The Effect of an Internal Compressible Fluid Column on the Breathing Vibrations of a Thin Pressurized Cylindrical Shell

Abstract

Abstract : Consideration is given to the determination of the inertia and compressibility effects of an internal liquid or gas column on the breathing vibrations of thin, pressurized, circular cylindrical shells. Breathing vibrations are those vibrations of the points of the cylinder walls which correspond to radial deformations proportional to cos ntheta or sin ntheta, where the integer n has at least the value 2. The report contains a discussion of the equations for transverse vibrations of pressurized, shallow cylindrical shells and gives a formula for the frequencies of free vibrations. This formula includes a term for an apparent inertia of the shell walls due to the presence of an internal fluid. The equations for the small motion of an inviscid, compressible, circular cylindrical, fluid column are discussed. The surface of the fluid column is assumed to be acted upon by a pressure which is a function of the axial and circumferential space coordinates and time. The natural frequencies of the elastic cylinder-internal fluid system are also discussed. (Author)