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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。
Adomian decomposition algorithm is used to transform the most general dynamical model of a mechanical system into a first order standard differential equation. Based on the expression of formal exact solution, an approximate analytic solution of the nonlinear model of a mechanical system is constructed. A-operator method (AOM); AOM-based symbolic-numerical method (SN method) was first proposed based on the established AOM. Finally, the expression of the approximate analytic solution of a single DOF cam-follower nonlinear system model is obtained by using AOM, and the error of the algorithm is analyzed. The numerical study of the S-N method based on AOM for a two-DOF cam-follower nonlinear system is carried out. The numerical results of the system are obtained. The example shows that AOM is a feasible and effective method for solving nonlinear equations.