Frequency analysis of longitudinal-radial vibrations of a cylindrical shell

Abstract

The article solves the problem of harmonic longitudinal-radial vibrations of a circular cylindrical shell with freely supported ends. To solve the problem, we used the refined equations of oscillation of such a shell, derived earlier from the exact three-dimensional formulation of the problem and its solution in transformations. An extensive review of works devoted to the study of harmonic and nonstationary processes in elastic bodies on the basis of classical (Kirchhoff-Love, Flyugge) and refined Timoshenko type (Hermann-Mirsky, Filippov-Khudoinazarov) theories is given. Four frequency equations are obtained for the main parts of the longitudinal and radial displacements of the cylindrical shell. These frequency equations admit, as special cases, frequency equations and a thin-walled shell. Based on the solution of the obtained frequency equations, the frequencies of natural vibrations of the shell, including the thin-walled one, are determined. A comparative frequency analysis of longitudinal vibrations of a circular cylindrical elastic shell is carried out on the basis of the classical Kirchhoff-Love theory, refined theories of Hermann-Mirsky and Filippov-Khudoinazarov. On the basis of the results obtained, conclusions were drawn regarding the applicability of the studied oscillation equations, depending on the waveform and shell length. In particular, it was found that all the considered equations are unsuitable for describing wave processes in short shells, the lengths of which are commensurate with the transverse dimensions of the shells.