linearitiesresult from the analysis and the respective Cauchy products are computed using Adomian polynomials.The use of AMDM to make calculations for such a cantilever beam/tip mass arrangement has not, tothe authors’ knowledge, been used before. The obtained analytical results are compared with numericalcalculations reported in the literature and good agreement is observed. The qualitative and quantitativeknowledge gained from this research is expected to enable the study of the effects of an eccentric tipmass and beam non-uniformity on the vibration of beams for improved dynamic performance.

Item Type: Article
Authors/Creators:Adair, D and Jaeger, M
Keywords: adomian decomposition method, cantilever beam, mechanical vibrations, tip mass
Journal or Publication Title: International Journal of Computational Methods and Experimental Measurements
Publisher: W I T Press
ISSN: 2046-0546
DOI / ID Number: 10.2495/CMEM-V6-N4-679-690
Copyright Information:

Copyright 2018 WIT Press

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