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

• The modes are defined as periodic motions induced by an additional (negative) damping term.
• They reflect the vibration behavior in the presence of a resonant excitation source.
• Standard methods for analyzing periodic motions can be applied.
• Capabilities and limitations are investigated for several numerical examples.
• The concept is valid when modal damping or modal coupling are comparatively weak.

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 to ‘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.