迟滞非线性振荡压实系统动态响应分析

Dynamic Response Analysis of Oscillator Compaction System with Hysteretic Nonlinearity

分析了振荡压实中材料发生弹塑性变形而表现出的迟滞非线性,建立了一种新的振荡压实非线性动力学模型。在一次近似的前提下,利用等效线性化方法,将迟滞恢复力转化为等效刚度和等效阻尼表示,根据谐波平衡原则求出了单自由度振荡压实系统的频响方程。数值求解表明,随着激励幅度的增大系统出现软化趋势,共振点随激励变化而漂移。将等效线性化的结果推广到二自由度振荡压实系统,得到了频响方程组。

After analyzing the hysteretic nonlinearity of materials with elastic and plastic deformation caused by oscillatory compaction, we establish a new nonlinear dynamic model for an oscillatory compaction system. We also employ the equivalent linearization method to express hysteretic restoration force as equivalent damping and equivalent stiffness. Following the harmonic balance principle, we derive the frequency response equation for a single- DOF（degree of freedom） oscillatory compaction system. Numerical analysis shows that the equivalent natural frequency decreases with the increasing of excitation amplitude and that the resonance frequency of the oscillatory compaction system changes with that of excitation amplitude. Finally we extend the equivalent linearization results to a two-DOF oscillatory compaction system and obtain the equations for nonlinear frequency response.