A study on multi-frequency patterns in nonlinear network oscillators using incremental harmonic balance method. (May 2020)

• Record Type: Journal Article
• Authors: Chen, Y.M.; Liu, Q.X.; Liu, J.K.
• Is Part Of: International journal of non-linear mechanics. Volume 121(2020)
• Publication Date: 2020-05
• Subjects: Multi-frequency pattern -- Coupled nonlinear oscillator -- Limit cycle -- Incremental harmonic balance method; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2020.103435
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: This paper presents a study on multi-frequency pattern (MFP) vibration of nonlinear network systems based on the incremental harmonic balance (IHB) method. Instead of solving the considered highly-dimensional systems straightforwardly, the IHB method is proposed to solve a single-degree-of-freedom system with a time delay. The time delay is also incorporated into the iteration scheme, by introducing its relations with the phase lag and the angular frequency of limit cycle solutions. As the delay is adjusted to be in preset certain relations with the phase lag and the angular frequency, limit cycle solutions of the time-delayed system can be utilized to generate solutions of the original system. Two network systems are investigated to verify the proposed approach. The presented method can provide both stable and unstable limit cycles, and hence multiple solutions can be tracked successfully. Surprisingly, the coexistence of stable MFP is revealed in the van der Pol-type network oscillators. The attained results are useful for in-depth understanding of the mechanism of MFP. With such high efficiency and accuracy, moreover, the presented analysis method could be applicable in more nonlinear network systems. Highlights: It presents a study on MFP vibration of nonlinear network systems. The highly-dimensional network system is solved as delayed system with single dof. It proposes an efficient semi-analytical analysis approach. The IHB method provides multiple limit cycles, resulting in multiple stable MFPs. The underlying mechanism behind MFP is elaborated based on the attained results.