随机窄带噪声作用下非线性碰撞振动系统的稳态响应研究

发布时间：2018-04-09 06:31

本文选题：碰撞振动系统　切入点：非光滑变化　出处：《应用数学和力学》2016年06期

【摘要】：研究了随机参激作用下一个非线性碰撞振动系统的随机响应.基于Krylov-Bogoliubov平均法,借助第一类改进的Bessel函数,得到了决定平凡解的几乎确定稳定性的最大Lyapunov指数.模拟结果发现,碰撞振动系统的最大Lyapunov指数特性不同于一般的非碰撞系统,其最小值为负.同时,在确定性情形下,得到了骨架曲线方程和不稳定区域的临界方程.进一步,利用矩方法,讨论了系统的一阶和二阶非平凡稳态矩,发现了碰撞振动系统中有频率岛现象的存在.最后,借助FokkerPlanck-Kolmogorov方程,利用有限差分法,讨论了碰撞振动系统中存在的随机跳现象.在随机强度较小时,稳态概率密度集中于响应振幅的非平凡分支;但是随着随机强度的增加,平凡稳态解的概率会变大.
[Abstract]:The random response of a nonlinear collisional vibration system under random parametric excitation is studied.Based on the Krylov-Bogoliubov averaging method and the improved Bessel function of the first kind, the maximum Lyapunov exponent, which determines the stability of trivial solution, is obtained.The simulation results show that the maximum Lyapunov exponent of the collisional vibration system is different from that of the general non-collision system, and its minimum value is negative.At the same time, in the case of certainty, the skeleton curve equation and the critical equation of unstable region are obtained.Furthermore, the first and second order nontrivial steady state moments of the system are discussed by using the moment method, and the existence of frequency islands in the collision vibration system is found.Finally, with the help of FokkerPlanck-Kolmogorov equation and finite difference method, the phenomenon of random jump in collisional vibration system is discussed.When the random strength is small, the steady-state probability density is concentrated on the nontrivial branch of the response amplitude, but the probability of the trivial steady-state solution increases with the increase of the random strength.
【作者单位】：西北工业大学应用数学系;应用数学和力学;
【基金】：国家自然科学基金(11472212,11532011)~~
【分类号】：O322

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