圆锥壳自由振动传递函数解

本文在线性弹性理论基础上，给出了一种求解圆锥薄壳自由振动的渐进传递函数解法，壳体的三个位移分量，外力和边界条件首先沿环向展开的Ｆｏｕｒｉｅｒ级数，然后关于时间变量进行Ｌａｐｌａｃｅ变换，这样就将壳体的控制方程化为一系列含复参数ｓ的变系数常微分方程组，通过定义状态变量。得到了壳体动力学问题的状态空间控制微分方程，引入一小参数，并利用摄动技术就可以得到微分方程的渐进传递函数解，将各于锥段的解进行综合，

TRANSFER FUNCTION SOLUTION ON FREE VIBRATION OF CONICAL SHELLS

Based on linear elastic theory, an asymptotic distributed transfer function method is presented in this paper to serve as the analysis of free vibration of conical shells. In this method, the three displacements of the shell, the external excitations and the boundary conditions are firstly expanded into Fourier series along the circumferetial direction; then, applying the Laplace transform with respect to time variable, the governing equations of the shell may be simplified into a system of ordinary differential equations containing a complex parameter s. Defining a state-space vector, the decoupled equation may be cast into the governing differential equation,of the statespace form. Introducing a small parameter, the perturbation technique and the distributed transfer function method may be used to solve the e-quations. Combined shells composed of several conical segments are then synthesized using the transfer functions of the sub-segments. Finally, numerical calculations are presented and their results are compared with those by the FEM.