# Petr VelmisovUlyanovsk State Technical University · Department of Higher Mathematics

Petr Velmisov

Doctor of Philosophy

## About

88

Publications

859

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

144

Citations

Citations since 2016

Introduction

Additional affiliations

September 1974 - present

September 1974 - present

## Publications

Publications (88)

Initial-boundary value problems for systems of differential equations are considered, which are mathematical models of the mechanical system "pipeline - pressure sensor". In such a system, to mitigate the effects of vibration accelerations and high temperatures, the sensor is located at a certain distance from the engine and is connected to it via...

In this paper, we propose asymptotic expansions for the velocity potential and obtain asymptotic equations of gas dynamics for irrotational isentropic flows of an ideal gas: an equation of linear theory, a nonlinear equation for supersonic flows, and a nonlinear transonic equation. We construct some exact particular solutions for the asymptotic non...

We study the stability of solutions to initial–boundary-value problems for coupled systems of partial differential equations that describe the dynamics of deformable structural elements interacting with a gas-liquid medium. The definitions of stability of deformable bodied adopted in this work correspond to the concept of the Lyapunov stability of...

The mathematical models describing the dynamics of elastic elements of wing structures and representing the initial-boundary value problems for systems of partial differential equations are proposed. The dynamics and stability of elastic elements of wings, flown around by a gas or liquid stream in a model of an incompressible medium, are investigat...

The search for new solutions in the field of energy, preventing negative impact on the environment, is one of the priority tasks for modern society. Natural gas occupies a stable position in the demand of the UES of Russia for fossil fuel. Biogas is a possible alternative fuel from organic waste. Biogas has an increased content of carbon dioxide, w...

The dynamics and stability of elastic elements of some aerohydroelastic systems – vibration devices designed to intensify of the technological processes, for example, for stirring gas-liquid media are investigated. The device is simulated by a flow channel containing elastic elements – deformable plates of variable thickness made from inhomogeneous...

We study the initial-boundary value problems corresponding to the mathematical model of the mechanical system “pipeline – pressure sensor” by using various analytic and numerical methods.

Nonlinear mathematical models are proposed that describe the dynamics of a pipeline with a fluid flowing in it: a) the model of bending-torsional vibrations with two degrees of freedom; b) the model describing flexural-torsional vibrations taking into account the nonlinearity of the bending moment and centrifugal force; c) the model that takes into...

The search and development of alternative energy sources for human life is a priority task for modern society. One of the promising directions is the use of biogas as a source of thermal energy for power plants. It is established that the main difference between biogas and natural gas is caused by the presence of more than 30% of carbon dioxide in...

The mathematical models of the mechanical systems “pipeline – pressure sensor” are considered. These systems are designed to measure the pressure in gas-liquid media, for example, to control the pressure of the working medium in the combustion chambers of engines. Based on the proposed models described by systems of differential equations, the join...

The derivation of asymptotic equations describing the processes of heat and mass transfer in axisymmetric swirling laminar flows of a viscous incompressible fluid. Self-similar solutions of these equations are obtained, on the basis of which steady hydrodynamic fields (velocities, pressures) and a temperature field in swirling jets are constructed....

On the basis of the developed mathematical models, a program complex was created for studying the dynamics and stability of an elastic pipeline, an elastic structural element in supersonic flow, elastic elements of wing profiles of several types with subsonic flow, elastic elements of vibration devices of several types. The complex generates three-...

Рассматриваются математические модели в задачах о динамике и устойчивости деформируемых элементов конструкций, взаимодействующих с потоком жидкости или газа. Математические модели представляют собой начально-краевые задачи для связанных систем дифференциальных уравнений с частными производными для гидродинамических функций и функций деформаций упру...

Рассматриваются математические модели вибрационных устройств, предназначенных для интенсификации технологических процессов. Математические модели представляют собой начально-краевые задачи для связанных систем дифференциальных уравнений с частными производными для гидродинамических функций и функций деформаций упругих элементов. Исследуется динамик...

