基于时间有限元的弹簧摆动力学新解法  

A NEW DYNAMIC SOLUTION OF SPRING PENDULUM BASED ON TIME FINITE ELEMENT METHOD

作　　者：陈德坤 丁幸波 温新婕 刘曼兰 兰朋[1] CHEN De-kun;DING Xing-bo;WEN Xin-jie;LIU Man-lan;LAN Peng(School of Mechatronics Engineering,Harbin Institute of Technology,Harbin 150001,China;Institute of Defense Engineering,AMS,PLA,Luoyang 471023,China;Beijing Materials Handling Research Institute Co.,Ltd,Beijing 100007,China;School of Mechanical and Electrical Engineering,Xi’an University of Architecture and Technology,Xi’an 710055,China)

机构地区：[1]哈尔滨工业大学机电工程学院,哈尔滨150001 [2]军事科学院国防工程研究院,洛阳471023 [3]北京起重运输机械设计研究院有限公司,北京100007 [4]西安建筑科技大学机电工程学院,西安710055

出　　处：《工程力学》2022年第4期209-218,共10页Engineering Mechanics

基　　金：国家自然科学基金项目(11802072);湖南省科技重大专项项目(2018GK1040)。

摘　　要：弹簧摆问题是一种刚柔耦合的非线性动力学问题,随着电力技术的发展,弹簧摆在高压电塔减震方面获得了大规模的应用,但其动力学仿真还存在很多不完善之处。对此该文提出了一种利用时间有限元与保辛递推算法求解弹簧摆问题的新方法。该方法通过对弹簧摆的非线性摆动问题进行了近似积分处理,并对作用量采用矩形和梯形积分的方法获得保辛递推的形式。在提高求解速度的同时,提高了长时间求解的数值稳定性。为了体现了该文方法在求解内共振系统上的速度和稳定性优势,同已有结果进行两次对比,显示本算法较传统算法的计算速度、时间稳定性与精度上均存在一定优势。最后初步讨论了采用该方法求解大摆角混沌问题的途径。The problem of spring pendulum is a kind of rigid flexible coupling nonlinear dynamic problem. With the development of power technology, spring pendulum has been widely used in high-voltage tower damping, but its dynamic simulation still has many imperfections. It presents a new method to solve the problem of spring pendulum by using time finite element method and symplectic recursive algorithm. In this method, the nonlinear swing problem of spring pendulum is treated by approximate integration, and the Symplectic recursive form is obtained by using rectangular and trapezoidal integral methods. It also improves the numerical stability of the long-term solution. In order to reflect the speed and stability advantages of the method proposed in solving an internal resonance system, two comparisons with existing results are carried out. The results show that the algorithm proposed has some advantages in computational speed, in time stability and in accuracy compared with the traditional algorithm. Finally, the approach to solve the chaotic problem with a large swing angle is discussed.

关 键 词：弹簧摆 时间有限元 保辛 内共振系统 混沌 

分 类 号：O242.21[理学—计算数学]