Comparing Analytical Approximation Methods with Numerical Results for Nonlinear Systems

Elliott, A.J., Cammarano, A. and Neild, S.A. (2017) Comparing Analytical Approximation Methods with Numerical Results for Nonlinear Systems. In: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics 2017, Garden Grove, CA, USA, 30 Jan - 02 Feb 2017, pp. 37-49. ISBN 9783319455038 (doi: 10.1007/978-3-319-54404-5_4)

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Modelling the dynamics of nonlinear systems poses a much more challenging problem than for their linear counterparts; as such, analytical solutions are rarely achievable and numerical or analytical approximations are often necessary to understand the system’s behaviour. While numerical techniques are undoubtedly accurate, it is possible to gain a greater understanding of the processes underpinning the workings of the dynamics. Therefore, it is valuable to investigate the accuracy and practicality of the aforementioned analytical approximation techniques and compare the results with numerical which are known to be accurate. In this paper, the unforced, undamped dynamics (known as backbone curves) of a non-symmetric two-mass oscillator will be calculated using the second-order normals forms (SONF), harmonic balance, and multiple scales techniques. The results of these will then be compared to responses found using numerical continuation. Furthermore, the forced responses will be approximated using the SONF and harmonic balance techniques. In addition, recent work has reported the possibility of using such analytical expressions for parameter estimation from experimental data.

Item Type:Conference Proceedings
Glasgow Author(s) Enlighten ID:Cammarano, Dr Andrea and Elliott, Mr Alexander
Authors: Elliott, A.J., Cammarano, A., and Neild, S.A.
College/School:College of Science and Engineering > School of Engineering
College of Science and Engineering > School of Engineering > Systems Power and Energy
Published Online:04 May 2017

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