Nonlinear modal analysis of nonconservative systems: Extension of the periodic motion concept

Abstract

As the motions of nonconservative autonomous systems are typically not periodic, the definition of nonlinear modes as periodic motions cannot be applied in the classical sense. In this paper, it is proposed 'make the motions periodic' by introducing an additional damping term of appropriate sign and magnitude. It is shown that this generalized definition is particularly suited to reflect the periodic vibration behavior induced by harmonic external forcing or negative linear damping. In a large range, the energy dependence of modal frequency, damping ratio and stability is reproduced well. The limitation to isolated or weakly-damped modes is discussed.

References in corpus (3)

• A method for nonlinear modal analysis and synthesis: Application to harmonically forced and self-excited mechanical systems
• Reliability optimization of friction-damped systems using nonlinear modes
• On the computation of the slow dynamics of nonlinear modes of mechanical systems

Cited by in corpus (4)

• A Phase Resonance Approach for Modal Testing of Structures with Nonlinear Dissipation
• Experimental assessment of polynomial nonlinear state-space and nonlinear-mode models for near-resonant vibrations
• Challenging an experimental nonlinear modal analysis method with a new strongly friction-damped structure
• On the Efficacy of Friction Damping in the Presence of Nonlinear Modal Interactions