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The paper deals with the problem of obtaining a given dynamic behavior of simply supported bridge beams from the impact of rolling stock. Resonant vibrations of beams become a reality at high speeds if the train is formed of identical cars, which is typical for passenger trains. The phenomenon of suppression of beam vibrations by a train, known from publications, is possible only with an exact ratio of the length of the car and the beam. This significantly reduces the possibilities of choosing the necessary spans of beams. Consideration of issues of interaction in the "bridge–track—train" system for security purposes requires the involvement of a rather complex mathematical apparatus and appropriate software. The paper proposes a new method for determining the specified dynamic behavior of bridge beams, suitable for any spans and available to engineers at the stage of pre-design assignment of dynamic parameters of beams. The requirements that are necessary and sufficient conditions for preventing the resonance of bridge beams on the HSR are determined. At the same time, it does not require the involvement of software based on a complex mathematical technique. [ABSTRACT FROM AUTHOR]

The equations described free longitudinal and lateral vibrations of the rectilinear elastic beams with the rectangular cross section are derived based on the theory of linear elasticity and the method of integrodifferential relations. The original system of partial differential equations is reduced to the system of ordinary differential equations with constant coefficients. The influence of geometrical and elastic properties of the beam on eigenvalues and eigenfunctions are investigated. The existence of the different displacement and internal stress types of the longitudinal motions are shown. The presence of two frequency zones corresponded to different kinds of the characteristic solutions for the lateral vibrations is detected. [ABSTRACT FROM AUTHOR]

The article presents the analysis of the stress-strain state of elastic bodies. It states that it is based on the linear theory of elasticity as well as the method of integro-differential relations. It notes that employing the integral formulation of Robert Hooke's law and polynomial representations of the obscure functions of stresses and displacements wherein it is reduced to an integrable system of ordinary differential equations with constant coefficients.

A variational approach to linear elasticity problems is considered. The family of variational principles is proposed based on the linear theory of elasticity and the method of integrodifferential relations. The idea of this approach is that the constitutive relation is specified by an integral equality instead of the local Hooke’s law and the modified boundary value problem is reduced to the minimization of a nonnegative functional over all admissible displacements and equilibrium stresses. The conditions of decomposition on two separated problems with respect to displacements and stresses are found for the variational problems formulated and the relation between the approach under consideration and the minimum principles for potential and complementary energies is shown. The effective local and integral criteria of solution quality are proposed. A numerical algorithm based on the piecewise polynomial approximations of displacement and stress fields over an arbitrary domain triangulation are worked out to obtained numerical solutions and estimate their convergence rates. Numerical results for 2D linear elasticity problems with cracks are presented and discussed. [ABSTRACT FROM AUTHOR]

The article discusses variational approaches in the linear theory of elasticity, which lead to the principles of the potential and additional energy minima. A numerical-analytical algorithm that is used for obtaining piecewise-polynomial approximations of desired functions is developed for this study.

The article presents equations describing the longitudinal and transverse oscillations in an elastic beam. The equations work within the framework of the planar linear elasticity theory and the method of integro-differential relations is used to solve the equations. The article studies the influence of beam geometry and elastic characteristics on the frequency and shape of oscillations in the beam. The characteristics of the longitudinal and transverse oscillations are mentioned.

Presents an integro-differential approach to solving problems of linear elasticity theory. Introduction of integral relations between components of the stress and strain tensors; Reduction of the integro-differential boundary value problem to a variational problem to which well-developed methods of numerical analysis are applicable; Employment of numerical-analytical method of finding approximations for desired stress functions and displacement functions.

This paper describes the issue of validity of running safety criterion on high-speed railways (HSR). In this research, the 2D model of 'car–track–bridge' system is used. A feature of HSR is the practical reaching of the critical speeds that cause resonance of bridge superstructures. The Eurocode establishes the limit of bridge superstructure acceleration below 5 m/s2 in case of nonballasted track. This limit does not suit in certain conditions such as resonance of the superstructure that is permitted in Eurocode. In this case, there is no correlation between acceleration limit and firm wheel–rail contact. The numerical analysis shows repeated wheel lift-off during train passing a bridge zone. It is resonance of the bridge deck that causes this effect because without resonance, the running train is safe. Lower damping in nonballasted track increases resonant vibration influence. [ABSTRACT FROM AUTHOR]

We report a design solution for a highly reliable, low-noise and extremely efficient cryogenically cooled transmit/receive unit for a large antenna system meant for radio-astronomical observations and deep-space communications in the X band. We describe our design solution and the results of a series of laboratory and antenna tests carried out in order to investigate the properties of the cryogenically cooled low-noise amplifier developed. The transmit/receive unit designed for deep-space communications (Mars missions, radio observatories located at Lagrangian point L2, etc.) was used in practice for communication with live satellites including 'Radioastron' observatory, which moves in a highly elliptical orbit. [ABSTRACT FROM AUTHOR]