Interaction of a spherical shockwave and an elastic circular cylindrical shell

Abstract

The paper studies the interaction of a spherical shock wave with an elastic circular cylindrical shell immersed in an infinite acoustic medium. The shell is assumed infinitely long. The wave source is quite close to the shell, causing deformation of just a small portion of the shell, which makes it possible to represent the solution by a double Fourier series. The method allows the exact determination of the hydrodynamic forces acting on the shell and analysis of its stress state. Some characteristic features of the stress state are described for different distances to the wave source. Formulas are proposed for establishing the safety conditions of the shell.Consider an infinitely long elastic circular cylindrical shell immersed in an infinite fluid. A point source of shock waves (SWs) is located at a distance R 0 from the shell axis. A spherical SW is diffracted by the shell, and while deforming, the shell generates radiation waves. Therefore, the stress analysis of the shell must involve the simultaneous solution of the equations of motion of the fluid and shell coupled by boundary conditions at the shell surface. Though various approaches were considered in [1-3, 5, 6, 11, 13, 14, etc.] to solve this problem, no exact and complete results have been obtained yet.The findings in nonstationary elasticity and hydroelasticity are discussed in [14,16,18]. We will solve the problem on the basis of linear theory. Let the shell radius r 0 , the density of the fluid ρ 0 , and the sonic velocity in the fluid c 0 be units of measurement. Then all other quantities are measured in terms of fractions of the power complex r c 0 0 0 α β γ ρ that has the same dimension as a given quantity. With such an approach, all dependences will be dimensionless, which is convenient for theoretical analysis. We will describe the deformation of the shell using the linear theory of shells based on the Kirchhoff-Love hypothesis. Let the displacements of the shell's median surface, u, ν, and w, be the basic variables. Then, written in a cylindrical coordinate system x, r, θ whose axis coincides with the shell axis, the equations of motion of the shell take the following form [11]:

Interaction of differently shaped bodies in a potential flow of perfect compressible fluid: Axisymmetric internal problem

“…The validity of these relations was proved in [11,12]. Issues associated with the interaction of differently shaped bodies in a fluid were addressed, for example, in [13,16,18,20,22].The present paper studies an axisymmetric system consisting of an infinitely long, thin-walled, elastic, cylindrical shell that contains a potential flow of perfect compressible fluid and a vibrating spherical inclusion. Our analysis of the phenomena occurring in this system will be mainly based on the monographs and publications [1, 3, 5, 7, 8, 13, 20, etc.…”

“…The validity of these relations was proved in [11,12]. Issues associated with the interaction of differently shaped bodies in a fluid were addressed, for example, in [13,16,18,20,22].…”

Generation of nonstationary waves by a thick-walled piezoceramic cylinder excited by electric signals

“…In addition to periodic publications (such as [12,13]), these results are partially generalized in the monograph [1] and review [14]. Of the recent studies on nonstationary continuum mechanics, it is worthwhile to mention the papers [9,16,17]. There are hydroelectroelastic systems where the piezoelectric transducer and the generator are spaced far apart and connected by a long cable.…”

On the deformation of a ribbed cylindrical shell with initial deflection under dynamic loading

“…The equations of motion (1)-(5), the initial conditions (6), and the boundary conditions (7), (8) constitute the statement of an axisymmetric nonlinear initial-boundary-value problem of elasticity for a rib-reinforced cylindrical shell with an initial deflection under dynamic loading.…”