Resonant phenomena in a cylindrical shell containing a spherical inclusion and immersed in an elastic medium

A method is proposed to investigate the behavior of an axisymmetric system consisting of an infinite thin elastic cylindrical shell immersed in an infinite elastic medium, filled with a perfect compressible fluid, and containing an oscillating spherical inclusion. The system is subjected to periodic excitation. The task is to detect so-called resonant phenomena, to establish conditions that cause them, and to examine the possibilities of using the characteristic parameters of such a hydroelastic system to influence these conditions. The method allows transforming the general solutions of mathematical physics equations from one coordinate system to another to obtain exact analytic solutions (in the form of Fourier series) to interaction problems for systems of rigid and elastic bodies __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 82–97, July 2006.     

Interaction of an infinite thin elastic cylindrical shell and a pulsating spherical inclusion in potential flow of ideal compressible liquid: internal axisymmetric problem

The paper proposes a method to analyze the behavior of a mechanical system consisting of an infinite thin cylindrical shell filled with a flowing compressible liquid and containing a pulsating spherical inclusion. This coupled problem is solved using linear potential flow theory and the theory of thin elastic shells based on the Kirchhoff–Love hypotheses. Use is made of the possibility to represent the general solutions of equations of mathematical physics in different coordinate systems. This makes it possible to satisfy the boundary conditions on both spherical and cylindrical surfaces and to obtain a solution in the form of a Fourier series. Some numerical results are given     

Interaction of a spherical shockwave and an elastic circular cylindrical shell

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.Translated from Prikladnaya Mekhanika, Vol. 40, No. 9, pp. 94–104, September 2004.     

Creep and long-time fracture of a cylindrical shell under external pressure in the presence of an aggressive medium

We consider the process of deformation and fracture of an oval ring modeling the behavior of a long cylindrical shell subjected to distributed external pressure. The shell deformation is studied in both the presence and absence of an aggressive medium. The hypothesis of nonlinear viscosity with a singular component is taken for the constitutive relation used to estimate the metal characteristics. This relation allows for the difference between the tensile and compression strength of the material. The singularity permits taking into account not only the nonlinear viscosity but also instantaneous fracture characteristics. We show that an aggressive medium can substantially decrease the shell operation life.     

Dynamics of an elastic cylindrical shell with a gas–liquid medium subject to two-frequency vibrational excitation

The paper presents experimental results on nonlinear dynamic processes such as the deformation of the elastic wall of a cylindrical shell filled with a fluid and the formation and clustering of gas bubbles, which interact under two-frequency excitation Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 112–122, November 2008.     

Shock loading of a cylindrical shell filled with viscous compressible liquid

The effect of a uniformly distributed shock load on a thin-walled cylindrical shell filled with viscous compressible liquid is considered. An analytical method of inverse Laplace transformation of the general solution of the linearized Navier-Stokes equations is proposed. A numerical example is presented. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 11, pp. 55–61, November, 1999.     

Nonlinear buckling of a spherical shell embedded in an elastic medium with imperfect interface

This work analyzes nonlinear buckling of a single spherical shell imperfectly bonded to an infinite elastic matrix under a compressive remote load. The inclusion is modeled using a nonlinear shell formulation and the matrix is treated as a linear elastic body. Imperfect bonding conditions are realized through a linear spring interface model. A variational method is used to derive the governing differential equations, which are cast into a tractable set of nonlinear algebraic equations using the Galerkin method. An incremental iterative technique based on the modified Newton–Raphson method is employed to find the critical load of the system. The accuracy and convergence properties of the proposed method are validated through finite element analysis. The study is relevant to the analysis of compressive failure of syntactic foams used in marine and aerospace applications. Results are specialized to glass particle-vinyl ester matrix syntactic foams to test the hypothesis as to whether microballoons’ buckling is a dominant failure mechanism in such composites under compression. Parametric studies are conducted to understand the effect of interfacial properties and inclusion wall thickness on the overall mechanical behavior of the composite. Comparisons between analytical findings and experimental results on compressive response of syntactic foams and isolated microballoons indicate that inclusion buckling is unlikely a determinant of compressive failure in vinyl ester-glass systems. In particular, the matrix is found to exert a beneficial stabilizing effect on the inclusions, which fail under brittle fracture before the onset of buckling.     

Dynamic interaction of an oscillating sphere and an elastic cylindrical shell filled with a fluid and immersed in an elastic medium

The paper studies the interaction of a harmonically oscillating spherical body and a thin elastic cylindrical shell filled with a perfect compressible fluid and immersed in an infinite elastic medium. The geometrical center of the sphere is located on the cylinder axis. The acoustic approximation, the theory of thin elastic shells based on the Kirchhoff—Love hypotheses, and the Lamé equations are used to model the motion of the fluid, shell, and medium, respectively. The solution method is based on the possibility of representing partial solutions of the Helmholtz equations written in cylindrical coordinates in terms of partial solutions written in spherical coordinates, and vice versa. Satisfying the boundary conditions at the shell—medium and shell—fluid interfaces and at the spherical surface produces an infinite system of algebraic equations with coefficients in the form of improper integrals of cylindrical functions. This system is solved by the reduction method. The behavior of the hydroelastic system is analyzed against the frequency of forced oscillations.Translated from Prikladnaya Mekhanika, Vol. 40, No. 9, pp. 75–86, September 2004.     

Interaction of a pulsating spherical body and an infinite cylindrical shell in an incompressible liquid

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 11, pp. 17–24, November, 1995.     

Unsteady processes in a cylindrical shell with an elastic medium under the influence of a shock load

International Applied Mechanics -     

Penetration of an elastic circular cylindrical shell into an incompressible liquid

The plane unsteady problem of impact of a thin elastic cylindrical shell on the surface of an ideal incompressible liquid is considered. The initial stage of interaction between the body and the liquid when the stresses in the shell attain peak values is studied. The problem is treated in a linearized formulation and is solved numerically by the normal modes method within the framework of the Wagner approach. The numerical results agree with experimental data for various types of circular cylindrical shells made from mild steel. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 186–197, November–December, 1999.