一类非线性振动系统改进状态空间模型及其数值方法  

An Improved State Space Model for Parts of Non-linear Oscillation Systems and Its Numerical Method

作　　者：王建平[1] 刘宏昭[1] 原大宁[1] 苏志霄[2] 

机构地区：[1]西安理工大学,西安710048 [2]清华大学,北京100084

出　　处：《应用力学学报》2002年第4期112-116,共5页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目 (5 0 0 75 0 86);陕西省自然科学基金资助项目 (98C12 )

摘　　要：导出了一类非线性振动系统的改进状态空间模型 ,提出了相应的数值计算方法 ,并利用迭代法有效地提高了计算精度。该数值方法与传统的Houbolt、Wilson θ、Newmark β法以及连续线性化模型及其Taylor变换法[3,4 ] 相比 ,具有更高的求解精度和效率。文末给出了非线性单摆、强迫Duffing方程、强迫VanDerPol方程以及两自由度非线性弹簧摆这几类典型非线性方程的数值计算结果 ,并与文献 [5～ 8]进行对比 ,进一步说明了该方法在计算精度和效率两方面的优越性。In this paper a state space model for parts of non linear oscillation systems is deduced. The model is an improvement on the traditional non linear oscillation equations in state space. A numerical calculation method is presented based on the analysis of the structure property of the model. The calculation precision is improved greatly through using iterative method. Compared with the traditional numerical methods, such as Houbolt method, Wilson θmethod, Newmark βmethod and the continuous linearization model as well as its numerical calculation using Taylor transform method. The presented numerical method has higher calculation precision and efficiency. Numerical calculation examples, such as non linear single pendulum equation, Duffing equation, van der Pol equation and two degree of freedom non linear spring pendulum, are presented by using the presented method. The higher calculation precision and efficiency of this method are demonstrated through comparing the results given in literatures.

关 键 词：非线性振动系统 状态空间模型 数值方法 非线性单摆 

分 类 号：O322[理学—一般力学与力学基础] O241.8[理学—力学]