黏弹性系统随机响应分析

Equivalent non-linearization technique for random response of viscoelastic system

应用等效非线性化方法分析了高斯白噪声激励作用下强非线性黏弹性系统随机响应。首先,通过广义谐和变换,黏弹性作用力可近似等效为拟线性阻尼和拟线性刚度两部分,进而原系统简化为无黏弹性项的非线性随机系统。其次,选取一类具有待定参数的等效非线性系统类。该等效非线性系统类具有精确稳态解,且和简化后的非线性随机系统具有相同的特性。然后,根据简化系统和等效非线性系统类之差的均方值最小原则,最终确定等效非线性系统类中的待定参数。最后以该系统的精确稳态随机响应近似表示原系统的随机响应。本文所提方法得到的解析结果与蒙特卡洛模拟方法得到的结果符合较好,证实了该方法的正确性。

The random response of the viscoelastic system to Gaussian white noise external excitation is investigated through a transformation procedure and the equivalent non-linearization technique. By adopting the generalized harmonic transformation, the viscoelastic force is approximately replaced by a quasi-linear damping and a quasi-linear stiffness with energy-dependent co- efficients. A reduced nonlinear system without viscoelastic term is established to approximate the original system with viscoe- lastic term, and the stationary probability density of system displacement and velocity are analytically obtained through the e- quivalent non-linearization technique. The agreements between the analytical results and the results from Monte Carlo simula- tions for the original viscoelastic system validate the effectiveness of the proposed technique.