多频激励下气动隔振系统非线性特性分析

Nonlinear characteristic analyses of pneumatic vibration isolation system with a multi-frequency excitation

运用非线性动力学的方法研究气动隔振系统在多个频率激励下的非线性动力学特性。通过试验的方法得到空气弹簧在一定初始压力下的相对载荷曲线,以空气弹簧工作高度为自变量,用三次多项式对该曲线进行非线性拟合,得到弹簧非线性恢复力与工作高度的三次多项式表达式。建立气动隔振系统在3个激励频率下的非线性模型,根据弹簧的非线性恢复力,得到系统的非线性动力学方程。运用多尺度法对该非线性动力学方程进行求解,分析3个频率共同作用下的组合共振,讨论各非线性参数对系统的影响。研究结果表明:当组合频率接近系统线性化固有频率时,系统具有很强的组合共振;三次非线性系数直接影响系统的非线性特性;激励幅值越大,非线性现象越明显。

The nonlinear dynamics characteristic of pneumatic vibration isolation system with a multi-frequency excitation was studied with the method of nonlinear dynamics.First,relative load curve of an air spring under a certain initial pressure was obtained by test,and based on the test data,a cube polynomial equation was obtained by means of nonlinear polynomial curve fitting according to the equilibrium heights of the air spring.Then,the nonlinear model of pneumatic vibration isolation system with a multi-frequency excitation was built and nonlinear dynamics equation was obtained according to nonlinear restoring force of the air spring.Next,the method of multiple scales was used to solve the nonlinear dynamics equation.Finally,combination resonance of pneumatic vibration isolation system with a multi-frequency excitation was analyzed and influences of the nonlinear parameter to the system were discussed.The results show that when combination frequencies are near the linearized natural frequency,combination resonance becomes strong.Cube nonlinear parameter directly influences nonlinear characteristic of the system,the greater the excitation amplitude,the more obvious of the nonlinear characteristic.