几何非线性黏性阻尼隔振系统动力学特性研究

Dynamic characteristics of geometrically nonlinear viscous damping vibration isolation system

针对舰船设备用隔振系统中普遍存在的非线性特性,建立了包含非线性刚度、库伦阻尼和几何非线性黏性阻尼的非线性隔振系统数学模型,采用平均法进行解析求解,根据Routh-Hurwitz判据得到系统稳定性边界条件,综合研究了线性阻尼、库伦阻尼和和几何非线性黏性阻尼对系统幅频响应和稳定性的影响规律;对非线性隔振系统进行了避跳参数设计,分析了系统参数对避跳边界的影响;通过振动试验进行验证。结果表明:线性阻尼、库伦阻尼和几何非线性黏性阻尼对降低软、硬隔振系统幅频响应峰值,提高系统稳定性都有积极作用,但由于库伦阻尼的“锁定”特性导致硬特性隔振系统幅频响应出现“频率岛”现象,系统稳定性未能得到有效改善,但库伦阻尼有效降低了软特性隔振系统幅频响应峰值,提高了系统稳定性;几何非线性黏性阻尼对降低幅频响应峰值,提高系统稳定性均具有显著作用,同时不会出现“频率岛”现象。

Aiming at the nonlinear characteristics of the vibration isolation system for naval equipments,a mathematical model of the nonlinear vibration isolation system including nonlinear stiffness,Coulomb damping and geometric nonlinear viscous damping is established,and the average method is used for analytical solution,the system stability boundary conditions are obtained according to the Routh-Hurwitz criterion.The influence of linear damping,Coulomb damping and geometrically nonlinear viscous damping on the system’s amplitude-frequency response and stability is comprehensively studied.The jump avoidance parameter design of the nonlinear vibration isolation system is carried out,and the influence of the system parameters on the jump avoidance boundary is analyzed.It is verified by vibration test.The results show that linear damping,Coulomb damping and geometrically nonlinear viscous damping have positive effects on reducing the amplitude-frequency response peaks and improving system stability of soft and hard vibration isolation systems.Due to the"locking"characteristic of Coulomb damping,the amplitude-frequency response of the hard vibration isolation system appears"frequency island",and the system stability cannot be effectively improved.However,Coulomb damping effectively reduces the amplitude-frequency response peak of the soft vibration isolation system and improves system stability;Geometrically nonlinear viscous damping has a significant effect on reducing the peak amplitude and frequency response and improving the stability of the system without the phenomenon of"frequency island".The design of the jump avoidance parameters of the nonlinear vibration isolation system and the obtained change rule of the jump avoidance parameters have an important guiding role in the parameter design of the nonlinear vibration isolation system.