Nonlinear Dynamic Analysis Of Driving Point Anti-resonant Vibrating Machine

Vibration is a common movement in daily life, in many cases, the vibration is harmful, but if used appropriately, the characteristic of vibration can also solve many practical problems in industry, the vibrating machine manufactured based on the theory of vibration is also widely used in mining, transportation, chemical industry, which is what is called Vibration And Utilization Project. As for the design of vibrating machine, two issues must be taken into consideration:Firstly, the requirements of vibration frequency, amplitude of system must be meted; Secondly, noise pollution of the environment and the load on the base can be decreased. The anti-resonant vibration machines designed according to anti-resonance theory precisely meet the two requirements mentioned above.Driving point anti-resonant vibrating machine is a vibrating mechanism firstly proposed by Liujie et[2] in1995, The exciter of this vibrating machine is not directly installed on the work body but on the lower body, thus the structure of the work body is greatly simplified, mass of vibration can be greatly reduced so that the excitation force decreases correspondingly. Due to being free from the direct interaction of the excitation force, lifetime of work machine can be improved, lower body almost doesn’t vibrate at all, the design requirements of stiffness and strength are easily to ensure, basically, exciter can be designed as the case of static load, and the noise of the whole machine is significantly reduced [2,3]When the driving point anti-resonance vibrating machine is in the normal work, frequency of excitor is equal to anti-resonance frequency, while it does not equate the natural frequency of the system,and when the system’s structural parameters satisfy certain conditions, there exists the1:2and1:3resonance, the study data for the non-primary resonance and the resonance of the system with two degrees of freedom were also rare.In this paper, the dynamic equations of second order nonlinear system is established for the mechanical model of driving point Anti-resonant vibration machines, considering factors including the cubic nonlinear spring and static deformation of the spring et, the condition for the system to produce internal resonance is obtained. By application of multi-scale method to establish the average equation of zhe system under1:3internal resonance, zhen using the Origin drawing software rendering amplitude frequency characteristics curve of the system under different physical parameters according to the average equation, amplitude frequency characteristics curve is discussed and analyzed, finally get the influence on the amplitude and bifurcation of zhe system under different physical parameters。...