Application of the Concepts of Short and Long Solutions for the Evaluation of the Natural Frequencies of Vibration of Cylindrical Shells

Abstract

On the basis of the Vlasov semimomentless theory, we present the approximations of the natural frequencies of vibration of cylindrical shells in the explicit form with regard for the deformation component. It is shown that the influence of this component is insignificant. We determine the limits of applicability of the approximating formulas and compare them with the data from the available literature. It is shown that the experimental data are satisfactorily described by the obtained dependences. Within the limits of applicability of the deduced relations, they better describe the low-frequency range of the spectrum of vibrations of cylindrical shells. We also present equations for the frequencies and modes of vibration for various possible conditions of support of the shells and propose simple engineering relations for the analysis of the frequency spectra of vibrations.