Brief description of important works performed:

1. M. Chelidze, V. Zviadauri, Natriashvili. Some problems with the mathematical modeling of electromagnetic vibrators used for transporting bulk materials. Transport Problems. Volume 17 Issue 5. 2022 pp. 55-65 DOI: 10.20858/tp.2022.17.4.05

2. A method has been developed for calculating structural damping caused by micro-opening of fixed joints under the influence of bending and twisting forces. The report is included in the six-volume collection “Vibration in Technology.” Publishing house – “Mashgyz” M. 1979;

3. A mathematical model describing the electromagnetic excitation of single-cycle electromagnetic vibrators has been studied. It has been clarified and established that during periods locked by a semiconductor diode, zeroing the current or the corresponding magnetic flux is unacceptable. And taking into account electromagnetic induction, the correct process for describing the interruption of current by a half-wave diode has been developed;

4. A guaranteed mathematical model of receiving the amplitude-frequency characteristic (ASM) for nonlinear oscillatory systems, which contains scientific innovation, was developed and a corresponding simulator was created;

5. In the mathematical model describing the nonlinear electromagnetic drag force fed by harmonic mains current, sin(ωt) should be replaced by cos(ωt), i.e., by sin(ωt-π/2) on the area 0-2π. Integrating sin(α) over area gives the sign of the invariant function cos(α);

6. Theoretical research has established that the mechanical and perturbing two differential equations that describe the oscillations of electromagnetic vibrators can be replaced with great accuracy by a single differential equation, as a result of which the mathematical modeling of an electromagnetic vibrator becomes quite simple;

7. In the field of acoustics, through theoretical and experimental research, a new simple and fairly accurate unique method has been developed, providing the simplest and most effective method for measuring sound absorption by materials, based on the use of resonator tubes prepared according to the length of the sound, as a result of which resonant reverberant sound is less affected by environmental conditions, due to which sound attenuation is carried out directly by the materials under study;

8. A simple program was developed, according to which it is possible to obtain resonance spectra or perform Fourier analysis with the digital data of oscillation amplitudes obtained by experimental or mathematical modeling of the oscillating system;

9. It was investigated that in order to increase the accuracy of the dynamic characteristics obtained by mathematical modeling of vibromachines working under technological load conditions, it is necessary to replace the one-mass vibromachine model with a two-mass model;

10. Taking into account the technological load, a mathematical model has been compiled for the first time to describe the dynamics and stability of vibration machines. The results obtained from mathematical experiments coincide quite well with the experimental results;

11. The ½ subharmonic caused by the nonlinearity of the excitation force was fundamentally investigated by theoretical and experimental studies, and the corresponding mode generation parameters were determined. It should be noted that the dynamics of the subharmonic regime obtained by mathematical modeling of the early period turned out to be overestimated from the point of view of stability and efficiency, since it did not take into account the technological load and, therefore, the need to significantly increase electricity consumption. The source of generation of the subharmonic mode is the difference in losses in the electromagnet that occurs at the corresponding minimum and maximum gaps;

12. The main task of the mathematical model describing the stability and oscillations of vibrators operating in vibration loading mode was taken to be the mass mt, which under the influence of gravity lies on the horizontal plane of the oscillating mass m. Using mathematical experiments, the dynamics and stability of vibrating machines and those oscillating in the horizontal plane and space (elliptical amplitudes) having vertical components were studied. The dynamics of vibration-transporting materials was also studied;

13. A mathematical model of the learning process has been created as a nonlinear resonant cyclic process of cognition based on process of lecture - learning;

14. A mathematical model was created, which describes the processes of economic relations between production and development, which is based on the course of processes characteristic of a non-linear resonant system;

Based on the analysis of the results obtained by mathematical simulation, it can be said that:
*The transition from one economic system to another requires a change in the mentality of society so that society adapts to the new conditions of economic relations. Otherwise, resistance will arise between the process of production and consumption, which manifests itself in a violation of the stability of the resonant state;
*Human thinking and behavior change non-linearly in relation to the development of the economic system, that is, the parameters determining the mentality of society are variable and correspond to the level of development and stability of the economic system;
*Abrupt (sharp) changes in the economic system lead to social resistance caused by the inertia of public (society) thinking;
*When the mentality of the society does not coincide with the management methods of the economic system, then there is an imbalance in the production-consumption system, that is, the resonant interaction process is broken. During the total economy, in order to maintain the level of mutual exchange of the resonant condition (market economy), it becomes necessary to increase capital investments sharply, which is characteristic of an inefficient (unprofitable) economy;
*Such events and processes occurs when incompatibility (disharmony) arises between the management process carried out by the state apparatus and society.

15. The development and creation of a mathematical model and a corresponding simulator continues, describing the occurrence of dynamic forces and the propagation of vibrations in structures caused by impulse loading (action) equipment (including artillery equipment).

Selected Publications