本文对12v主副连杆式2206kW柴油机惯性力进行了全面的分析计算，明确指出了该类柴油机的三阶惯性力是引起其振动的主要干扰力之一。并对简化为六个自由度的柴油机系统进行了强迫振动计算和实验。将此理论计算结果与在内燃机车定置条件下柴油机系统的振动实测结果进行比较，发现理论计算结果与振动实测结果基本吻合。

利用接近恒同的非线性变换，计算出了非共振双Hopf分叉系统规范形和系数。利用广义坐标变换，将非共振单自由度非线性强迫振动系统变换为双Hopf分叉系统，用规范形理论给出了一种计算该类系统定常解及分叉特性的方法。

efficient method for calculating the normal form and the associated non-linear transformations for the semi-simple case without central manifold reduction is given in this paper. The one-step transformation concept is adopted for easy programming. This method can be used to calculate high order normal forms of high-dimensional ordinary differential equations of non-linear oscillators. Aprog ram in MATHEMATICA language is designed to perform the calculation. Three examples are given in order to verify the method and to show the efficiency of the program.

An efficient method to calculate the normal form and the associated nonlinear transfolmations for the semi-simple case is given in this paper. The one step transforma-tion concept is adopted to make the approach very easy to be programmed. An intelligent judgement is used to simplify the tedious calculation. This method can be used to calculate high order normal form (without limitation, up to the capacity of the computer) of high dimensional (until dimension 9) ordinary differential equations of the nonlinear oscillators. A program in Mathematica language is designed to perform the calculation. Six examples are given in order to verify the method and to show the efficiency of the program.

利用非线性变换，本文推导出了一种只需通过简单代数运算即可算出Hopf分叉、Normal Form系数的简单方法。用这种方法求解非线性振动问题，只需把原方程变换成本文。讨论的典财形式的一阶散分方程组，然后进行简单的代数运算即可得到原非线性振动方程的解，这种方法简单方便容易掌握。