中文摘要：

论文从偏心圆柱壳截面的几何特性出发,将偏心圆柱壳问题转化为一个周向变厚度圆柱壳问题,随后利用其状态向量之间的传递矩阵将壳体的振动控制方程转化为矩阵微分方程形式,通过Magnus级数法求解传递矩阵得到频率方程.采用Lagrange插值法得到偏心圆柱壳体自由振动状态下的固有频率,并且与圆柱壳的固有频率进行了比较.对影响结构固有频率的主要参数进行了分析,得到了这些参数和固有频率之间的关系.论文不仅提出了一种有效求解偏心圆柱壳固有频率的新方法,同时亦可为检测偏心圆柱壳的偏心距提供一种新的思路和方法.

英文摘要：

Taking the geometry characteristic of the cross section of eccentric cylindrical shell into ac- count, we convert the eccentric problem into a circumferentially varying thickness problem in this contribu tion. The vibration equations are expressed as a matrix differential equation by using the transfer matrix of the state vector of the shell. The natural frequencies of eccentric cylindrical shell are solved and compared with those of cylindrical shell. Then the main parameters which influence the natural frequency are ana- lyzed carefully,and the relationships between these parameters and the natural frequency are obtained. This paper not only propose an effective new method to obtain the natural frequencies of an eccentric cylindrical shell,but also provide a new idea and method for detecting the eccentricity of eccentric cylindrical shell.