Sessions 2024-2025

A series of dynamic problems related to the peculiarities of wave front formation in quasi-one-dimensional rod systems is studied. The problems are solved using the finite element method with Ansys software. Rods with circular cross-sections made of structural steel and ultrafine-grained titanium are analyzed. The objective of the study is to modify the Kolsky method, which employs split Hopkinson pressure bars, for the rapid assessment of the incubation characteristics of specimen failure.

In the dynamic contact problem of interaction between quasi-one-dimensional rod elements, the wave front formation time of stress waves is determined depending on the diameters of rods.

In dynamic loading and unloading problems of a quasi-one-dimensional rod element, the wave front formation time of stress waves is analyzed in relation to the duration of the applied load. The transformation of the wave front as it propagates along the rod is examined.

In the dynamic unloading problem of a composite system consisting of coaxially connected quasi-one-dimensional rod elements with different diameters, the influence of the number of thread steps on the stress wave front propagating into the larger-diameter rod is studied. A comparison of the wave fronts in the larger and smaller rods is conducted. The numerical simulation results are compared with physical experiments. The incubation time for a titanium specimen is determined.

The paper discusses the peculiarities of the dynamics of a graviplane, which is a spacecraft consisting of two masses connected by a long tether. The idea of using such a spacecraft is the possibility of thrustless change of the orbit altitude due to the difference of gravitational forces acting on the end masses of the system. The motion of a graviplane in the equatorial plane is studied. The problem of a graviplane orientation to provide the desired change of the orbital altitude of its center of mass is considered. An analytical study of the system of differential equations of motion is carried out. The asymptotic solution is obtained using a series expansion by a small parameter. The justification of the choice of the equilibrium positions for the most effective change of the orbit altitude is given based on the analytical solution. Numerical modeling of the considered problem is carried out. The obtained results are compared.

The research is devoted to the analytical study of the dynamics of a non-deformable conducting solid body in a contactless electromagnetic suspension. Using the mathematical apparatus of perturbation theory, the stability regions of the stationary levitation mode are determined, and the features of nonlinear oscillations are investigated. Various approaches to accounting for induction currents in a solid body within the coupled electromechanical model are considered. In the context of the development of high-precision micromechanical sensors, the analytical estimates of the effective quasi-zero stiffness of the contactless suspension are compared with known experimental data.

Free vibrations of a thin cylindrical shell supported by rings are considered in the report. The shell is clamped at one end and joint with the thin circular plate at the other end. Two types of free vibrations are studied: shell-like and plate-like vibrations. the formula for the eigenfrequency parameter is derived by means of asymptotic and averaging methods. The curves for the shell and plate frequencies vs the relative thickness of a plate and shell are plotted.

It is proposed to optimize the frequency spectrum by varying the thicknesses of structural elements while maintaining the total weight of a structure. The optimal set of parameters would be one in which the minimum value of the frequency reaches maximum.

The research is devoted to the study of the adaptability of a vessel under pressure and thermocyclic loads. The problem was posed in the late 1960s in the work of J. Bree, who built an analytical solution for a vessel made of an elastically ideal plastic material under pressure with a temperature gradient cyclically varying in wall thickness. The result of the work was a diagram of the characteristic zones of vessel adaptability (ratcheting), which in the literature was called the "Bree diagram". Further development of the problem by Russian and international scientists using rigorous and approximate analytical, as well as numerical methods, allowed us to consider the features of adaptability (ratcheting) when changing various system parameters (variation in the type of load, taking into account the hardening of the material, and others).

The paper presents the results of the development of a compact numerical procedure based on the Abaqus software, which allows solving adaptability (ratcheting) problems with arbitrary system parameters. The issue of the influence of material hardening mechanisms (isotropic, kinematic, and mixed) on the type of adaptability (ratcheting) diagram and the nature of the stress-strain state of the system under thermomechanical cyclic loads is considered.

The report addresses the problem of hydrostatics: the bending of a thin ice plate resting on an elastic foundation under a concentrated vertical load, which simulates the landing and takeoff of helicopters. The study includes the calculation of the minimum ice thickness required for safe landing, as well as an analysis of the stress-strain state (SSS) of the ice. The ice is treated as a floating plate or beam. This problem is analogous to the classical Hertz problem—the bending of a thin circular plate subjected to a vertical load applied at the center of its upper surface.

The bending of the ice plate is examined in two configurations. In the first configuration, the plate is rigidly clamped along its edges. In the second configuration, the plate is also clamped along its edges but rests on an elastic foundation, modeled as the water beneath the ice. Mathematical modeling and calculations are performed using the finite element method in the ANSYS 15.0 software for two loading scenarios: first, the plate is loaded at its center, and then the load is applied at three points, corresponding to the actual conditions of a helicopter landing on ice.

