Buckling of a clamped supported cylindrical shell

The paper considers problem of buckling of a thin elastic cylindrical shell, supported by rings of various stiffness. The approximate solution for clamping edge was obtained with analytical Rayleigh-Ritz method. The parameters of the optimal distribution of the mass of the structure between the shell and the stiffeners are found in order to maximize the critical pressure. Frames with zero eccentricity are considered. The obtained analytical solutions are compared with the solution by the finite element method.

LONGITUDINAL-RADIAL VIBRATIONS OF THE ELASTIC CYLINDRICAL SHELL FILLED WITH A VISCOUS COMPRESSIBLE FLUID

In this paper, the longitudinal-radial vibrations of the elastic cylindrical shell filled with a viscous compressible fluid are studied using the mathematical model proposed. The general equations for the longitudinal-radial vibrations of the shell made of the homogeneous and isotropic material are derived. These equations can be used to obtain refined equations of vibrations. The proposed algorithm allows one to uniquely determine the stress-strain state of points in any section of the considered hydroelastic system using the field of the required functions in coordinates and time. The benchmark problem of harmonic oscillations in a cylindrical shell with a viscous fluid is solved. The dependences of the frequency on the wave number are obtained for various shell- fluid interaction cases.

Scattering acoustic from one-layered cylindrical shell: Estimation of the radius ratio using reduced cutoff frequencies of circumferential waves

The obtained results from previous studies done in the acoustic scattering of a plane wave by an elastic cylindrical shell, show that the acoustic resonances of a cylindrical shell are related to its physical and geometrical properties. In order to estimate the radius ratio of an airfield immersed cylindrical shell, using reduced cutoff frequencies of circumferential waves that propagate around it. In this work, an approach based on the artificial neural networks was proposed. This approach uses the reduced cutoff frequencies of circumferential waves, extracted using modal isolation plan representation us the analyzing data, in the object to obtain the value of the radius ratio corresponding to the studied cylindrical shell. The proposed approach allows us to estimate accurately the values of the radius ratio of a copper cylindrical shell, and can help us to resolve other problems related to scattering acoustic. Furthermore, it can be used to estimate various parameters of a cylindrical shell starting from the characteristics of which it is disposed. The proposed approach used in this study does not present any approximation as in the case of the natural mode method which assimilate the cylindrical shell to the plate with the same thickness.

A STUDY OF THE IMPACT OF THE PNEUMATIC LOADING RATE ON DYNAMIC PARAMETERS FOR A LARGE-SIZED CYLINDRICAL SHELL

The solid mechanics problem on the packaging and subsequent pneumatic deployment of large-sized shells is relevant due to the need to operate such structures in hard-to-reach places. In particular, such a place is outer space. The paper considers the elastic cylindrical shell deployment from a packed state by internal pressure in a finite time interval. The packaged shell consists of two rectangular plates joined by ideal (with no bending resistance) joint-hinges arranged at the edges. Both static and dynamic problems are considered. Solutions are obtained on the basis of a geometrically nonlinear model of an elastic body using the ANSYS engineering package. It is shown that the pneumatic loading of an elastic structure is accompanied by its oscillations with increasing frequency and the amplitude decreasing in time. The period of shell oscillations is found to be dependent on the operating loading pressure and independent of the pressure supply rate, and it almost equals the period of oscillations of the statically loaded shell under the same pressure. The wide range variation in the natural oscillation frequencies of the structure during pneumatic deployment, which is revealed in the study, is of great importance since it makes possible to predict resonant modes accompanying the process. The results of the study will be used in problems of mechanics related to the pneumatic deployment of shell structures (for example, telescope reflectors, antennas, etc.) in space.

