Mathematical Description and Laboratory Study of Electrophysical Methods of Localization of Geodeformational Changes during the Control of the Railway Roadbed

Currently, the load on railway tracks is increasing due to the increase in freight traffic. Accordingly, more and more serious requirements are being imposed on the reliability of the roadbed, which means that studies of methods for monitoring the integrity of the railway roadbed are relevant. The article provides a mathematical substantiation of the possibility of using seismoelectric and phasemetric methods of geoelectric control of the roadbed of railway tracks in order to identify defects and deformations at an early stage of their occurrence. The methods of laboratory modeling of the natural–technical system “railway track” are considered in order to assess the prospects of using the presented methods. The results of laboratory studies are presented, which have shown their high efficiency in registering a weak useful electrical signal caused by seismoacoustic effects against the background of high-level external industrial and natural interference. In the course of laboratory modeling, it was found that on the amplitude spectra of the output electrical signals of the investigated geological medium in the presence of an elastic harmonic action with a frequency of 70 Hz, the frequency of a harmonic electrical signal with a frequency of 40 Hz is observed. In laboratory modeling, phase images were obtained for the receiving line when simulating the process of sinking the soil base of the railway bed, confirming the presence of a transient process that causes a shift in the initial phase of the signal Δφ = 40° by ~45° (Δφ’ = 85°), which allows detection of the initial stage of failure formation.

Sources of Harmonic Force and Speed in Mechatronic Automatic Systems

To study resonance and near-resonance phenomena, a symbolic (complex) method was used, which makes it possible to significantly increase productivity, simplify and formalize mathematical transformations. Parallel and sequential connections of elements of a mechanical system with a source of harmonic force or a source of harmonic speed as a source of external mechanical harmonic action are considered. The analytical descriptions of resonance in theoretical mechanics courses correspond to parallel connection. There are devices, in a satisfactory approximation, capable of performing the functions of sources of force and sources of speed. The source of harmonic speed can be a crank-yoke drive and a flywheel with a large moment of inertia. The source of the harmonic force can be the rod of the pneumatic cylinder, the cavity of which communicates with the cavity of another pneumatic cylinder, the diameter of which is immeasurably higher than that of the first, and the piston performs harmonic oscillations. The mechanical harmonic influences described in the courses of theoretical mechanics correspond to the source of the force. Four modes are described — resonances and antiresonances of forces and velocities. The use of the symbolic (complex) method has significantly simplified the study of resonance and near-resonance phenomena, in particular, it has made it possible to deeply unify and formalize the consideration of various mechanical systems. The cumbersome and time-consuming operations associated with the preparation and solution of differential equations have been replaced by simple algebraic transformations. Resonance and antiresonance of forces, resonance and antiresonance of velocities are determined.

The features of solutions of dynamical systems with an external exciting load and non-conservative dynamical systems with pairwise interaction of degrees of freedom

When mathematical models are developed, as a rule, a number of assumptions is done, which makes it possible to simplify the model, reduce its dimension and simulation time, or use the dimension reduction method. When modeling non-conservative systems with pairwise interaction of degrees of freedom, e.g. mechatronic systems, an elastic aircraft in a flow, an aeroelastic aircraft with an automated control system, etc., there is a desire to reduce the problem to a conservative dynamic system with harmonic action. The study shows that despite the apparent similarity of the tasks, they have significant differences that cannot be ignored. Differences in the behavior of conservative dynamical systems and non-conservative dynamical systems with pair interaction of degrees of freedom are considered. The results are demonstrated on the simplest example with an analytical solution, and in the finite element software package MSC.Nastran. The results of the solution in MSC.Nastran are compared with the results of the analytical solution.

Резонансный отклик масштабно-инвариантных функций случайного процесса с турбулентным спектром

Scale-invariant random processes with large fluctuations are modeled by a system of two stochastic nonlinear differential equations describing interacting phase transitions. It is shown that under the action of white noise, a critical state arises, characterized by a turbulent spectrum and a scale-invariant distribution function. The critical state corresponds to the maximum entropy, which indicates the stability of the process. An external harmonic action on a random process with a turbulent spectrum gives rise to a resonant response of scale-invariant functions.

TURBULENCE AND COHERENT STRUCTURES IN SUBSONIC SUBMERGED JETS: CONTROL OF THE TURBULENCE

The onset of turbulence and formation of large-scale patterns (coherent structures) in subsonic submerged jets are considered from the standpoint of noise-induced nonequilibrium phase transitions of the second kind. It is shown by the example of noise-induced oscillations of a pendulum with a randomly vibrating suspension axis that such a transition can be controlled by an additional harmonic action. The known possibility of notable suppression or intensification of turbulence in jets and free shear layers by means of a slight acoustic action at one or another frequency can be attributable to such control.