Sessions 2024-2025

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Man is a slow, sloppy, and brilliant thinker;
computers are fast, accurate, and stupid.

March 4, 2025

R. V. Fedorenko (SPbPU)
Adaptability of a vessel under pressure and thermocyclic loads
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.
Roman V. Fedorenko – research engineer at the Advanced Engineering School "Digital Engineering" of Peter the Great St. Petersburg Polytechnic University. Research interests - theory of plasticity, computational mechanics, numerical approaches for modeling reinforced concrete structures. The scientific supervisor - Asso. Prof. Alexey V. Lukin.

February 25, 2025

N.D. Tregulov (SPbSU)
Bending of ice plates accounting the elastic base under concentrated vertical loads
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.
Nikita D. Tregulov – the 5th year student of the program «Fundamental mechanics» at the Faculty of mathematics and Mechanics of St. Petersburg State University. The area of scientific interests – computationsl mechaics of solids. Scientific supervisor – Asso. Prof. G.V. Pavilaynen.

February 19, 2025

A.V. Lukin (SPbPU)
Synthesis of geometrically nonlinear reduced-order models for distributed elastic systems based on the finite element method.
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.
Lukin Alexey V. – PhD, Associate Professor of the Higher School of Mechanics and Control Processes of the Physics and Mechanical Institute of Peter the Great St. Petersburg Polytechnic University. Research interests: nonlinear dynamics; strength, stability and vibrations in engineering; computational mechanics; nano- and microelectromechanical systems.

November 19, 2024

M.I. Ivanov (SPbSU)
Analytical approach on modelling of medium loaded airplane’s coaxial airscrews.
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.
Matwey I. Ivanov – the 1st year master's student of the Department of Hydroaeromechanics of the Faculty of Mathematics and Mechanics of St. Petersburg State University. Research interests: aerodynamics of subsonic UAVs, aerodynamics of parachutes.

November 12, 2024

N.K. Egorova (SPbSU)
Modeling the human body under vibrations.
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.
Nadezhda K. Egorova – 2nd year postgraduate student of the Department of Theoretical and Applied Mechanics of the Faculty of Mathematics and Mechanics of St. Petersburg State University. Research interests: modeling of biomechanical systems. Supervisors - Profs S.M. Bauer and V.P. Tregubov.

November 5, 2024

Tupitsyna A.D. (SPbSU)
Translational and rotational oscillations of parallelepipeds in the air flow.
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.
Anna D. Tupitsyna – the 1st year master's student of the Department of Hydroaeromechanics of the Faculty of Mathematics and Mechanics of St. Petersburg State University. Research interests: experimental aerodynamics of low speeds. The scientific supervisor – Prof. A.N. Ryabinin.

October 1, 2024

Lutsek V.V. (SPbSU)
Numerical modeling of electrocoalescence and decoalescence of water droplets.
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.
Vladimir V. Lutsek – 1st year master student of the Department of Theory of elasticity, Faculty of Mathematics and Mechanics, St. Petersburg State University. Research Interests: spallation fracture in solids. Scientific supervisor – Asso.Prof. V.A. Chirkov and Prof. Yu.V. Petrov.

September 10, 2024

Dolya A.I. (SPbSU)
The effect of the Coriolis force on the motion of a body thrown at an angle to the horizon.
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.
Alexei I. Dolya – 4th year student of the Department of Theoretical and Applied Mechanics, Faculty of Mathematics and Mechanics, St. Petersburg State University. Research Interests: ballistics. Scientific supervisor – Prof. S. B. Filippov.

September 3, 2024

Dzebisashvili G.T., Smirnov A. L. (SPbSU)
Calculation of axial moments of inertia of regular polygons.
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.
Georgii T. Dzebisashvili – PhD student of the Department of Theoretical and Applied Mechanics, Faculty of Mathematics and Mechanics, St. Petersburg State University. Research Interests: shell theory. Scientific adviser – Prof. S. B. Filippov.
Andrei L. Smirnov – PhD, Associate Prof. at the Department of Theoretical and Applied Mechanics SPbSU. Author papers on mechanics of thin-walled structures.

April 16, 2024

Pavlov S.A. (SPbSU)
Calculation of transport coefficients in high-speed flow modeling.
The accurate calculation of transport coefficients in high-speed flow modeling of reacting air is essential in the analysis of heat transfer processes in various problems of gas dynamics, for example, in design of thermal protection of descent vehicles. The most accurate from the physical point of view within the continuum approximation is the state-to-state approach. However, it has a significant computational complexity. One of the most effective and accessible method of applying such models is a machine learning regression. We study the application of this approach to the problem of modeling viscosity and thermal conductivity coefficients. Further prospects of machine methods in modeling of high-speed flows are considered.
Semen A. Pavlov – master student of the Department of Hydroaeromechanics of St. Petersburg State University. Area of scientific interests: computational fluid dynamics (CFD). Scientific supervisor - V.A. Istomin, PhD.

