Abstract

The low eigenfrequencies and vibration modes of a structure consisting of a closed circular cylindrical shell with an end cap in the form of a shallow spherical segment attached to it are investigated using numerical and asymptotic methods. Three types of natural vibrations of the structure are distinguished. The eigenfrequencies and vibration modes of the first type are close to the frequencies and vibration modes of a shallow spherical shell, the modes and frequencies of the second type, to the frequencies and modes of a cylindrical shell, and the third type, to the frequencies and vibration modes of a cantilever beam with a load at the end. In this article, approximate values for the frequencies of vibrations of the first type are found using asymptotic methods. Asymptotic and numerical results obtained using the finite-element method are in good agreement.

中文翻译：

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带端盖的圆柱壳的自然振动。一、渐近分析

摘要

使用数值和渐近方法研究了结构的低特征频率和振动模式，该结构由闭合圆柱壳组成，端盖以浅球段形式附在其上。区分了结构的三种类型的自然振动。第一类特征频率和振动模态接近浅球壳的频率和振动模态，第二类特征频率和振动模态接近圆柱壳的频率和模态，第三类特征频率和振动模态接近圆柱壳的频率和模态。端部有载荷的悬臂梁的振动模式。在本文中，使用渐近方法找到第一类振动频率的近似值。