Propagation of Waves in a Fluid in a Thin Elastic Cylindrical Shell

Abstract

The oscillatory process of a viscoelastic shell of a cylindrical tipe filled with a liquid is considered. Unlike other works, this paper focuses on the viscoelastic properties of a cylindrical shell and a liquid. Differential equations for joint vibrations of a shell and liquid are obtained by the equations of a thin shell that satisfies the Kirchhoff–Love hypotheses, and the equations of motion of a viscous liquid obey the Navier–Stokes equation. After simple transformations, the integro-differential equations are reduced to ordinary differential equations and solved using Godunov's orthogonal run method combined with Muller's method. Based on the developed algorithm, natural frequencies and corresponding vibration modes were obtained. For steady-state oscillations, all eigenvalues and eigenmodes turned out to be complex. For the first time, it was found that the damping coefficient branches out after certain values of wave numbers. It was found that the motion in a cylindrical shell is localized on the surface of the shell. At slow localization, starting from a certain wave number, the natural oscillations become aperiodic.