scholarly journals The Problem of Damping the Transverse Oscillations on a Longitudinally Moving String

2018 ◽  
pp. 472-485
Author(s):  
Leonid A. Muravey ◽  
Victor M. Petrov ◽  
Alexandr M. Romanenkov
Keyword(s):  
Hyperbolic Equation ◽  
Moment Problem ◽  
Classical Method ◽  
Vertical Section ◽  
Basic Research ◽  
Generalized Solution ◽  
Trigonometric System ◽  
Time Interval ◽  
Coriolis Acceleration ◽  
Transverse Oscillations

Introduction. The problem under consideration is relevant to production processes associated with the longitudinal movement of materials, for example, for producing paper webs. For these processes transverse disturbances, which in the vertical section are described by the hyperbolic equation of a longitudinally moving string, are extremely undesirable. That gives the problem of damping these oscillations within a finite time. Materials and Methods. To solve the problem of damping the oscillations, the authors suggest reducing it to the trigonometric problem of the moments at an arbitrary time interval. When considering moving materials, the construction of the basis systems forming the moment problem is a special challenge, since the hyperbolic equation contains a mixed derivative (Coriolis acceleration). Therefore, the classical method of separating variables is not applicable in this case. Instead, a new method is used to find self-similar solutions of non-stationary equations, which makes it possible to find the basis systems explicitly. Results. In the case of paper web, it is necessary to find a minimal in the whole class of admissible perturbations time interval, within which the trigonometric system forming the problem of moments is the Riesz basis, that make it possible through using the system conjugate with it to find the optimal control way in the form of a series and, therefore, to build a so-called optimal damper. Conclusions. As a result of the study, a generalized solution of the problem of transverse oscillations is constructed. For the problem of damping oscillations, the exact damping time is obtained, namely, a time T0 at which the total energy of the system is zero. Optimum control is found in the form of a Fourier series. Keywords: damping oscillations, hyperbolic equation, Coriolis acceleration, trigonometric moment problem, Riesz base For citation: Muravey L. A., Petrov V. M., Romanenkov A. M. The Problem of Damping the Transverse Oscillations on a Longitudinally Moving String. Vestnik Mordovskogo universiteta = Mordovia University Bulletin. 2018; 28(4):472–485. DOI: https://doi.org/10.15507/0236-2910.028.201804.472-485 Acknowledgements: The work was supported by grant No. 16-01-00425 A from the Russian Foundation for Basic Research.

scholarly journals On initial boundary value problem with Dirichlet integral conditions for a hyperbolic equation with the Bessel operator

2003 ◽  
Vol 2003 (10) ◽  
pp. 487-502
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
Hyperbolic Equation ◽  
A Priori ◽  
Weighted Sobolev Spaces ◽  
A Priori Estimate ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Generalized Solution ◽  
Bessel Operator ◽  
Integral Conditions ◽  
Initial Boundary Value

We consider a mixed problem with Dirichlet and integral conditions for a second-order hyperbolic equation with the Bessel operator. The existence, uniqueness, and continuous dependence of a strongly generalized solution are proved. The proof is based on an a priori estimate established in weighted Sobolev spaces and on the density of the range of the operator corresponding to the abstract formulation of the considered problem.

scholarly journals Synthesis of controllers for electromechanical tracking systems

2018 ◽  
Vol 28 (4) ◽  
pp. 47-51
Author(s):  
Yu. P. Korniushin ◽  
A. V. Mazin
Keyword(s):  
Moment Problem ◽  
Controller Design ◽  
Tracking Error ◽  
Control Object ◽  
Main Element ◽  
Current Phase ◽  
Time Interval ◽  
Initial State ◽  
Final State ◽  
Servo Systems

