Towards a technique for nonlinear modal reduction

Hill, T.L., Cammarano, A., Neild, S.A. and Wagg, D.J. (2014) Towards a technique for nonlinear modal reduction. Foss, Gary and Niezrecki, Christopher (eds.) In Special Topics in Structural Dynamics, Volume 6: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014. Springer Cham. pp. 121-128 . (doi:10.1007/978-3-319-04729-4_11).

Abstract

In this paper we discuss an analytical method to enable modal reduction of weakly nonlinear systems with multiple degrees-of-freedom. This is achieved through the analysis of backbone curves—the response of the Hamiltonian equivalent of a system—which can help identify internal resonance within systems. An example system, with two interacting modes, is introduced and the method of second-order normal forms is used to describe its backbone curves with simple, analytical expressions. These expressions allow us to highlight which particular interactions are significant, as well as specify the conditions under which they are important. The descriptions of the backbone curves are validated against the results of continuation analysis, and a comparison is also made with the response of the system under various levels of forcing and damping. Finally, we discuss how this technique may be expanded to systems with a greater number of modes.

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Contributors

Author: A. Cammarano

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