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Using numerical and asymptotic methods, the lowest natural frequencies and vibration modes of a structure consisting of a closed circular cylindrical shell with an end cap attached to it, having the shape of a shallow spherical segment, are studied in the paper. Three types of natural vibrations of the structure are described. Eigenfrequencies and modes of vibrations of the first type, close to the frequencies and modes of vibrations of a shallow spherical shell, were studied in previous works. In this paper, we study the forms and frequencies of the second type of vibrations (cylindrical shell) and the third type (cantilever beam with the load). An optimization problem is solved to determine the values of the structure parameters, the relative thickness of its elements and the curvature of the end cap, at which the minimum value of the natural frequency is maximum. A comparison of the asymptotic and numerical results reveals their good agreement.

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.

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