Dynamic Motion of Parametrically Excited Asymmetric Nonlinear System With Time Delay. Analysis of 1/2-th Subharmonics by Averageing Method.

Abstract

This paper studies subharmonic responses of a parametrically excited asymmetric nonlinear system with time delay. It is known that it is difficult to investigate the nonlinear system with time delay by analytical methods because the system is described by a difference-differential equation hard to be solved. To analyze this kind of a system, we have already introduced an averaging method for the functional differential equation. The previous work showed that this averaging method is effective for self excited vibrations and forced vibrations arising in a Duffing type vibration system with time delay. However, the previous work dealt only with a fundamental harmonic responses and the target system has a relatively simple structure. To investigate a more practical example, this paper studies not only fundamental but also higher harmonic responses of a more practical vibration system with time delay such as a one dimensional rotor system of asymmetric rigidity supported by plain bearings. The result showed that stability conditions estimated by the averaging method is deeply connected with behaviors obtained from a direct numerical simulation of the target system.