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Towards a Technique for Nonlinear Modal Reduction

  • T. L. Hill
  • A. Cammarano
  • S. A. Neild
  • D. J. Wagg
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

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.

Keywords

Backbone curves Second-order normal forms Modal analysis Modal interaction Modal reduction 

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Copyright information

© The Society for Experimental Mechanics, Inc. 2014

Authors and Affiliations

  • T. L. Hill
    • 1
  • A. Cammarano
    • 1
  • S. A. Neild
    • 1
  • D. J. Wagg
    • 1
  1. 1.Department of Mechanical EngineeringUniversity of BristolBristolUK

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