The article discusses the initial-boundary value problems for systems of differential equations, which are mathematical models of the mechanical system "pipeline - pressure sensor that is designed to measure pressure in gas-liquid media. On the basis of the proposed models, the joint dynamics of the pressure sensor sensitive element and of the work...

Jet flows of liquids and gases are used in various fields of technology as means of controlling the processes of heat and mass transfer, for the intensification and stabilization of the combustion process, as means of protecting structures from exposure to thermal fields, for coating, etc. The jets of liquids and gases in technology are formed by s...

The stability of solutions of the boundary value problem for a coupled nonlinear system of integrodifferential partial differential equations, describing the dynamics of a deformable element of a vibrating device, is investigated. The definitions of the stability of a deformable body adopted in the work correspond to the concept of the stability of...

We consider the plane problem of aerohydroelasticity on small oscillations arising during bilateral flow around a viscoelastic element located on the rectilinear wall of an infinite channel. A mathematical model describing the problem in a linear formulation and corresponding to small perturbations of homogeneous subsonic flows and small deflection...

The dynamics and stability of the elastic elements of vibration devices, modeled by a channel containing elastic elements, are investigated. Inside the channel flows a stream of stirred liquid. The model of the device with two elastic elements is considered. The solution of the aerohydrodynamic part of the problem, based on the methods of the theor...

In the article mathematical models of a mechanical system consisting of a pipeline with a working gas-liquid medium and a sensor, of which the elastic element is a part, are proposed. The sensor is designed to measure the pressure of the working medium (for example, at the exit from the engine combustion chamber). Differential equations have been o...

The dynamics and stability of elastic elements of vibration devices modeled by channels containing elastic elements are investigated. The stream of the stirred fluid flows inside the channel. To solve the aerohydrodynamic part of the problem, two approaches are used. The first is based on the application of the Fourier method, the second uses the m...

A mathematical model of a mechanical system for measuring the pressure of the working medium in an engine is proposed. The system includes an axisymmetric pipe with fluid and a fluid pressure sensor. An integro-differential equation of the dynamics of the elastic element of the sensor is obtained, which relates its deformation to the pressure and t...

Исследуется устойчивость решений начально-краевых задач для связанных систем дифференциальных уравнений с частными производными, описывающих динамику деформируемых элементов конструкций, находящихся во взаимодействии с газожидкостной средой (обтекаемых потоком жидкости или газа). Принятые в работе определения устойчивости деформируемого тела соотве...

Предложены асимптотические разложения для потенциала скорости, на основе которых выводятся асимптотические уравнения газовой динамики для безвихревых изоэнтропических течений идеального газа: уравнение линейной теории, нелинейное уравнение для сверхзвуковых течений, нелинейное трансзвуковое уравнение. Построены некоторые точные частные решения асим...

In this paper, the dynamic stability of elastic elements of a class of structures that are in interaction with a gas or liquid flow is investigated. The definition of the stability of an elastic body corresponds to the concept of the stability of dynamical systems by Lyapunov. As examples, mathematical models of elastic pipelines and mathematical m...

Obtained asymptotic local equations for a viscous incompressible gas with a weak twist,which differ from the analogous boundary-layer equations for flows with finite twist. The solutions of these equations are used to construct "internal" flows in the center of free weakly twisted jets. Equations and their solutions describing the "external" flows...

In designing structures and devices interacting with the flow of gas or liquid, it is necessary to solve the problems associated with the investigation of the stability required for their functioning and operational reliability. The definition of stability of an elastic body taken in the article corresponds to Lyapunov’s concept of stability of a d...

A nonlinear mathematical model of a device related to vibratory technology is considered. The device is intended for the intensification of technological processes, for example, the mixing process. The action of such devices is based on the vibrations of the elastic elements when they are flowed by the flow of the mixing medium. The dynamical stabi...