The article presents an algorithm for the synthesis of regulators for servomechanisms, in which the control object is linear. The algorithm is focused on electromechanical systems, the main element of which is a controlled electric drive. The synthesis algorithm is based on the use of the L–Markov moment problem. The advantage of the proposed algorithm with respect to the others is that the regulators synthesized on its basis ensure the minimization of energy for the objects control. The essence of the proposed algorithm of synthesis is that the control, according to the provisions underlying the L – moment problem, can be determined not only through the system of moment functions, but also through the moments. The latter depends both on the time interval during which the object is transferred from the initial state to the final state, but also on the state of the object itself. To solve the problem of controller design for servo systems, the following is proposed: 1. Explicitly express management through moments. 2. Perform «unfreezing» the initial and final states of the object. When «unfreezing» the initial state of the object is considered to be the current phase, and the final state is determined by the monitored signal. The time interval during which the object is transferred from one state to another is set arbitrarily in the general case. However, the longer this interval, the smaller the control rate, but, respectively, the greater the tracking error.

scholarly journals On the Gevrey well-posedness for second order strictly hyperbolic Cauchy problems under the influence of the regularity of the coefficients

2008 ◽  
Vol 102 (2) ◽  
pp. 283 ◽  
Author(s):  
Massimo Cicognani ◽  
Fumihiko Hirosawa
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Equation ◽  
Second Order ◽  
Time Interval ◽  
Well Posedness ◽  
Cauchy Problems ◽  
End Point ◽  
Stabilization Condition ◽  
Loss Of Regularity

We consider the loss of regularity of the solution to the backward Cauchy problem for a second order strictly hyperbolic equation on the time interval $[0,T]$ with time depending coefficients which have a singularity only at the end point $t=0$. The main purpose of this paper is to show that the loss of regularity of the solution on the Gevrey scale can be described by the order of differentiability of the coefficients on $(0,T]$, the order of singularities of each derivatives as $t\to0$ and a stabilization condition of the amplitude of oscillations described by an integral on $(0,T)$. Moreover, we prove the optimality of the conditions for $C^\infty$ coefficients on $(0,T]$ by constructing a counterexample.

scholarly journals ON CERTAIN NONLOCAL PROBLEM FOR HYPERBOLIC EQUATION WITH INTEGRAL CONDITIONS OF THE FIRST KIND

2017 ◽  
Vol 17 (5) ◽  
pp. 29-36
Author(s):  
A.V. Duzheva
Keyword(s):  
Hyperbolic Equation ◽  
Existence And Uniqueness ◽  
Nonlocal Problem ◽  
Integral Condition ◽  
Generalized Solution ◽  
Integral Conditions

In this article, we consider a nonlocal problem for hyperbolic equation with integral conditions of the first kind. The main goal of this article is to show the method which allows to reduce posed problem to the problem with integral condition of the second kind. Existence and uniqueness of generalized solution is proved.

scholarly journals Morphological Characteristics of Different Rates of Dying

2018 ◽  
Vol 14 (4) ◽  
pp. 35-43 ◽  
Author(s):  
V. A. Putincev ◽  
D. V. Bogomolov ◽  
D. V. Sundukov
Keyword(s):  
Statistical Analysis ◽  
Classical Method ◽  
Scientific Evidence ◽  
Morphological Characteristics ◽  
Time Interval ◽  
Forensic Practice ◽  
Morphological Criteria ◽  
Study Results ◽  
First Time ◽  
Further Development

