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    Wyświetlanie 1-10 z 10
    Tytuł:
    A Jurdjevic-Quinn theorem for stochastic differential systems under weak conditions
    Autorzy:
    Florchinger, Patrick
    Powiązania:
    https://bibliotekanauki.pl/articles/2183489.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    stochastic differential system
    weak solution of stochastic differential equation
    asymptotic stability in probability
    Barbashin–Krasovskii theorem
    stabilizing state feedback law
    Opis:
    The purpose of this paper is to provide sufficient conditions for the stabilizability of weak solutions of stochastic dif- ferential systems when both the drift and diffusion are affine in the control. This result extends the well–known theorem of Jurdjevic–Quinn (Jurdjevic and Quinn, 1978) to stochastic differential systems under weaker conditions on the system coefficients than those assumed in Florchinger (2002).
    Źródło:
    Control and Cybernetics; 2022, 51, 1; 21--29
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solving linear Fredholm integro-differential equation by Nyström method
    Autorzy:
    Tair, Boutheina
    Guebbai, Hamza
    Segni, Sami
    Ghiat, Mourad
    Powiązania:
    https://bibliotekanauki.pl/articles/1839836.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Fredholm integral equation
    system of integral equations
    integro-differential equations
    Nyström method
    równanie całkowe Fredholma
    układ równań całkowych
    równanie całkowo-różniczkowe
    metoda Nyströma
    Opis:
    The study of the solution’s existence and uniqueness for the linear integro-differential Fredholm equation and the application of the Nyström method to approximate the solution is what we will present in this paper. We use the Neumann theorem to construct a sufficient condition that ensures the solution’s existence and uniqueness of our problem in the Banach space C1 [a,b]. We have applied the Nystrom method based on the trapezoidal ¨ rule to avoid adding other conditions in order to the approximation method’s convergence. The Nyström method discretizes the integro-differential equation into solving a linear system. Only with the existence and uniqueness condition, we show the solution’s existence and uniqueness of the linear system and the convergence of the numerical solution to the exact solution in infinite norm sense. We present two theorems to give a good estimate of the error. Also, to show the efficiency and accuracy of the Nyström method, some numerical examples will be provided at the end of this work.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 3; 53-64
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Pseudo-differential equations and conical potentials: 2-dimensional case
    Autorzy:
    Vasilyev, Vladimir B.
    Powiązania:
    https://bibliotekanauki.pl/articles/255700.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    pseudo-differential equation
    wave factorization
    Dirichlet problem
    system of linear integral equations
    Opis:
    We consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and then after some transformations to a system of linear algebraic equations. The unique solvability for the Dirichlet problem was proved in Sobolev-Slobodetskii spaces and a priori estimate for the solution is given.
    Źródło:
    Opuscula Mathematica; 2019, 39, 1; 109-124
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Feedback design of differential equations of reconstruction for second-order distributed parameter systems
    Autorzy:
    Maksimov, V. I.
    Mordukhovich, B. S.
    Powiązania:
    https://bibliotekanauki.pl/articles/330817.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    partial differential equation
    equations of reconstruction
    distributed parameter system
    równanie różniczkowe cząstkowe
    układ o parametrach rozłożonych
    równanie drugiego rzędu
    Opis:
    The paper aims at studying a class of second-order partial differential equations subject to uncertainty involving unknown inputs for which no probabilistic information is available. Developing an approach of feedback control with a model, we derive an efficient reconstruction procedure and thereby design differential equations of reconstruction. A characteristic feature of the obtained equations is that their inputs formed by the feedback control principle constructively approximate unknown inputs of the given second-order distributed parameter system.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2017, 27, 3; 467-475
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A proposition of a torsional-bending vibrations modelling of combustion engines
    Autorzy:
    Dąbrowski, Z.
    Chiliński, B.