November 28, 2023

Piskun N.V., Lukin A. V., Popov I. A., Shtukin L. V. (Peter the Great SPbPU, IPME RAS)
On the measurement of ultra-low mass of deposited particles with micromechanical mode-localized detectors
The report is devoted to methods for measuring ultra-low mass of deposited particles using micromechanical sensors based on the phenomenon of mode localization. Two types of sensitive elements of a mass detector are considered – a beam with an initial curvature and a system of two mechanically weakly coupled beams. In the first case, mass detection is supposed to be carried out by the amplitude ratio of beam vibrations on different natural modes. It is shown that with the correct choice of geometric parameters in the system, an exchange of energy is observed between the first asymmetric and second symmetric modes of vibration. The work proposes a system of electrodes that makes it possible to excite and detect vibrations in selected forms. In the case of a system of two weakly coupled beams, it is shown that in the presence of a disturbance in the form of a deposited particle, an oscillation mode with different amplitudes is observed in the system, the ratio of which is the output signal of the device. A comparison is made of the output characteristics of the devices, primarily sensitivity, with known mass detectors presented in the literature.
Piskun N. V. – graduate student of the Higher School of Mechanics and Control Processes of the Physico-Mechanical Institute, research engineer at the Digital Engineering School of the Peter the Great St. Petersburg Polytechnic University. Area of scientific interests: Nonlinear dynamics, mechanics of deformable solids, computational mechanics, nano/microelectromechanical systems, bifurcation theory. Scientific suppervizor - Asso. Prof. A.V. Lukin.
Lukin A. V. – Associate Professor of the Higher School of Mechanics and Control Processes of the Physico-Mechanical Institute of Peter the Great St. Petersburg Polytechnic University.
Popov I. A. – Research Engineer at the Advanced Engineering School “Digital Engineering” of the Higher School of Mechanics and Control Processes of the Physico-Mechanical Institute of Peter the Great St. Petersburg Polytechnic University.
Shtukin L. V. – Associate Professor at the Higher School of Mechanics and Control Processes of the Physico-Mechanical Institute of Peter the Great St. Petersburg Polytechnic University.

October 10, 2023

A. S. Smirnov, S. A. Kravchinskiy (Peter the Great SPbPU, IPME RAS)
Oscillations of a double pendulum with a weak nonlinearity
The report considers nonlinear oscillations of a double mathematical pendulum with identical parameters of links and end weights. Exact nonlinear equations of motion of the system are derived, from which a classical linear model of small oscillations is obtained, as well as a weakly nonlinear oscillation model that takes into account cubic nonlinearity. A well-known solution of the problem of small oscillations of a double pendulum is given, which serves as a basis for further research. With the help of asymptotic methods of nonlinear mechanics, an approximate solution is constructed for a weakly nonlinear model under arbitrary initial conditions of motion. It is shown that the found solution has a nontrivial structure and represents polyharmonic oscillations on eight different frequencies. The resulting approximate formulas are accompanied by graphical illustrations that compare the behavior of the angles of deviation of the links of a double pendulum from the vertical when using linear and weakly nonlinear models, as well as the original nonlinear model, which is calculated using numerical integration. The conclusions drawn are of interest for analytical mechanics and theory of oscillations, and they can also be used in practice in applied problems of robotics and biomechatronics.
Smirnov Alexey S. – Assistant Professor at the Higher School of Mechanics and Control Processes (Peter the Great St. Petersburg Polytechnic University), Junior Researcher at the Laboratory of Mechatronics (Institute of Problems of Mechanical Engineering of the Russian Academy of Sciences). Research interests: analytical mechanics, theory of mechanical oscillations, rigid body dynamics, stability of equilibrium and motion, control of mechanical systems, optimization in mechanics.
Kravchinskiy Sergey A. – Master's Student at the Higher School of Mechanics and Control Processes (Peter the Great St. Petersburg Polytechnic University). Research interests: analytical mechanics, theory of mechanical oscillations, computational mechanics, computer engineering. Scientific supervisor - Assistant Professor A. S. Smirnov.
Smirnov Alexey S. – Assistant Professor at the Higher School of Mechanics and Control Processes (Peter the Great St. Petersburg Polytechnic University), Junior Researcher at the Laboratory of Mechatronics (Institute of Problems of Mechanical Engineering of the Russian Academy of Sciences). Research interests: analytical mechanics, theory of mechanical oscillations, rigid body dynamics, stability of equilibrium and motion, control of mechanical systems, optimization in mechanics.