非理想参数下准零刚度隔振器的次谐波响应

Subharmonic Response of Quasi-Zero-Stiffness Isolator Under Non-Ideal Parameters

准零刚度隔振器具有高效的低频隔振特性,但在实际工程中很难达到理想的准零刚度状态,存在正刚度和超重情况。为了研究非理想条件对准零刚度隔振器的3次超谐波和1/3次亚谐波响应的影响,采用多尺度法求得次谐波响应的稳定解,并且通过参数调整,研究非理想参数对谐波的影响。通过绘图分析得出,超载量变大,三次恢复力的减小,线性刚度的增加,阻尼的增加会使3次超谐波的峰值减小。对于1/3次亚谐波共振,超载量,线性刚度和阻尼的变化对其影响不大,而三次恢复力的减小,会使得曲线的弯曲程度减弱,即非线性特性减弱。结果表明:非理想条件可以削弱3次超谐波共振,但是对1/3次亚谐波共振影响不大。

Quasi-zero-stiffness of vibration isolation has high efficient characteristics of low frequency vibration isolation,but in the practical engineering it is hard to reach the ideal state of quasi zero stiffness,and positive stiffness and overweight conditions exist.In order to study the influence of the non-ideal condition on the responses of third super-harmonic and the third sub-harmonic of quasi-zero-stiffness isolator,the multi-scale method was used to obtain the stable solution of the subharmonic response,and the influence of the non-ideal parameters on the harmonic was studied by adjusting the parameters.Through graphic analysis,it is concluded that the peak value of the third super-harmonic will decrease with the increase of overload,the decrease of the third restoring force,the increase of linear stiffness and the increase of damping.For 1/3 sub-harmonic resonance,the changes of overload,linear stiffness and damping have little impact on it,while the reduction of the third restoring force will weaken the bending degree of the curve,that is,the nonlinear characteristics.The results show that the non-ideal condition can weaken the third super-harmonic resonance,but has little effect on the third subharmonic resonance.