非线性振动分析的均向量场法  

An Average Vector Field Method for Nonlinear Vibration Analysis

作　　者：鲍四元[1] 邓子辰[2] BAO Siyuan;DENG Zichen(School of Civil Engineering,Suzhou University of Science and Technology,Suzhou,Jiangsu 215011,P.R.China;School of Natural and Applied Sciences,Northwestern Polytechnical University,Xi'an 710072,P.R.China)

机构地区：[1]苏州科技大学土木工程学院,江苏苏州215011 [2]西北工业大学理学院,西安710072

出　　处：《应用数学和力学》2019年第1期47-57,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11202146)~~

摘　　要：通过构造向量形式的振动微分方程组,利用均向量场(AVF)法得到振动响应的向量差分迭代格式.该离散格式能够保能量,同时具有二阶精度的特征,从而给出非线性振动问题的均向量场法.介绍了均向量场法的基本步骤.在建立AVF格式时,对于微分方程中若干常见的项,直接给出相应的映射项.应用均向量场法研究了非线性单摆问题和Kepler(开普勒)问题,数值结果说明了该方法保能量和具有长时间求解能力的特性.Through construction of differential equations in the vector form,the differential iteration form of the vibration response was obtained according to the average vector field( AVF) method. This discrete form is energy-preserving for the Hamiltonian system,and has the characteristics of 2 nd-order accuracy.The detailed steps of the AVF method were given. To establish the AVF scheme,the mapping forms were deduced directly for several common items in the differential equations. The pendulum problem and the Kepler problem were studied with the AVF method. The numerical results demonstrate the advantages of the AVF method in solving nonlinear vibration problems,i. e. the conservation of energy and the longterm solution stability.

关 键 词：均向量场法 非线性振动 保能量 单摆问题 Kepler问题 

分 类 号：O322[理学—一般力学与力学基础] O326[理学—力学]