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V. Vinod,Bipin Balaram,M. D. Narayanan,Mihir Sen 대한기계학회 2015 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.29 No.5
This paper investigates the dynamical behavior of coupled van der Pol oscillators in a ring to understand vibrations that may occur insystems such as turbine blades mounted on a single shaft. The objective is to investigate the effect of spatial differences in oscillator parametersand initial conditions that occur in realistic systems. The coupling between the neighboring oscillators is modeled as a lineardissipative element, and the mathematical model is analyzed asymptotically and numerically. Synchronization of self excited oscillatorsin mechanical systems has been predominantly investigated in recent literature by focusing on its parameter dependence. This work investigatesthe dependence of dynamics of such systems on initial conditions. The analysis is conducted for identical oscillators as well asoscillators with a frequency mismatch, along with three different sets of initial conditions. The dynamics of the system is discussed basedon time plots, frequency plots, instantaneous dynamics of each oscillator by Hilbert transform and the phase equation obtained by asymptoticexpansion. The study reveals interesting phenomena like amplitude death, oscillation suppression, oscillation resurrection, frequencylocking and beat frequency in the model when subjected to the different set of initial conditions.