非线性动力系统失效时间的胞参考点映射方法  

A Cell Reference Point Mapping Method for the Failure Time of Nonlinear Dynamical Systems

作　　者：吴晓奇 郭空明[1] 江俊[2] 徐亚兰[1] Wu Xiaoqi;Guo Kongming;Jiang Jun;Xu Yalan(School of Mechano-Electronic Engineering,Xidian University,Xi’an 710071,China;State Key Laboratory for Strength and Vibration,Xi’an Jiaotong University,Xi’an 710049,China)

机构地区：[1]西安电子科技大学机电工程学院,西安710071 [2]西安交通大学机械结构强度与振动国家重点实验室,西安710049

出　　处：《动力学与控制学报》2025年第1期8-14,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(12172267)。

摘　　要：本文研究在给定状态空间失效状态集的情况下,非线性动力系统状态失效时间的快速计算方法.首先对非线性动力系统全局分析的一种经典方法——胞参考点映射法进行改进,以计算失效时间.然后用改进的方法对Duffing系统、一类受迫双稳态结构和弹簧负载倒立摆模型进行了计算,并分析方法的收敛阈值对计算误差和计算时间的影响.结果表明,文中提出的方法可以在满足一定精度的前提下,实现大量状态点失效时间的高效计算.This article studies a fast calculation method for the state failure time of nonlinear dynamic systems given the failure state set.Firstly,a classic method for global analysis of nonlinear dynamical systems,the point mapping under cell reference method,is improved to calculate the state failure time.Then the improved method is used to calculate Duffing system,a forced bistable structure,and spring loaded inverted pendulum model.The influence of the convergence threshold of the method on the calculation error and time is analyzed.The results show that the proposed method can achieve efficient calculation of failure time of a large number of state points while meeting certain accuracy requirements.

关 键 词：非线性动力系统 全局分析 胞映射 点映射 失效时间 

分 类 号：O313[理学—一般力学与力学基础]