噪声激励下恢复系数和噪声强度对碰撞系统的影响  

Influence of the Recovery Coefficient and Noise Intensity on the Vibro-impact System Under the Noise Excitation

作　　者：景康康 JING Kangkang(School of General Education,Xi’an Mingde Institute of Technology,Xi’an 710124,China)

机构地区：[1]西安明德理工学院通识教育学院,西安710124

出　　处：《自动化与仪表》2024年第12期7-11,17,共6页Automation & Instrumentation

基　　金：陕西省教育厅科学研究计划项目资助(23JK0571)。

摘　　要：对于碰撞系统,物块在碰撞面的速度会发生突变,即系统在碰撞面具有非光滑性,导致无法直接求解该系统的概率密度函数。利用Ivanov非光滑变换,将碰撞系统转化为连续系统,并利用计算机数值仿真系统的相图,直观展示了碰撞系统在碰撞面的非光滑性。研究了系统在不同的恢复系数下,Ivanov非光滑变换前后碰撞系统的相图,发现即使当恢复系数远远小于1时,变换前后系统解的拟合度仍然很高,即Ivanov非光滑变换具有优良特性。在此基础上,利用路径积分法结合Ivanov非光滑变换数值求解分析了碰撞恢复系数和噪声强度对碰撞系统概率密度函数的影响。最后利用蒙特卡洛算法模拟验证了该方法的正确性。The difference between the vibro-impact system and continuous system is that the velocity will change suddenly when the impact occurs,that is,the system has discontinuity on the impact plane.As a result,it is difficult to solve the probability density function of such systems directly.In this paper,based on the Ivanov non-smooth transform,the vibro-impact system is transformed into a continuous system.Then,the phase diagram of the vibro-impact system is simulated to visually show the non-smoothness on the impact surface.Furthermore,we study the phase diagram of the system with Ivanov non-smooth transformation under different recovery coefficients.It is found that even when the recovery coefficient is much less than 1,the fitting degree of the system solution is still very high after the transformation,which means the Ivanov non-smooth transformation has excellent characteristics.On this basis,the path integration method combined with Ivanov non-smooth transformation is used to analyze the probability density function of the vibro-impact system under the different impact recovery coefficient and noise intensity.Finally,Monte Carlo algorithm is used to verify the correctness of the proposed method.

关 键 词：碰撞系统 路径积分法 恢复系数 概率密度 

分 类 号：O313[理学—一般力学与力学基础] TP391.9[理学—力学]