Dynamics of the Moving Ring Load Acting in the System “Hollow Cylinder + Surrounding Medium” with Inhomogeneous Initial Stresses

This paper studies the influence of the inhomogeneous initial stress state in the system consisting of a hollow cylinder and surrounding elastic medium on the dynamics of the moving ring load acting in the interior of the cylinder. It is assumed that in the initial state the system is compressed by uniformly distributed normal forces acting at infinity in the radial inward direction and as a result of this compression the inhomogeneous initial stresses appear in the system. After appearance of the initial stresses, the interior of the hollow cylinder is loaded by the moving ring load and so it is required to study the influence of the indicated inhomogeneous initial stresses on the dynamics of this moving load. This influence is studied with utilizing the so-called three-dimensional linearized theory of elastic waves in elastic bodies with initial stresses. For solution of the corresponding mathematical problems, the discrete-analytical solution method is employed and the approximate analytical solution of these equations is achieved. Numerical results obtained within this method and related to the influence of the inhomogeneous initial stresses on the critical velocity of the moving load and on the response of the interface stresses to this load are presented and discussed. In particular, it is established that the initial inhomogeneous initial stresses appearing as a result of the action of the aforementioned compressional forces cause to increase the values of the critical velocity of the moving load.     

Dynamics of the Moving Load Acting on the Hydro-elastic System Consisting of the Elastic Plate,Compressible Viscous Fluid and RigidWall

The subject of the paper is the study of the dynamics of the moving load acting on the hydro-elastic system consisting of the elastic plate, compressible viscous fluid and rigid wall. Under this study the motion of the plate is described by linear elastodynamics, and the motion of the compressible viscous fluid is described by the linearized Navier-Stokes equations. Numerical results are obtained for the case where the material of the plate is steel, but the fluid material is Glycerin. According to these results, corresponding conclusions related to the influence of the problem parameters, such as fluid viscosity, plate thickness, fluid depth, fluid compressibility and initial stresses on the inter-phase normal stress and normal and tangent velocities of the fluid caused by the load which moves with constant velocity, are made. In particular, it is established that the influence of the fluid viscosity of the aforementioned quantities becomes more considerable under lower velocities of the moving load. Moreover, it is established that there exists a critical velocity of the moving load under which a resonance type event takes place.     

The Influence of Third Order Elastic Constants on Axisymmetric Wave Propagation Velocity in the Two-Layered Pre-Stressed Hollow Cylinder

By the use of the Murnaghan potential the influence of third order elastic constants on axisymmetric longitudinal wave propagation velocity in a pre-stressed two-layered circular hollow cylinder is investigated. This investigation is carried out within the scope of the piecewise homogeneous body model by utilizing the first version of the small initial deformation theory of the Three-dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies. Numerical results are obtained and analyzed for the cases where the material of the outer hollow cylinder material is aluminum, but the material of the inner cylinder is steel (Case 1) and tungsten (Case 2). These results are obtained not only for the case where the initial uniaxial stress is a stretching one, but also for the case where the initial uniaxial stress is a compressing one. According to these results, it is established that the third order elastic constants of the selected materials influence not only quantitatively, but also qualitatively the axisymmetric wave propagation velocity in the initially stressed two-layered hollow cylinder. It is also established that the mentioned influence in Case 2 is more significant than that in Case 1.     

The Interface Stress Field in the Elastic System Consisting of the Hollow Cylinder and Surrounding Elastic Medium Under 3D Non-axisymmetric Forced Vibration

The paper develops and employs analytical-numerical solution method for the study of the time-harmonic dynamic stress field in the system consisting of the hollow cylinder and surrounding elastic medium under the non-axisymmetric forced vibration of this system. It is assumed that in the interior of the hollow cylinder the point-located with respect to the cylinder axis, non-axisymmetric with respect to the circumferential direction and uniformly distributed time-harmonic forces act. Corresponding boundary value problem is solved by employing of the exponential Fourier transformation with respect to the axial coordinate and by employing of the Fourier series expansion of these transformations. Numerical results on the frequency response of the interface normal stresses are presented and discussed.