There has been a common assumption that neglects the in-plane inertia or rotary inertia of a cylindrical shell to yield analytical and numerical solutions of the vibration characteristics. This assumption can largely simplify some derivation processes and result in a unified governing equation, nevertheless, precondition and justification of this assumption have not been examined yet. Presented herein is a critical examination on the in-plane inertia and rotary inertia for breathing vibration of the cylindrical shell. Analytical solutions are presented based on Donnell’s shell theory and the first-order shear deformation theory, respectively, in which simply-supported, clamped and free ends of the cylindrical shell are considered. Finite-element analyses about breathing modes and vibration characteristics are conducted to confirm the validity of present solutions. Furthermore, the mechanisms of some phenomenons are interpreted. It is shown herein that the influences of ignoring the in-plane and rotary inertias on natural frequencies of the cylindrical shell depend on the breathing modes, principally by the number of waves in the circumferential direction of the breathing modes. The in-plane inertia along the axial direction has a very limited effect on natural frequencies compared with those along the radial and circumferential directions. There are large relative differences by using the functions of beam-like modes to calculate the vibration characteristics of the cylindrical shell with clamped or free ends under the cases of lower number waves.

有一个普遍的假设，即忽略圆柱壳的面内惯性或旋转惯性以产生振动特性的解析解和数值解。这个假设可以在很大程度上简化一些推导过程，并导致一个统一的控制方程，但是，这个假设的前提和论证还没有得到检验。这里介绍的是对圆柱壳呼吸振动的平面惯性和旋转惯性的批判性检查。分别基于唐奈尔壳理论和一阶剪切变形理论提出了解析解，其中考虑了圆柱壳的简支、夹紧和自由端。对呼吸模式和振动特性进行了有限元分析，以确认当前解决方案的有效性。此外，解释了一些现象的机制。此处表明，忽略面内惯性和旋转惯性对圆柱壳固有频率的影响取决于呼吸模式，主要取决于呼吸模式圆周方向上的波数。与沿径向和圆周方向的惯性相比，沿轴向的面内惯性对固有频率的影响非常有限。利用类梁模态函数计算具有夹紧端或自由端的圆柱壳在小波数情况下的振动特性存在较大的相对差异。此外，解释了一些现象的机制。此处表明，忽略面内惯性和旋转惯性对圆柱壳固有频率的影响取决于呼吸模式，主要取决于呼吸模式圆周方向上的波数。与沿径向和圆周方向的惯性相比，沿轴向的面内惯性对固有频率的影响非常有限。利用类梁模态函数计算具有夹紧端或自由端的圆柱壳在小波数情况下的振动特性存在较大的相对差异。此外，解释了一些现象的机制。此处表明，忽略面内惯性和旋转惯性对圆柱壳固有频率的影响取决于呼吸模式，主要取决于呼吸模式圆周方向上的波数。与沿径向和圆周方向的惯性相比，沿轴向的面内惯性对固有频率的影响非常有限。利用类梁模态函数计算具有夹紧端或自由端的圆柱壳在小波数情况下的振动特性存在较大的相对差异。此处表明，忽略面内惯性和旋转惯性对圆柱壳固有频率的影响取决于呼吸模式，主要取决于呼吸模式圆周方向上的波数。与沿径向和圆周方向的惯性相比，沿轴向的面内惯性对固有频率的影响非常有限。利用类梁模态函数计算具有夹紧端或自由端的圆柱壳在小波数情况下的振动特性存在较大的相对差异。此处表明，忽略面内惯性和旋转惯性对圆柱壳固有频率的影响取决于呼吸模式，主要取决于呼吸模式圆周方向上的波数。与沿径向和圆周方向的惯性相比，沿轴向的面内惯性对固有频率的影响非常有限。利用类梁模态函数计算具有夹紧端或自由端的圆柱壳在小波数情况下的振动特性存在较大的相对差异。与沿径向和圆周方向的惯性相比，沿轴向的面内惯性对固有频率的影响非常有限。利用类梁模态函数计算具有夹紧端或自由端的圆柱壳在小波数情况下的振动特性存在较大的相对差异。与沿径向和圆周方向的惯性相比，沿轴向的面内惯性对固有频率的影响非常有限。利用类梁模态函数计算具有夹紧端或自由端的圆柱壳在小波数情况下的振动特性存在较大的相对差异。