Analysis of free oscillations of thin-walled cylindrical shells containing a compressible liquid

Abstract

Free oscillations of a thin-walled cylindrical cell containing a compressible liquid were investigated. At some values of the parameters of the system, its eigenfrequencies were determined, and the influence of the geomet- ric and physical parameters of the cylindrical shell-liquid system on the free oscillation of cylinder was in- vestigated. Introduction. Shells as elements of machines and constructions are widely used in aircraft industry, shipbuild- ing, and so on. Therefore, in recent years the problems associated with the dynamic behavior of thin-walled structures that are in contact with environment under operating conditions attract considerable interest of researchers. The frequencies and forms of free oscillations of spherical and cylindrical shells coming in contact with elas- tic and liquid media were investigated in (1, 2). Approximate simple formulas were obtained by asymptotic methods for calculating the frequency and determining the form of oscillations of the system considered; this limits the use of the results obtained, because in a number of cases the possibility of carrying out a qualitative analysis of investigated processes is eliminated. Statement of the Problem. In this work we consider free asymmetric oscillations of an infinite thin-walled cylindrical shell containing a compressible liquid. Since finding the eigenfrequencies of the cylindrical shell-liquid sys- tem is associated with the solution of transcendental equations, the frequency of oscillations of a shell without a liquid is expressed in terms of the frequency of oscillations of the system in an explicit form; this allows one to investigate the spectra of the system's frequencies both analytically and graphically. The equations of radials oscillations of cylindrical shells have the form (3) ∂ 2 u