机械非线性动力学分析的A-算符方法

A-OPERATOR METHOD FORNONLINEAR DYNAMIC ANALYSIS OFMECHANICAL SYSTEM

用Adomian分解算法的思想,把机械系统中最一般的动力学模型转化为一阶标准型微分方程组,以形式上的精确解的表达式为基础构造了求解机械系统非线性模型近似解析解的A-算符方法（AOM）;在所建立的AOM的基础上,首次提出了基于AOM的符号-数值方法（S-N方法）。最后,应用AOM得到了单自由度凸轮-从动件非线性系统模型近似解析解的表达式,分析了该算法的误差。对两自由度凸轮-从动件非线性系统应用基于AOM的S-N方法进行了数值研究,得到了系统的数值计算结果。算例表明,AOM是求解非线性方程的一种可行而有效的方法。

By adopting the thought of Adomian's decomposi-tion method, the common dynamic model in mechanical sys-tems are transformed into a standard first-order-differential-equations, and then the A-operator method (AOM) for the approximate analytic solution of nonlinear mechanical system is developed based on the exact solution in form. The symbolic-numeric (S-N) method on the bases of the AOM is proposed for the first time. Finally, the dynamic responses of one-degree and two-degree nonlinear cam-follower systems are investigated by using the AOM. Numerical examples show that AOM is of high accuracy and high efficiency for solving nonlinear equa-tions. It shows that the method is of potential application value in nonlinear dynamic analysis of mechanical system.