基于平均法的金属橡胶隔振器非线性振动特性研究

Nonlinear Vibration Characteristics of Metal Rubber Vibration Isolator Based on Average Method

目的研究金属橡胶隔振系统的非线性振动特性和机理。方法建立该金属橡胶隔振系统的非线性动力学模型,利用平均法推导出系统的自由振动运动方程和在简谐激励下的受迫振动幅频响应方程,通过数值计算分析影响隔振系统位移传递率的因素。随后设计一种结构紧凑的金属橡胶隔振器,通过静压试验得到加载卸载迟滞回线,利用拟合方法建立金属橡胶的指数型刚度模型。该模型在相同拟合效果下参数较少,将指数型非线性刚度模型代入到振动方程中进行求解,得到理论幅频响应曲线。同时,进行金属橡胶隔振系统的正弦扫频试验,得到不同振动幅值下的实测传递率幅频响应,与理论计算结果进行对比。结果拟合参数与系统的振动特性相关,拟合参数k_(1)越大,系统共振频率越低,拟合参数k_(2)越大,系统共振频率越高。理论计算与试验结果共振频率的误差最大为2.1%,放大倍数最大误差为17.1%。该理论方法可以较为准确地计算出隔振系统的共振频率、共振放大倍数以及非线性振动的跳跃现象。结论该方法可以较为准确地通过金属橡胶隔振器的静压试验数据预估出金属橡胶隔振系统的非线性振动特性,对于金属橡胶隔振设计具有一定的应用价值。

In order to study the nonlinear vibration characteristics and mechanism of metal rubber vibration isolation system,the nonlinear dynamic model of the metal rubber vibration isolation system is established.The free vibration motion equation of the system and the forced vibration amplitude frequency response equation under simple harmonic excitation are derived by using the average method.The factors affecting the displacement transmissibility of the vibration isolation system are analyzed by numerical calculation.Then a compact metal rubber vibration isolator is designed,and the loading and unloading hysteresis loop is obtained through the static pressure test.The exponential stiffness model of metal rubber is established by using the fitting method.Under the same fitting effect,the parameters of the model are less.The nonlinear stiffness is brought into the vibration equation for solution,and the theoretical amplitude frequency response curve is obtained.At the same time,the sinusoidal sweep frequency experiment of the metal rubber vibration isolation system is carried out.The measured transmissibility amplitude frequency response under different vibration amplitudes is obtained and compared with the theoretical calculation results.The results show that the fitting parameters are related to the vibration characteristics of the system.The larger the fitting parameter k_(1),the lower the resonance frequency of the system,and the larger the fitting parameter k_(2),the higher the resonance frequency of the system.The maximum error between theoretical calculation and experimental results of resonance frequency is 2.1%,and the maximum error of amplification is 17.1%.This theoretical method can accurately calculate the resonance frequency,resonance amplification and jumping phenomenon of nonlinear vibration of the vibration isolation system.The method in this paper can accurately predict the nonlinear vibration characteristics of metal rubber vibration isolation system through the static pressure test data of metal rubber vibration isolator,and has certain application value for the design of metal rubber vibration isolation.