    Pankiewicz, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/244766.pdf
    Data publikacji:
    2016
    Wydawca:
    Instytut Techniczny Wojsk Lotniczych
    Tematy:
    rotational system
    system of differential equation
    crankshaft system
    numerical solutions
    Opis:
    The article presents the problem of modelling coupled bending-torsional vibrations in crank systems. Because during the design of modern drive systems a growing number of phenomena are taken into account, model description of such vibrations has a practical meaning. Commonly used models of dynamics of systems assume the independence of torsional and bending vibrations, which leads to simultaneous analysis of transverse and angular vibrations. Further analysis is carried out with the use of superposition principle. Such an approach is justified in the case of quite rigid drive shafts, where vibrations are relatively small. Current trends in the design of reducing weight, reduction of toxic emissions and reducing fuel consumption, lead to the situation where shafts in crank systems become less stiff. Therefore, phenomena neglected earlier may have significant meaning. Analysis of couplings of transverse and torsional vibrations is so important that the occurrence of these phenomena usually leads to new critical states, which may be especially dangerous for engine operation. Considerations on the reasons of the occurrence and kinds of vibration couplings were presented in the introduction of the article. Further part of the article proposes the linear-bending model of the crankshaft, where transverse and angular displacements are dependent. It was tantamount to the assumption of linear relation between the vector of generalized co-ordinates and generalized forces occurring in the system. The next chapter presents the system of equations describing the dynamics of the crankshaft together with a discussion of the co-ordinate system used in the considerations. In addition, there were presented the results of numerical simulations in frequency domain confirming the conclusions taken from the analysis. The whole paper is concluded with synthetic conclusions on the formulated system of equations, simulations and the influence of the coupling on the dynamics of the whole crank system.
    Źródło:
    Journal of KONES; 2016, 23, 4; 71-77
    1231-4005
    2354-0133
    Pojawia się w:
    Journal of KONES
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Coupled lateral-torsional vibrations of a symmetric rotor
    Autorzy:
    Chiliński, B.
    Pakowski, R.
    Stanik, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/245654.pdf
    Data publikacji:
    2016
    Wydawca:
    Instytut Techniczny Wojsk Lotniczych
    Tematy:
    rotational system
    nonlinear differential system of equation
    perturbation method
    critical states
    analytical solutions
    Opis:
    The paper presents a cross-sectional analysis of dynamics of rotating systems with different characteristics, starting from the search for solutions in an analytical way, and ending with the numerical attempt to verify the results. There is presented a problem of bending and torsional vibrations in rotational systems, using possibly the simplest model of the phenomenon. It is a heavy disk embedded on the deformable massless shaft. The rotor is symmetric and it is assumed that stiffness can be nonlinear. The analysis of vibrations occurring in rotors is made with the use of this model. This is followed by a preliminary discussion on the problem and the conclusions of the pilot studies. There are presented basic problems related to the phenomenon of lateral-torsional coupling in rotational systems with an emphasis on critical states. Formulation of the problem is the conclusion of preliminary part of the paper. Next, there are discussed the selected methods currently used to solve such problems, together with a discussion of their application in this case. In addition, there is discussed a problem of numerical or analytical character of obtained results and the range of using methods in modelling, designing and experimental studies. The next part of the paper focuses on the solution of the model presented in the introduction, using the following analytical or numerical methods: Krylov-Bogolubov, Adams and Runge-Kutta methods. There are presented assumptions, simplifications of the model, technical details of searching for solutions and the results together with a discussion of their correctness. The results, which were obtained from analysis, are polyharmonic. Due to this fact, the spectra of each solution were presented. These aspects are discussed in the context of the solving methods and motion analysis for rotor systems. The whole paper is summarized with a discussion of the results and their confrontation with reality.
    Źródło:
    Journal of KONES; 2016, 23, 4; 41-47
    1231-4005
    2354-0133
    Pojawia się w:
    Journal of KONES
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The analysis of the influence of a torsional vibration damper on transversal displacement of a crankshaft
    Autorzy:
    Chiliński, B.