Исследуется устойчивость деформируемого элемента конструкции в виде пластины-полосы при обтекании ее сверхзвуковым потоком идеального газа. Принятые в работе определения устойчивости соответствуют концепции устойчивости динамических систем по Ляпунову. Для описания динамики упругого тела используется математическая модель, учитывающая поперечные и...

Applying bifurcation theory methods to nonlinear boundary value problems for ordinary differential equations (ODEs) of the fourth and higher orders encounters technical difficulties related to studying the spectrum of direct and adjoint linearized problems and constructing Green functions (i.e., proving the spectral problems to be Fredholm and dete...

The article is dedicated to the development asymptotic theory of gas flowing at speed next to sound velocity, particularly of gas transonic flows, i.e. the flows, containing both, subsonic and supersonic areas. The main issue, when styding such flows, are nonlinearity and combined type of equations, describing the transonic flow. Based on asymptoti...

In the paper, the stability of elastic elements of a class of designs that are in interaction with a gas or liquid flow is investigated. The definition of the stability of an elastic body corresponds to the concept of stability of dynamical systems by Lyapunov. As examples the mathematical models of flowing channels (models of vibration devices) at...

We consider the problem of stability of the motion of an deformable plate which is a part of the border dividing the areas filled with viscous incompressible fluid. Two models of a deformable solid are considered. The first (nonlinear) model of an elastic body takes into account the longitudinal and transverse deformation of the plate, but does not...

At designing of the constructions and the devices interacting with the flow of gas or liquid, it is necessary to solve the problems associated with the investigation of the stability required for their functioning and operational reliability. The definition of stability of an elastic body corresponds to the Lyapunov’s concept of stability of dynami...

We propose a mathematical model of a system of wing profiles of tandem type with elastic ailerons in subsonic flow of an ideal gas (liquid). The aerohydroelasticity problem is reduced to the study of a system of integro-differential equations. The solution is constructed by the Bubnov–Galerkin method. Numerical experiments are presented in the case...

At designing structures and devices interacting with the flow of gas or liquid, it is necessary to solve the problems associated with the investigation of the stability required for their functioning and operational reliability. The definition of stability of an elastic body, taken in the article, corresponds to the Lyapunov concept of stability of...

Lyapunov stability of elastic elements (plates) of a wing profile in interaction with the flow of a fluid or a gas is studied.

We suggest the method of constructing the solutions for systems of partial differential equations and consider its application to some aerohydromechanic equations. This method is parameterization-based and effective for finding exact particular solution of first-order systems of partial quasi-linear differential equations. The existence of the para...

Dynamic stability of elastic elements (plates in this work) of thin-shelled constructions in interaction with fluid or gas flow is studied. Subsonic regime is considered. The definition of elastic body stability corresponds to Lyapunov's concept of dynamical system's stability. Aerodynamic load is determined by asymptotic aerohydromechanical equati...

The problem of the dynamics of an elastic element of a sensor, that is the component of the pipeline-pressure sensor mechanical system, is studied.

The conditions for the statical instability (bifurcation) of a plate in a supersonic gas flow and a pipeline are obtained.

Dynamic stability of a lattice viscoelastic plates interacting with a flow of ideal incompressible fluid is investigated. Stability of oscillations of viscoelastic elements of channel walls is investigated too. For the deflection function of the plates, oscillation equations are derived and sufficient stability conditions of its solutions are obtai...

Dynamic stability of viscoelastic elements of thin-shelled
constructions under interaction with flow of fluid or gas is studied.
The definition of viscoelastic body's stability corresponds to
Liapunov's concept of dynamical system's stability. Have been considered
the following problems: problem about dynamics of elements of a plane
channel, throug...

(For abstract see issue 13, p. 1904, Accession no. A76-29457)

## Projects

Project (1)

Исследуется динамическая устойчивость колеблющейся пластины с шарнирно закрепленными концами, являющейся частью стенки прямолинейного канала, по которому протекает идеальная несжимаемая жидкость