Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 296, Issue -, Pages 18-38Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2015.07.017
Keywords
Harmonic balance; Continuation of periodic solutions; Bifurcation detection and tracking; Floquet exponents; Quasiperiodic oscillations; Detached resonance curves
Funding
- European Union (ERC) [NoVib 307265]
- European Union
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The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation analysis, i.e., for the detection and tracking of bifurcations of nonlinear systems. To this end, an algorithm that combines the computation of the Floquet exponents with bordering techniques is developed. A new procedure for the tracking of Neimark-Sacker bifurcations that exploits the properties of eigenvalue derivatives is also proposed. The HB method is demonstrated using numerical experiments of a spacecraft structure that possesses a nonlinear vibration isolation device. (C) 2015 Elsevier B.V. All rights reserved.
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