文献类型：期刊文献

中文题名：用谐波—能量平衡法求解单摆方程

英文题名：HARMONIC-ENERGY BALANCE METHOD FOR SOLVING PENDULUM EQUATION

作者：李银山[1];李彤[2];韦炳威[1];李欣业[1]

机构：[1]河北工业大学机械工程学院力学系,天津300130;[2]华东理工大学承压系统与安全教育部重点实验室,上海200237

年份：2016

卷号：14

期号：3

起止页码：197

中文期刊名：动力学与控制学报

外文期刊名：Journal of Dynamics and Control

收录：CSTPCD;;Scopus

基金：国家自然科学基金资助项目(10872063)~~

语种：中文

中文关键词：强非线性;单摆;谐波—能量平衡法

外文关键词：strong nonlinear, pendulum, harmonic-energy balance method

摘要：应用谐波—能量平衡法求解了强非线性单摆方程,谐波-能量平衡法与经典的摄动法和谐波平衡法不同,不是把微分方程和初始条件分离处理;而是把微分方程和初始条件同时处理.用谐波平衡,将描述动力系统的二阶常微分方程,化为以角频率、振幅为变量的非线性代数方程组,考虑能量平衡,构成角频率、振幅为变量的封闭方程组求得解析解.谐波-能量平衡法将谐波平衡与能量平衡相结合,克服了二者的缺点吸取了二者的优点.实例表明,谐波-能量平衡法方法简单,取较少谐波就可以达到较高的精度.
A harmonic-energy balance method is put forward to solve the strong nonlinear pendulum equation. The difference from the classical perturbation method is that the harmonic balance method does not account the differential equation and initial conditions separately, but it considers both simultaneously. Through the harmon- ic-balance method, two-order ordinary differential equations describing dynamic systems become a set of nonlinear algebraic equations with the variables of angular frequency and amplitude. Considering the balance of energy, the close equations with angular frequency and amplitude as the variables can be solved. The harmonic-energy bal- ance method is a combination of harmonic-balance and energy balance. It overcomes the shortcomings of both methods and takes their advantages. A case study also shows that the harmonic-energy balance method is simpler higher precision although it takes less harmonics.