The generalization of Faraday's classic problem about the parametric resonance of the free surface during vertical oscillations of the tank according to the periodic law of the modulus of the cosine is considered. Regions of stability and instability are designed, which are compared with similar results for the classical Faraday problem. The behavior of the system is considered on the basis of a nonlinear multimode model, which describes the combined movement of the tank and fluid under the influence of external force excitation or kinematic disturbance.

A rectangular isotropic layered plate is considered, which is convectively heated by the external environment. The thermal stress state of the plate is determined in two stages. At the first stage, the nonstationary temperature field is determined from the ratios of the non-stationary thermal conductivity problem. At the second stage, using the five-modal mathematical model of the shear theory of thermoelasticity, the parameters of the stress-strain state are determined.

The procedure for complexite evaluation of complex systems objects that have a hierarchical-network structure has been formalized.In order to realization this procedure in real time mode, parallel computation algorithms are proposed.Speed up estimates were obtained for the mentioned algorithms, which confirm their high efficiency. The proposed parallel algorithms are oriented for execution on modern computing means with shared and distributed memory: computers with multi-core processors, clusters, hybrid architectures and in high performance distributed environments.

A boundary-integral approach for the study of the stress-strain state of an infinite body-matrix with single-periodic array of cracks healed by a ductile material and under static torsion loaded is proposed. The ptoblem is reduced to solving a system of 2-d boundary integral equation with respect to an unnown jump functions of shear displacements of defect surfaces.

The work includes an analysis of the accuracy of estimating the determined quantity of paper sheets on vibratory conveyors from the perspective of probability theory and mathematical statistics. A resulting formula for determining the confidence interval of measurement error was obtained. It was found that for paper with a coefficient of variation in the range of 0.52%–1.29% (with a total number of sheets of 4000), the confidence interval of error due to the weight non-uniformity of sheets exceeds the confidence interval of error due to inaccuracies in large and small weights by approximately 5 times.

Theproblemabouttransient modes of motion of acylindricalreservoirwiththeliquidwithafreesurfaceon a pendulum suspension under short-time moment pulse applies to reservoir walls is under consideration. The problem is considered in nonlinear combined statement. It was ascertained that manifestation of internal mechanisms of nonlinear interaction between normal modes of oscillations of a liquid differs considerably from the case of harmonic moment disturbance on the resonant frequency. For advanced studying the nature of these differences we study problems about harmonic disturbance of oscillations for the system under the moment with a frequency, which is not resonant and immediately resonant disturbance.

The subject of the article is a review of the author's proposed dynamic models of the interaction of the primary electromagnetic harmonic field of mobile electromagneticexploratorysystems and the secondary (eddy current) field of a conducting body with ferromagnetic properties and proposals for new applications of such and similar systems.These models make it possible to theoretically substantiate the shape of the signal from a ferromagnetic body. A signal of this form was often observed by moving systems in practice, but it had no theoretical explanation and was therefore not used. The purpose of the review is to acquaint the wider scientific community with the new possibilities of mobile electromagnetic exploratory systems. In particular, this is the ability of mobile electromagnetic exploratory systems to detect conductive bodies not only with diamagnetic properties, but also with ferromagnetic ones in the ground and water, based on appropriate signals.

Hysteresis is a well-known phenomenon that occurs in ferromagnetic materials when they are exposed to external magnetic fields. It results from the inherent properties of magnetic domains, which tend to align with an external field direction. However, when the field is removed, the domains do not return to their initial state but retain a residual magnetization, which leads to the formation of a hysteresis loop. This behavior can have a significant impact on the performance of electromagnetic devices, which rely on magnetic fields for their operation. Hysteresis can cause energy losses, reduced efficiency, and other undesired effects in devices such as transformers, inductors, and electric motors

The methodology to estimate the service life of the drum of the boiler unit of a power plant with operational damages is considered. It developed on the basis of three-dimensional thermoelastic plasticity and the finite element method.