The purpose of the study: scientific evidence and development of accessible morphological criteria that allow to determine the duration of dying and the rate of dying.Materials and methods. The material of the main study included 206 identified deaths of persons with different pre-known processes of dying, which served as criterion for selection from1500 deaths (n=206, 14%). Of these, 110 cases were observed by the forensic medical expertize, 79 cases were revealed by the forensic medical examination of the dead body and 17 cases were included after the postmortem autopsy. The sample included from 30 to 57 cases subdivided in 5 groups. 53 cases were selected for the first time interval, 30 observations for the second one, 32 observations for the third one, 34 observations for the fourth one and 57 observations for the fifth time interval. The following methods were used to study the material: analysis of information about the circumstances of death (based on the records), retrospective clinical and anatomical analysis, the main (classical) method of autopsy of human corpses in sectional studies and histological examination. In addition, an immunohistochemical test, as well as morphometric, macroscopic and photographic methods were used. For the accuracy and reliability of the findings, morphological and statistical analysis was used, which included both statistical analysis of morphological characteristics and tanatogenetic analysis of the cases of the sampled material.Study results. We developed and scientifically proved a methodology for determining 5 rates of dying according to the morphological characteristics systematized in morphological complexes: fulminant rate ≤15-30 min; fast rate >30 min — ≤2 h; moderate rate >2 — ≤6 h; slow rate >6 — ≤12 h; lingering rate >12 h. Approbation of the proposed method on the gross experimental material allowed to set the diagnostic limit of the total significance for each morphological complex, and thereby, to improve the methodology of establishing the rate of dying in accordance to the morphological characteristics for the use in forensic practice.Conclusion. The morphological complexes of the rate of dying established in this work would serve as a base for further development of not only forensic thanatology, but also for the aim of improving the medical and preventive care.

scholarly journals ON SMOOTHNESS OF SOLUTION OF ONE NONLOCAL PROBLEM FOR HYPERBOLIC EQUATION

2021 ◽  
Vol 26 (2) ◽  
pp. 15-22
Author(s):  
V. A. Kirichek
Keyword(s):  
Hyperbolic Equation ◽  
Nonlocal Problem ◽  
Generalized Solution ◽  
Integral Boundary ◽  
Apriori Estimates ◽  
The Space L2 ◽  
Elastic Fixation ◽  
The Right ◽  
Derivatives Of ◽  
Smoothness Of Solution

In this paper we consider a nonlocal problem with integral boundary condition for hyperbolic equation. The conditions of the problem contain derivatives of the first order with respect to both x and t,, which can be interpreted as an elastic fixation of the right end rod in the presence of a certain damper, and since the conditions also contain integral of the desired solution, this condition is nonlocal. It is known that problems with nonlocal integral conditions are non-self-adjoint and, therefore, the study of solvability encounters difficulties that are not characteristic of self-adjoint problems. Additional difficulties arise also due to the fact that one of the conditions is dynamic. The attention of the article is focused on studying thesmoothness of the solution of the nonlocal problem. The concept of a generalized solution is introduced, and the existence of second-order derivatives and their belonging to the space L2 are proved. The proof is basedon apriori estimates obtained in this work.

Development of a domestic methodology for assessing the risks of acid effluent formation during storage and use of wastes from coal mining and processing

2021 ◽  
pp. 107-112
Author(s):  
T. O. Gushchina ◽  
E. E. Sokolovskaya ◽  
Hao Jie ◽  
S. A. Epshtein
Keyword(s):  
Classical Method ◽  
Basic Research ◽  
Preliminary Assessment ◽  
Neutralization Potential ◽  
Static Test ◽  
Water Formation ◽  
The Russian Federation ◽  
Basic Research Grant ◽  
Acidic Wastewater ◽  
Research Grant

It is shown that the main ecologically significant characteristics of wastes from mining and processing of coal, which are considered when assessing their impact on the environment, are the indicators reflecting the risks of acidic water formation and leaching of macro- and microelements from rocks. A review of the methods used abroad to determine the risks of formation of acidic effluents during storage or use of wastes is carried out. It is shown that at present in the Russian Federation there is no regulatory support for assessing this indicator in wastes from mining, processing and combustion of coals. It is noted that for a preliminary assessment of the risks of acidic wastewater drainage, the most common method for determining the neutralization potential of waste is the so-called A. Sobek static test (ABA). The main stages of the development of the domestic method for determining the potential of neutralization in waste are presented and its approbation is carried out on existing research objects. The developed methodology takes into account the main provisions of the classical method for determining the neutralization potential of A. Sobek and makes additions to the procedure for testing of the samples, which makes it possible to increase the accuracy of the obtained results and extend the domestic methodology not only to wastes from mining and benefication of coals, but also to wastes from combustion and processing of coal, such as fly ash, slag and ash and slag wastes. The study was supported by the Russian Foundation for Basic Research, Grant No. 19-35-90117.

