Nonlinear normal modes, modal interactions and isolated resonance curves

Abstract

The objective of the present study is to explore the connection between the nonlinear normal modes of an undamped and unforced nonlinear system and the isolated resonance curves that may appear in the damped response of the forced system. To this end, an energy balancing technique is used to predict the amplitude of the harmonic forcing that is necessary to excite a specific nonlinear normal mode. A cantilever beam with a nonlinear spring at its tip serves to illustrate the developments. The practical implications of isolated resonance curves are also discussed by computing the beam response to sine sweep excitations of increasing amplitudes.

Journal paper

References in corpus (3)

• The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems
• A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions
• A method for nonlinear modal analysis and synthesis: Application to harmonically forced and self-excited mechanical systems

Cited by in corpus (6)

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• Robust and fast backbone tracking via phase-locked loops
• Force appropriation of nonlinear structures
• An efficient method for approximating resonance curves of weakly-damped nonlinear mechanical systems
• Stability of Forced-Damped Response in Mechanical Systems from a Melnikov Analysis
• Energy Transfer and Coherence in Coupled Oscillators with Delayed Coupling: A Classical Picture for Two-Level Systems