    Dziurdź, J.
    Zawisza, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/949500.pdf
    Data publikacji:
    2016
    Wydawca:
    Instytut Techniczny Wojsk Lotniczych
    Tematy:
    crankshaft system
    torsional vibrations damper system of differential equation
    numerical simulations
    Opis:
    The article presents a consideration of the influence of a damper of torsional vibrations (TVD) on transverse dynamics of the crankshaft. Dampers of this type work based on the dynamic eliminator of vibrations. The systems of this type in modern combustion engines are more often used to reduce torsional vibrations. It is strictly connected with the increase of fatigue life of the crankshaft in case when its amplitude of vibrations has a crucial meaning. Computation models used to choose a damper assume that transverse and torsional vibrations occurring in a crank system are not coupled. Modern trends in machine design make the new devices lighter and less rigid. Therefore, the couplings between small vibrations may be more important. Therefore, the effects observed in angular vibrations can be transmitted to transverse vibrations. In this context, the impact of dampers TVD on transverse dynamics is particularly interesting. In the introduction, the article discusses the basic types of torsional vibration dampers and the method of selection of this type of systems. The next part of the article presents the model of a combustion engine with a dynamic eliminator of vibrations, which includes bending-torsional vibrations occurring in the system. For this purpose, the linear relation of the vector of generalized co-ordinates and generalized forces in the system was assumed. The next part shows numerical simulations, which were carried out in the paper. The paper presents obtained results with their further analysis in frequency domain. The whole paper is summarized with synthetic conclusions on the simulations, the impact of applied eliminator on the dynamics of the entire crank system, in particular transverse vibrations. In addition, there was indicated a possibility of using presented results in research and diagnostics used in automotive industry of torsional vibration dampers.
    Źródło:
    Journal of KONES; 2016, 23, 4; 33-39
    1231-4005
    2354-0133
    Pojawia się w:
    Journal of KONES
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Combined algorithm for finding conservation laws and implectic operators for the Boussinesq-Burgers nonlinear dynamical system and its finite dimensional reductions
    Autorzy:
    Kindybaliuk, A.
    Prytula, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/122896.pdf
    Data publikacji:
    2014
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    nonlinear dynamical system
    conservation laws
    implectic operators
    method of undetermined coefficients
    differential algebraic algorithm
    combined algorithm
    finite dimensional reduction
    Hamiltonian system
    exact solutions
    Boussinesq-Burgers equation
    nieliniowy układ dynamiczny
    prawa zachowania
    algebraiczny algorytm różniczkowy
    system Hamiltona
    rozwiązania dokładne
    równanie Boussinesqa-Burgersa
    Opis:
    In the article the combined algorithm for finding conservation laws and implectic operators has been proposed. Using the Novikov-Bogoyavlensky method the finite dimensional reductions have been found. The structure of invariant submanifolds has been examined. Having analyzed phase portraits of Hamiltonian systems, partial periodical solutions have been found.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 3; 85-99
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor
    Autorzy:
    Nowak, T. K.
    Duzinkiewicz, K.
    Piotrowski, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/229399.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional differential equation
    fractional derivatives and integrals
    system of equations
    nuclear reactor
    neutron point kinetics
    Opis:
    This paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme in the FOMCON Toolbox in MATLAB environment. Third is the method proposed by Edwards. The impact of selected parameters on the model’s response was examined. The results for typical input were discussed and compared.
