Analysis of radial vibrations of poroelastic circular cylindrical shells immersed in an acoustic medium

Abstract

Waves propagating in radial direction of a poroelastic circular cylinder are termed as radial vibrations. Radial vibrations of poroelastic circular cylindrical shell of infinite extent immersed in an inviscid elastic fluid are examined employing Biot’s theory. Biot’s model consists of an elastic matrix permeated by a network of interconnected spaces saturated with liquid. Frequency equation is obtained each for a permeable and an impermeable surface. Poroelastic cylindrical shell is assumed to be homogeneous and isotropic. Particular cases are considered when the outer and inner fluid vanishes. (1). When the outer fluid is vanished, the considered problem reduces to the problem of radial vibrations of fluid-filled poroelastic circular cylindrical shell. (2). When the inner fluid vanishes, the considered problem reduces to the problem of radial vibrations of poroelastic circular cylindrical shell surrounded by fluid. (3). When both outer and inner fluids vanish, the considered problem is reduced to the problem of radial vibrations of poroelastic circular cylindrical shell in vacuum. For the case, when the inner radius of the poroelastic cylindrical shell approaches to zero, the considered problem is reduced to radial vibrations of poroelastic solid cylinder immersed in fluid. Frequency equation each for a permeable and an impermeable surface is obtained for the said cases. Effect of wall-thickness of the poroelastic circular cylindrical shell in presence of fluid is studied for different cases. Results of previous investigations are shown as a particular case of the present study. By ignoring the liquid effects, the results of purely elastic solid are obtained as a special case.

Keywords: Radial vibrations, cylindrical shell, frequency, elastic fluid, permeable surface, impermeable surface.