Transient Surface Strains and the Deconvolution of Thermoelastic States and Boundary Conditions

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
A. E. Segall ◽  
D. Engels ◽  
A. Hirsh
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Analytical Solutions ◽  
A Priori ◽  
Generalized Solution ◽  
Time Interval ◽  
Thermal Excitation ◽  
Unknown Boundary ◽  
Stress States ◽  
Natural Boundaries

Thermoelastic states as they pertain to thermal-shock are difficult to determine since the underlying boundary conditions must be known or measured. For direct problems where the boundary conditions such as temperature or flux, are known a priori, the procedure is mathematically tractable with many analytical solutions available. Although this is more practical from a measurement standpoint, the inverse problem where the boundary conditions must be determined from remotely determined temperature and/or flux data are ill-posed and therefore inherently sensitive to errors in the data. Moreover, the limited number of analytical solutions to the inverse problem rely on assumptions that usually restrict them to timeframes before the thermal wave reaches the natural boundaries of the structure. Fortunately, a generalized solution based on strain-histories can be used instead to determine the underlying thermal excitation via a least-squares determination of coefficients for generalized equations for strain. Once the inverse problem is solved and the unknown boundary condition on the opposing surface is determined, the resulting polynomial can then be used with the generalized direct solution to determine the thermal- and stress-states as a function of time and position. For the two geometries explored, namely a thick-walled cylinder under an internal transient with external convection and a slab with one adiabatic surface, excellent agreement was seen with various test cases. The derived solutions appear to be well suited for many thermal scenarios provided that the analysis is restricted to the time interval used to determine the polynomial and the thermophysical properties that do not vary with temperature. While polynomials were employed for the current analysis, transcendental functions and/or combinations with polynomials can also be used.

scholarly journals ABOUT SOLVABILITY OF ONE PROBLEM WITH NONLOCAL CONDITIONS FOR HYPERBOLIC EQUATION

2021 ◽  
Vol 26 (4) ◽  
pp. 36-43
Author(s):  
V. A. Kirichek
Keyword(s):  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Nonlocal Problem ◽  
Nonlocal Conditions ◽  
Integral Condition ◽  
Generalized Solution ◽  
Loaded Equation ◽  
Apriori Estimates ◽  
The Given

In this article we consider a nonlocal problem with integral condition of the second kind for hyperbolic equation. The choice of a method for investigating problems with nonlocal conditions of the second kind depends on the type of nonintegral terms. In this article we consider the case when the nonintegral term is a trace of required function on the boundary of the domain. To investigate the solvability of the problem we use method of reduction for loaded equation with homogeneous boundary conditions. This method proved to be effective for defining a generalized solution, to obtain apriori estimates and to prove existence of unique generalized solution of the given problem.

scholarly journals INITIAL-BOUNDARY VALUE PROBLEM FOR ONE-DIMENSION HYPERBOLIC EQUATION WITH INTEGRAL BOUNDARY CONDITION

2017 ◽  
Vol 17 (8) ◽  
pp. 95-101
Author(s):  
M.V. Strigun
Keyword(s):  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Boundary Value ◽  
Integral Condition ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Generalized Solution ◽  
Integral Boundary ◽  
Nonlocal Integral Condition ◽  
Initial Boundary Value

In this paper, we study an initial-boundary value problem with nonlocal integral condition for a hyperbolic equation. The existence and uniqueness of a generalized solution of the problem is proved.

Sign in / Sign up

Export Citation Format

Share Document