    Źródło:
    Archives of Control Sciences; 2014, 24, 2; 129-154
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of disturbance torque influence on critical state in rotational systems
    Analiza wpływu zaburzenia momentu skręcającego na stany krytyczne układów wirujących
    Autorzy:
    Chiliński, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/375562.pdf
    Data publikacji:
    2013
    Wydawca:
    Politechnika Śląska. Wydawnictwo Politechniki Śląskiej
    Tematy:
    rotational system
    nonlinear differential system of equation
    analytical solutions
    Galerkin method
    system rotacyjny
    nieliniowe równania układu różnicowego
    metoda Galerkina
    stany krytyczne
    rozwiązania analityczne
    Opis:
    Currently most of existing means of transport contains different types of rotational systems. In many cases the dynamics of such rotors substantially can influence exploitation of the whole vehicle. Moreover, in order to minimize mass of the whole object modern construction materials are applied. This causes that the dynamic phenomena may be fundamental of exploitation. The paper presents preliminary analysis of disturbance torque influence on critical state in rotational system. The consideration assumed simple physical object in the form of heavy disk embedded on weightless, elastic shaft. The shaft was supported on two bearings. In particular chapters of paper, path leading from proposition of physical model, by solution of it, to qualitative conclusions about considered object and torque disturbances influence of motion of this system, was presented. In introduction, outline of considered problem and potential opportunities of it, were demonstrated. In the next chapter, physical and mathematical model of the analysed object, was described. Next and also the last but one chapter gives a detailed discussion of mathematical model in the form of nonlinear ordinary differential equations proposed earlier. The first part of the chapter presents the possibility to solve such a problem, then it shows the simplifications which are used. Furthermore, the influence of used simplifications on the shape of analysed problem was demonstrated. Additionally, the possibility of equations solution presented in the paper was discussed. Moreover, the series of interesting properties of analysed system of equations has been shown based on founded approximate solutions. The whole paper was summarized with plans for future work and synthetic conclusions concerning the innovative control method of critical states.
    Aktualnie większość istniejących środków transportu zawiera różnego typu układy wirujące. W wielu przypadkach dynamika takich wirników w istotny sposób wpływa na eksploatacje całego pojazdu. Ponadto w celu zminimalizowania masy całego obiektu stosuje się nowoczesne materiały konstrukcyjne. To powoduje, że zjawiska dynamiczne, mogą mieć podstawowe znaczenie eksploatacyjne. Artykuł przedstawia wstępną analizę wpływu zaburzenia momentu skręcającego na stany krytyczne układu wirującego. Do rozważań przyjęto prosty obiekt fizyczny w postaci ciężkiego krążka osadzonego na nieważkim podatnym wale podpartym w dwóch łożyskach. W poszczególnych rozdziałach artykułu przedstawiono drogę prowadzącą od zaproponowania modelu fizycznego, przez jego rozwiązanie do jakościowych wniosków o rozpatrywanym obiekcie i wpływie zaburzenia momentu skręcającego na jego ruch. We wstępie przedstawiono zarys rozpatrywanego problemu oraz potencjalne możliwości wykorzystania opracowanego zagadnienia. W kolejnym rozdziale zaprezentowano model fizyczny oraz matematyczny dla obiektu będącego podstawą niniejszego artykułu. Następny i zarazem przedostatni rozdział w sposób szczegółowy przedstawia dyskusję zaproponowanego wcześniej modelu matematycznego w postaci układu nieliniowych równań różniczkowych zwyczajnych. Na początku rozdziału przedstawiono rozwiązywalność takiego zagadnienia, następnie opisano zastosowane uproszczenia. W dalszym ciągu zademonstrowano wpływ zastosowanych uproszczeń na kształt analizowanych równań. Dodatkowo podjęto dyskusję o możliwości rozwiązania równań przedstawionych w pracy. Ponadto na podstawie znalezionych przybliżonych rozwiązań wykazano szereg ciekawych własności analizowanego układu równań. Całość została podsumowana celami dalszej pracy oraz syntetycznymi wnioskami, dotyczącymi propozycji innowacyjnej metody sterowania stanami krytycznymi.
    Źródło:
    Transport Problems; 2013, 8, 4; 137-146
    1896-0596
    2300-861X
    Pojawia się w:
    Transport Problems
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-10 z 10

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