Analysis and design of nonlinear resonances via singularity theory

Abstract

Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity theory with one distinguished parameter. While tracking bifurcations reveals the qualitative changes in the behaviour, tracking singularities reveals how structural changes are themselves organised in parameter space. The complementarity of that information is demonstrated in the analysis of detached resonance curves in a two-degree-of-freedom system.

References in corpus (4)

• The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems
• Nonlinear Generalization of Den Hartog's Equal-Peak Method
• Performance, robustness and sensitivity analysis of the nonlinear tuned vibration absorber
• Isolated large amplitude periodic motions of towed rigid wheels

Cited by in corpus (2)

• Nonlinear analysis of forced mechanical systems with internal resonance using spectral submanifolds, Part I: Periodic response and forced response curve
• Hidden vibrational bistability revealed by intrinsic fluctuations of a carbon nanotube