计算旋转薄壳自由振动的传递矩阵法

 本文介绍了计算旋转薄壳自由振动的一种传递矩阵法。以计算截锥壳振动的传递矩阵公式为基础,通过适当的变换,进一步对一般旋转薄壳结构的固有频率及振型进行计算。

A TMM FOR THE FREE VIBRATION OF SHELLS OF REVOLUTION

A transfer matrix method is presented for the free vibration of shells of revolution. This method is based on the formulas of transfer matrix of truncated conical shells. From the theory of truncated conical shells, a set of differential equations about the state parameters are derived. By expressing the state parameters as Taylor series, the formulas of the transfer matrix can be obtained. A shell of revolution with curved meridian can be modeled by a series of truncated conical shells. By using the displacement continuity condition at the joint of the two adjacent truncated conical shells, formulas for calculating the state parameters at the two side of the joint are derived. For a branched structure, a sub-structure method is proposed. By using the displacement continuity and equilibrium conditions at the joint, the state paremeters among the substructures can be established so that the frequency equation can be obtained. This method is economic and easy to program. The examples given by the paper show that the accuracy is satisfactory.