ANALYSIS OF THE FREQUENCY CHARACTERISTICS OF LONGITUDINAL AND RADIAL VIBRATIONS IN A CIRCULAR CYLINDRICAL SHELL

Abstract

The paper addresses the problem of harmonic longitudinal-radial vibrations in a circular cylindrical shell with free ends. The solution is based on refined oscillation equations for the shell, which were derived earlier from an exact three-dimensional formulation and its solution through transformations. A thorough review of studies on harmonic and nonstationary processes in elastic bodies is presented, focusing on both classical theories (such as Kirchhoff-Love and Flyugge) and refined Timoshenko-type theories (like Hermann-Mirsky and Filippov-Khudoinazarov). Four frequency equations are derived for the main components of the longitudinal and radial displacements of the shell, with special cases corresponding to thin-walled shells. Using the solutions to these frequency equations, the natural vibration frequencies of the shell, including for thin-walled versions, are determined. A comparative frequency analysis of the longitudinal vibrations of a circular cylindrical elastic shell is conducted based on the classical Kirchhoff-Love theory and the refined Hermann-Mirsky and Filippov-Khudoinazarov theories. The results lead to conclusions about the applicability of the studied oscillation equations, depending on the shell's waveform and length. Specifically, it is concluded that all the equations are unsuitable for describing wave processes in short shells, where the lengths are comparable to their transverse dimensions.