In this paper we discuss a theoretical technique for decomposing multi-degree-of-freedom weakly nonlinear systems into a simpler form — an approach which has parallels with the well know method for linear modal analysis. The key outcome is that the system resonances, both linear and nonlinear are revealed by the transformation process. For each resonance, parameters can be obtained which characterise the backbone curves, and higher harmonic components of the response. The underlying mathematical technique is based on a near identity normal form transformation. This is an established technique for analysing weakly nonlinear vibrating systems, but in this approach we use a variation of the method for systems of equations written in second-order form. This is a much more natural approach for structural dynamics where the governing equations of motion are written in this form as standard practice. In fact the first step in the method is to carry out a linear modal transformation using linear modes as would typically done for a linear system. The near identity transform is then applied as a second step in the process and one which identifies the nonlinear resonances in the system being considered. For an example system with cubic nonlinearities, we show how the resulting transformed equations can be used to obtain a time independent representation of the system response. We will discuss how the analysis can be carried out with applied forcing, and how the approximations about response frequencies, made during the near-identity transformation, affect the accuracy of the technique. In fact we show that the second-order normal form approach can actually improve the predictions of sub- and super-harmonic responses. Finally we comment on how this theoretical technique could be used as part of a modal testing approach in future work.
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ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 12–15, 2012
Chicago, Illinois, USA
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-4500-4
PROCEEDINGS PAPER
Towards a Technique for Nonlinear Modal Analysis
Simon A. Neild,
Simon A. Neild
University of Bristol, Bristol, UK
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Andrea Cammarano,
Andrea Cammarano
University of Bristol, Bristol, UK
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David J. Wagg
David J. Wagg
University of Bristol, Bristol, UK
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Simon A. Neild
University of Bristol, Bristol, UK
Andrea Cammarano
University of Bristol, Bristol, UK
David J. Wagg
University of Bristol, Bristol, UK
Paper No:
DETC2012-70322, pp. 497-505; 9 pages
Published Online:
September 9, 2013
Citation
Neild, SA, Cammarano, A, & Wagg, DJ. "Towards a Technique for Nonlinear Modal Analysis." Proceedings of the ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 1: 24th Conference on Mechanical Vibration and Noise, Parts A and B. Chicago, Illinois, USA. August 12–15, 2012. pp. 497-505. ASME. https://doi.org/10.1115/DETC2012-70322
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