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

TL;DR

This paper extends the concept of nonlinear modal analysis to nonconservative systems by introducing an additional damping term, enabling the definition of periodic motions and capturing the energy-dependent behavior of such systems.

Contribution

It proposes a novel approach to define nonlinear modes in nonconservative systems through an added damping term, broadening modal analysis applicability.

Findings

Effective in modeling periodic vibrations with external forcing or negative damping

Accurately reproduces energy-dependent modal properties over a wide range

Discusses limitations for isolated or weakly-damped modes

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.