Research paperVibration analysis of nonlinear systems with the bilinear hysteretic oscillator by using incremental harmonic balance method
Section snippets
Introduction
Recent theoretical [1], [2], [3], [4] and experimental [5], [6], [7] researches of systems comprising substructures and nonlinear attachments provided validation of nonlinear vibration absorption and mitigation applied to mechanical engineering. Numerous novel designs [8], [9], [10] have been proposed to bring more efficient and robust nonlinear vibration absorbers by purposeful transformation of nonlinearities. Nonlinear systems that involve hysteresis such as magneto-rheological damper,
The mathematical models of the system with a metal-rubber absorption
The profile of instrument installation plate of spacecraft coupled to a metal-rubber vibration absorber is presented in Figs. 1 and 2, simplified model of Fig. 1 has an obvious hysteretic nonlinear structure. It is clear that the relationship between restoring force and displacement is two snap stress-strain structure. Meanwhile, it is obvious that the nonlinearity of metal-rubber absorber differs from NES which has pure cubic stiffness in references [2], [3].
Therefore, mechanical model
Single-DOF nonlinear system
One of the distinctive advantages of the IHB method can be used in a wide range of frequency and it is suitable for strongly nonlinear system to obtain the nonlinear property of dynamical system. Specially, amplitude-frequency plot and stability analysis of system can be obtained effectively with some tracing algorithms and Floquet theory.
In the current section, numerical verifications of the analysis are performed. Taking a simple nonlinear systems depicted in Fig. 2 as a numerical example of
Conclusions
In this paper, vibrations analysis of a single DOF bilinear hysteretic system was investigated by the improved IHB method that the hysteretic restoring force were considered in the iteration formulation. Similarly, the hysteretic term of nonlinear system was added for analysing the stability of the periodic solutions. Although Floquet multipliers of bilinear hysteretic system have become more complicated, it could be resolved effectively by the precise Hsu' method. The basic idea of improved
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