Wear problem for tube with thin nonuniform inner coating and rigid insert with complex profile

The article describes the formulation of the problem of wear of an elastic pipe with a nonuniform internal coating by a rigid insert, the diameter of which is variable. For this problem, a mathematical model is built, which is a mixed integral equation. The resulting integral equation contains functions related to the variable properties of the coating and the shape of the insert. When constructing an analytical solution, a special approach was used, since standard methods do not allow taking into account the presence of rapidly changing functions in the equation, which can describe the shapes and properties of materials. In the resulting solution, the functions describing the variable properties of the coating and the profile of the insertion are separated by separate terms. This allows you to always get accurate results.

Dynamics of Welded Rails Gap and Hardness of Rail Base

The problem of gap estimation for a break of a continuous welded rail is studied. The track is represented as a semi-infinite rod on elastic-based damping. Static and dynamic solutions are obtained. It is shown that during the rail break, the dynamic factor does not exceed 1.5. We derive equations for thermal deformation of the welded rail of jointless track on an elastic foundation in the presence of the insert into the base with another characteristic stiffness. It is shown that the presence of the insertion of up to 20% of the length of the rail, with both large and small stiffness, has a little effect on the stress-strain state (SSS) of the track. The presence of a rigid insert may increase the clearance of an accidental break of the rail, which has a negative effect on traffic safety.

Damper as a Rigid Insert for Rigid Bus Structures Oscillation Damping

One of the main problems in a design of rigid bus structures in open switchgears devices is a structural stabilization under the influence of various dynamic loads. The implementation of rigid bus structures with large spans of pipe-bus showed a real danger of the wind resonance for cylindrical pipe-bus structures (aeroelastic oscillations). This phenomenon is dangerous in that at low wind speeds there are intense pipe's oscillations in vertical plane, adding to the static loads an essential dynamic component. Its level is comparable with the loads from the weight of the structures and can, in combination with the rest loads, cause stresses close to the maximum admissible for the 1st group of limit states. The problem of reducing the level of structural oscillations in many cases is associated with the need to increase the rigidity and reduce the material consumption, but it's important to meet the technological requirements imposed by operating conditions and protect people from harmful vibration. In a paper are considering a new method for damping oscillations for rigid bus structures under the action of a wind vortex excitation – damper as a rigid insert. Is presented a mathematical model of the joint work of the rigid bus structure with the damper as the rigid insert. Have carried out analytical researches of the joint work of the rigid bus structure with the damper as the rigid insert.

Axisymmetric Free Vibration of Shallow Spherical Shells With a Circular Rigid Insert

A general solution for the third-order partial differential equations for the axisymmetric free vibration of thin isotropic shallow spherical shells with a rigid insert is presented in this paper. The frequency equation in terms of Bessel functions as well as modified Bessel functions is solved for the fundamental vibrational frequency and mode shape. Both linear and non-linear boundary conditions are applied and the results are compared. The relationship between the vibrational frequency, mode shape and the size of the rigid insert is discussed.