摘要
相对运动中质点的运动方程大多数是非线性的,其精确显式求解是一个难点。本文基于同伦摄动分析方法,研究了相对运动中一类质点运动非线性微分方程的近似显式解。先构造了系统的同伦方程,再结合Lindstedt–Poincare方法和系统的初始条件,推导了系统自由振动的固有频率,求解了系统的位移近似响应,并通过数值仿真验证了理论分析解的正确性,为相对运动的质点运动方程求解提供了一种新的求解方法。
Most of the motion equations of particles in relative motion are nonlinear,and their exact explicit solutions are difficult to obtain.Based on the method of homotopy perturbation analysis,the approximate explicit solutions of a class of nonlinear differential equations of particle motion in relative motion are studied.First,the homotopy equation of the system is constructed,then the natural frequency of the free vibration of the system is derived by combining the Lindstedt–Poincare method and the initial conditions of the system,and the approximate displacement response of the system is solved.The correctness of the analytical solution is verified by numerical simulation,which provides a new solution method for solving the motion equations of relative moving particles.
作者
姜文安
刘若冰
顾叶彤
李浚超
JIANG Wenan;LIU Ruobing;GU Yetong;LI Junchao(Faculty of Civil Engineering and Mechanics,Jiangsu University,Zhenjiang 212013,Jiangsu,China)
出处
《力学与实践》
北大核心
2023年第6期1399-1402,共4页
Mechanics in Engineering
基金
国家自然科学基金项目(12372001)
校级高等教育教改研究课题(2021JGYB037)
2023年校级大创--工程力学案例及其力学原理分析项目资助。
关键词
理论力学
相对运动
非线性
同伦摄动
theoretical mechanics
relative motion
nonlinearity
homotopy perturbation
