Abstract

In this paper, the lowest eigenfrequencies and vibration modes of a structure consisting of a closed circular cylindrical shell with an end cap attached to it in the shape of a shallow spherical segment are analyzed using numerical and analytical methods. Three types of free vibrations of the structure are described. Eigenfrequencies and modes of the first-type vibrations have been studied in previous papers, being close to the frequencies and vibration modes of a shallow spherical shell. In this study, modes and frequencies of second-type- (a cylindrical shell) and third-type vibrations (a cantilever beam with a load) are analyzed. An optimization problem is solved in order to determine the values of the structure parameters and the relative thickness of elements as well as the curvature of the end cap at which the minimum value of the eigenfrequency is maximal. A comparison between the asymptotic results and the numerical ones demonstrates their good agreement.

中文翻译：

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带帽圆柱壳的自由振动。二。频谱分析

摘要

在本文中，使用数值和解析方法分析了一个结构的最低特征频率和振动模式，该结构由一个封闭的圆柱壳组成，其上附有一个浅球形端盖。描述了结构的三种类型的自由振动。前人研究了第一型振动的特征频率和模态，接近于浅球壳的频率和振动模态。在这项研究中，分析了第二类振动（圆柱壳）和第三类振动（带负载的悬臂梁）的模式和频率。求解优化问题以确定结构参数的值和元件的相对厚度以及特征频率的最小值最大时端盖的曲率。渐近结果与数值结果之间的比较表明它们具有良好的一致性。