旋转壳的数值传递函数方法

Numerical Distributed Transfer Function Method for the Analysis of Revolution Shells

应用数值传递函数方法建立了一种用于分析旋转壳静力、动力响应的截锥壳单元。在本方法中，单元的位移在环向展开为Fourier级数的形式，应用薄壳理论可以得到解耦的微分方程。通过Laplace变换可以将方程转化为频域内的常微分方程，将其表示为状态空间形式后，可以应用数值传递函数方法求解。对复杂的系统可以应用与有限元类似的方法，划分多个单元组合求解。文中给出了几种旋转壳的动力、静力问题的数值算例，并与其它方法进行了比较，表明本文方法具有精度高、计算方便等特点。

Truncated conical element is developed for analysis of revolution shells, using numerical distributed transfer function method (NDTFM). In this method, displacement of shell are expanded in Fourier series in the circumferential direction, and the decoupled partial differential equations are obtained by the thin shell theory. These equations can be transfer to ordinary differential equations through Laplace transform, and cast into state space form. Then they can be solved by NDTFM. Complicate revolution shells are divided into several truncated conical elements, and synthesized with the similar technique in FEM. Numerical results are given for static and dynamic response of revolution shells, and compared with other methods, which show the high precision and easiness in computation of this method.