基于改进传递矩阵法的环肋圆柱壳固有振动分析

摘要

为了简化传统传递矩阵法中状态向量一阶微分方程复杂推导和得到不同边界条件下环肋圆柱壳的振动特性，基于Flügge壳体理论，通过采用改进传递矩阵法改进状态向量的选取，直接快速地从振动方程推导出圆柱壳结构场传递矩阵，并对场传递矩阵使用精细积分求解。根据环肋和壳体连接处变形连续条件导出环肋处点传递矩。最后通过自由、简支、固支三种不同边界条件下环肋圆柱壳固有频率计算结果与有限元计算结果进行对比，验证了改进传递矩阵法进行环肋圆柱壳振动分析有效性和适用性。%In order to simplify the derivation of the state vector’s first order differential equation in the traditional transfer matrix method and obtain the vibration characteristics of ring-stiffened cylindrical shells under different boundary conditions, the improved transfer matrix method is proposed based on Flügge shell theory. This method can be used to improve the selection of the state vectors to get the field transfer matrix which can be solved by a precise integration from the vibration equation directly and quickly. The point transfer matrix can be derived according to the continuous deformation at the connection of the ring and the shell. Finally, comparing the natural frequency calculated by the improved transfer matrix method with the results of FEM under the conditions of free plate, simply supported plate and clamped plate, it is shown that the improved transfer matrix method has effectiveness and applicability.