Two models are compared: a phenomenological model based on experimental data and a mathematical model implemented in ANSYS using the finite element method. The results demonstrate a qualitative agreement.

The report is devoted to the problems of development and verification of computational algorithms for the synthesis of compact models of the dynamics of continual elastic systems in a geometrically nonlinear formulation (primarily thin-walled structures: strings, membranes, beams, plates, shells) based on the finite element method. The approaches under consideration are based on the idea of??identifying a nonlinear (quadratic-cubic) stiffness characteristic of an elastic system in its modal coordinates with the subsequent application of the apparatus of the theory of nonlinear normal modes and Poincare normal forms to construct an invariant manifold tangent to the modal subspace of interest. The resulting dynamic reduced-order model takes into account the nonlinear elastic coupling of the working vibration modes with high-frequency longitudinal and volume modes of the structure, which ensures the correctness of the calculated nonlinear stiffness characteristic of the system for the selected principal coordinates. The developed algorithm is applied to a number of problems of nonlinear dynamics of strings and beams that admit an approximate analytical solution using asymptotic methods of nonlinear mechanics. The features of the software implementation of the presented method based on the ABAQUS finite element analysis software system are discussed.

Well engineered coaxial airscrew offers advantage in efficiency to airplane’s propulsion system. However modern approach on designing coaxial propellers is based on analysing and semi-empirical enhancing of already existing geometries. Present study provides realised in code and validated method for computing thrust and power coefficients for low and medium loaded airplane’s coaxial airscrew.

New approach is based on combination of elder approaches on aerodynamic calculation of coaxial airscrew and on aerodynamic calculation of highly loaded airscrew. The idea is then realized with implementation of convenient computational schemes and validated through comparison with full-scale experiment. Close agreement of calculations and experiment is found in areas of low and medium loads.

Present study is used to demonstrate the potential of such approach, as it only points out the way and necessity of further research.

Problems that arise when constructing mechanical models of the human body subject to vibration are discussed. In particular, the previously unconsidered question of the uniqueness of the set of parameters of such models is examined, the questions that is fundamentally important when using them in the construction of vibration protection systems.

An example of the simplest mechanical model of a chain structure located on a vibrating base and consisting of two masses connected in series by linear springs and dampers is considered. The necessary conditions for the uniqueness of the model parameters are found. Next, a study is carried out of systems simulating the muscular structure of the human body (with multi-link connections) and the intervertebral disc (with a non-integer number of degrees of freedom). Computer modeling made it possible to identify the features of such models.

The work is devoted to the experimental study of oscillations of a parallelepiped in an air stream. Poorly streamlined bodies of a similar shape, serving as parts of bridges or high-rise structures, are capable of being subjected to fluctuations of various types in the incoming wind flow.

In the study, a parallelepiped with end washers was fixed in the working part of the wind tunnel on two types of suspensions containing springs. The body on the suspension containing eight springs had only steady translational oscillations in the direction perpendicular to the velocity of the incoming flow. For a body on a suspension containing two springs, at sufficiently high flow velocities, only rotational oscillations with a constant amplitude were observed. Although the parallelepiped can perform both translational and rotational vibrations under the action of the airflow, the occurrence of both translational and rotational vibrations on the same suspension was not observed.

Using the methods of tensometric measurements of unsteady forces in an aerodynamic experiment, after processing the data, it was found that the square of the oscillation amplitude linearly depends on the Struhal number.

The electrocoalescence of droplets is studied - the process of merging liquid droplets under the effect of an electric field. This process plays an important role in a variety of process applications including liquid handling, emulsion separation and fuel purification.

During the study, a map of droplet interaction modes was created, showing how the form of droplet fusion depends on the electric field strength and the droplet size ratio.

The report addresses a problem related to ballistics, a field that studies the motion of objects in the gravitational field of Earth. Ballistics involves calculating trajectories, determining velocities and accelerations, and accounting for various factors that affect motion, such as the Coriolis effect and medium resistance. The effect of Coriolis force on ballistic trajectories and optimal parameters is studied without taking into account other factors. The solution to the problem of projecting a body at an angle with respect to the horizontal plane has been explicitly derived. Due to the low angular velocity of Earth's rotation, a complicated solution was significantly simplified by breaking it down into a small parameter and omitting insignificant terms.

For the task of projecting at a given point, the main optimization criteria considered are energy and energy-time efficiency. Using these criteria, optimal initial velocities and angles of projection to the horizon can be determined.

The moment of inertia of the solid and hollow regular n-gon cross-section with respect to the axis passing through its center in the section plane is evaluated. The ability to take such points into account is necessary when analyzing the deformations, stability and vibrations of beams and prismatic shells. The method discussed in the paper allows one to analytically calculate axial moments of inertia for regular polygonal sections of beams and shells with an arbitrary number of sides.