具有强非线性振动台动力学特性研究

摘要

The dynamic model is established considering geometric nonlinearity and support nonlinearity, and the dynamic differential equation is derived and discreted by Galerkin method. On that basis, the approximate analytical solution of the vibration system is obtained by incremental harmonic balance method.The effects of excitation amplitude and support position are analysed and discussed on dynamic characteristics. The steady-state amplitude increases, hardening nonlinearity enhances, hysteretic region broadens near primary resonance and multiple solution region widens with increasing excitation amplitude and the support moves to both ends. Besides, super-harmonic resonance is reduced of the vibration system with changing system parameters.%建立了考虑几何非线性和支撑非线性等因素的振动台系统的动力学模型,推导了振动台的动力学微分方程,并采用Galerkin方法对其进行离散化处理.在此基础上,应用增量谐波平衡法对振动台系统进行求解进而获得其近似解析解.研究了外激励幅值、支撑位置等参数的变化对振动台动态特性的影响.随着激励幅值的增大和支撑位置向两边间移动,振动系统的最大稳态幅值明显增大,硬式非线性增强,主共振附近的滞后区域变宽,多解区域变宽.除此之外,随着参数的变化,振动系统的超谐波共振减弱.