Harmonic Resonance Nonlinear Effects

In a single degree-of-freedom weakly nonlinear oscillator subjected to periodic external exaction,, a small excitation amplitude changes may cause a large vibration amplitude of the entire system, and at the same time may produce a jump and hysteresis phenomena in the system, resulting in instability of the system vibration, so always introduce a linear vibration absorber to suppress the nonlinear vibration system. At present, the linear vibration absorber and nonlinear vibration absorber is widely used to suppress the linear forced vibration systems, better inhibitory effect.In nonlinear systems, when the excitation frequency is close to the natural frequency of the system, the nonlinear amplitude frequency response curve will produce the phenomenon of multi-valued, making the system unstable, so the nonlinear vibration absorber is not suitable to control the nonlinear forced vibration. In this paper, the linear vibration control nonlinear forced vibration, focusing on studying the evaluation parameters.In this paper, following work has been done:(1)In one-degree-of-freedom system with quadratic, cubic and quartic nonlinearities, the effect of the change of inherent frequency, nonlinear parameter, excitation frequency and amplitude to system is investigated. Then the change of amplitude with time and the phase diagram are analyzed.(2)Vibration system is not stable due to small changes in the parameters, so the absorber is tried to introduce. In order not to influence the main structure nature of the system, the quality of the absorbing vibration ware which is introduced into should be less than the main structure. Then the corresponding mathematical model is established, and the perturbation method has been carried on the theoretical analysis of the model, simulating the amplitude frequency response curve of the system, and summed up the system before and after the vibration of the main resonance is suppressed and jumping disappear.(3)Base on theoretical analysis, the change of amplitude of the main structure and the change of amplitude of saddle-point bifurcation before and after vibration absorb joined are investigated, the attenuation ratio of response amplitude and the desensitisation ratio of the critical amplitude of excitation are put forward to suppress the effect.