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The method of multiple scales was used to solve the Duffing equation, the solutions were used to analyze qualitatively the effect of boundary conditions, ratio of damp, external excitation, and ratio of inner radius to outer radius on the second-harmonic resonance of an annular thin plate.

用多尺度方法求此振动控制方程的3次超谐共振解和1/3亚谐共振解，并且定性地探讨边界条件、内外半径比、激振力和阻尼对环形薄圆板在这两种次谐共振下的动态响应。

According to the result of literature search, the theoretical researches of end face harmonic gear drive of oscillating teeth have not been founded.

根据文献检索和申请专利时查新的结果，目前国内外还没有进行过这种新型传动装置的研究。

Furthermore, the posterior dominating researches on end face harmonic gear drive of oscillating teeth are discussed.

此外，对进一步研究活齿端面谐波齿轮啮合副的主要课题进行了讨论和展望。

The reports of the end face harmonic gear drive of oscillating teeth are little by investigating the literature.

根据文献检索和申请专利时查新的结果，目前国内外还没有进行过这种新型传动装置的研究。

1The structure and the transmission theory of end face harmonic gear drive of oscillating teeth are introduced, and the structure models which could be used are also designed in this paper.

本文主要进行了如下一些基础性的理论研究工作：（1）提出了活齿端面谐波齿轮传动装置的结构和传动原理；设计了各种可能用到的活齿端面谐波齿轮传动装置的结构型式。

The end face harmonic gear drive of oscillating teeth was a new type of the spatial oscillating teeth transmission.

活齿端面谐波齿轮是一种新型的传动机构，可以在保留现有谐波齿轮传动所有优点的基础上，大幅度地提高所传递的功率。

It is helpful for the basically theoretical researches and the design of end face harmonic gear drive of oscillating teeth. And it has a definite application expectation and economic value.

关于活齿端面谐波齿轮啮合副的齿面方程及其修形的理论研究，奠定了活齿端面谐波齿轮减速器设计的理论基础，为这种新型传动装置的推广应用铺平了道路。

The end face harmonic gear drive of oscillating teeth is a new type of transmission drive;it can be applied in the reducers where large speed ratio and high power is needed.

活齿端面谐波齿轮传动是一种新型的传动方式，可以应用于大传动比、大功率的减速器中。

Besides, the asymmetrical tooth of the end face harmonic gear drive of oscillating teeth interrelated subjects which will be researched further of are discussed in this paper, it provides good basis for the manufacture and popularization of the new kind of the oscillating teeth drive.

对于非对称齿形所得出的结果，为活齿端面谐波齿轮的活齿部分的应用提供了理论依据，为这种新型活齿传动装置的研制和推广打下了良好的基础。

The new kind of transmission theory introduced in this article has been applied for patent (the application number is 200410012992.6) Some fundamental theory of the end face harmonic gear drive of oscillating teeth is investigated in this paper, which can benefit the design of the product and the popularization of the patent.

这种新型的传动装置属于空间的活齿传动机构，可以从根本上克服传统的径向谐波齿轮传动中柔轮的变形与其承载能力之间的矛盾，并可增加同时啮合的齿数，加大齿轮的模数，从而可以在保留径向谐波齿轮传动所有优点的基础上，使其所传递的功率增加数十倍。

This matter overthrew all basises I learned from Sunday school .

这件事把我从周日学校学到的所有道理都颠覆了。

It's one of the cruel ironies of aging: if you want to remember your favorite restaurants, the less you should eat at them.

这是一个老化的残酷讽刺：如果你想记住你最喜欢的餐馆，你应该更少吃到它们。