Natural vibrations of a cylindrical shell with the end cap. I. Asymptotic analysis

Low natural frequencies and vibration modes of the structure, consisting of a closed circular cylindrical shell with the end cap, having the shape of a shallow spherical segment, are examined in the paper using numerical and asymptotic methods. There are three types natural vibrations of the structure. Natural frequencies and vibration modes of the first type are close to the frequencies and vibration modes of a shallow spherical shell, modes and frequencies of the second type - to frequencies and modes of a cylindrical shell, and those of the third type - to frequencies and modes of vibration of a cantilever beam with a load at the end. In the first part of the research approximate values for the frequencies of vibrations of the first type are found by asymptotic methods. Asymptotic and numerical results obtained with finite element method are in good agreement.