Model of the dynamics of a shallow tunnel under the action of a traffic load

A mathematical model has been developed for the effect of an arbitrary transport load on a shallow tunnel, supported by a multilayer elastic cylindrical shell located in an elastic half-space. The displacement of the layers of the shell and the elastic half-space is described by the Lame equations in a moving coordinate system. An analytical solution is obtained for the problem of determining the components of the stress-strain state of a rock mass and a shell at arbitrary loading speeds in the subsonic case, when the transport load moves at a speed lower than the propagation velocities of longitudinal and transverse waves in the rock and shell. The results of computer experiments are presented, which illustrate the stress-strain state of pipelines and the earth's surface under moving traffic loads.

About a new approach to calculating spiral clamps

The bearing capacity of spiral clamps, which are mounted on wires (cables) for their tension, connection, repair, etc., is studied. The design of spiral clamps is formed from stretched spirals that are wound onto conductors with an interference fit, which makes it possible to obtain tensile connections practically inseparable. The general problem of the interaction of spiral clamps and overhead line conductor layers is formulated. Different asymptotic solutions are given for initial and boundary value problems, and the design parameters of spiral clamps are determined to provide their carrying capacity. A wire layer is represented by the energy approach as an equivalent anisotropic elastic cylindrical shell, and wire construction as a whole is considered as a system of cylindrical shells inserted each other and interacting by forces of pressure and friction. The equivalence of the elastic properties of the shell to the properties of the wire layer is established using energy averaging. The constitutive relations obtained using the Castigliano theorem relate the generalized displacements and the corresponding forces. The matrix in these ratios is a stiffness matrix or flexibility matrix of a spiral wire structure. Such approach allows variety of interaction problems for spiral clamps with conductor layers to be solved, and the force transfer mechanism to be investigated from common positions. Static equations are written from the equilibrium of the elementary shell ring. It is considered that the length of the clamp is so great that the mutual influence of its ends can be neglected; the clamp is modeled as semi-infinite shell. This model allows the different initial and boundary value problems to be formulated, depending on the boundary conditions and clamp mounting methods on a conductor.

Elastic guide rail oscillation due to moving concentrated load

This article illustrates the solution of a differential equation describing oscillations of an elastic tensioned guide rail, which consist of string bundle enclosed in an elastic cylindrical shell, while concentrated load, simulated by a material point, moves along it. The oscillatory system is considered in such way that the guide rail supports freely. The existing external and internal forces of resistance to movement of the guide rail are also taken into account. Initial and boundary conditions are zero. In article «A string bend under a moving load», published in the journal «Vestnik BGU. Seriya 1, Fizika. Matematika. Informatika» (2004, No. 1), the deflection of a flexible guide rail under load was obtained by solving an equation with deviating argument. In this article, an algorithm is constructed for finding deflection of an elastic tensioned guide rail in the form of a cubic splines. All the results of calculations are presented in a dimensionless form.

Elastic Response of Acoustic Coating on Fluid-Loaded Rib-Stiffened Cylindrical Shells

Reinforced cylindrical shells are used in numerous industries; common examples include undersea vehicles, aircraft, and industrial piping. Current models typically incorporate approximation theories to determine shell behavior, which are limited by both thickness and frequency. In addition, many applications feature coatings on the shell interior or exterior that normally have thicknesses which must also be considered. To increase the fidelity of such systems, this work develops an analytic model of an elastic cylindrical shell featuring periodically spaced ring stiffeners with a coating applied to the outer surface. There is an external fluid environment. Beginning with the equations of elasticity for a solid, spatial-domain displacement field solutions are developed incorporating unknown wave propagation coefficients. These fields are used to determine stresses at the boundaries of the shell and coating, which are then coupled with stresses from the stiffeners and fluid. The stress boundary conditions contain double-index infinite summations, which are decoupled, truncated, and recombined into a global matrix equation. The solution to this global equation results in the displacement responses of the system as well as the exterior scattered pressure field. An incident acoustic wave excitation is considered. Thin-shell reference models are used for validation, and the predicted system response to an example simulation is examined. It is shown that the reinforcing ribs and coating add significant complexity to the overall cylindrical shell model; however, the proposed approach enables the study of structural and acoustic responses of the coupled system.