Analysis of nonlinear vibration of couple-mass–spring systems using iteration technique
Multidiscipline Modeling in Materials and Structures
ISSN: 1573-6105
Article publication date: 18 May 2020
Abstract
Purpose
An iteration technique has been developed based on the Mickens iteration method to obtain approximate angular frequencies. This technique also offers the periodic solutions to the nonlinear free vibration of a conservative, coupled mass–spring system having linear and nonlinear stiffnesses with cubic nonlinearity. Two real-world cases of these systems are analysed and introduced.
Design/methodology/approach
In this paper, the truncated terms of the Fourier series have been used and utilized in every step of the iteration.
Findings
The obtained results are valid for whole ranges of vibration amplitude of the oscillations. The approximated results are compared with existing and corresponding numerical (considered to be exact) results which show excellent agreement. The error analysis has been carried out and shown acceptable results for the proposed iteration technique.
Originality/value
Effectiveness of the proposed iteration technique is found in comparison with other existing methods. The method is demonstrated by examples.
Keywords
Acknowledgements
The work was supported by The World Academy of Science (TWAS), Research Grant Agreement No. 18-075 RG/MATHS/AS_I-FR3240303632.
Citation
Hosen, M.A. (2020), "Analysis of nonlinear vibration of couple-mass–spring systems using iteration technique", Multidiscipline Modeling in Materials and Structures, Vol. 16 No. 6, pp. 1539-1558. https://doi.org/10.1108/MMMS-11-2019-0196
Publisher
:Emerald Publishing Limited
Copyright © 2020, Emerald Publishing Limited