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EN
The article describes the new oscillation criteria which improves the existing results for the third order neutral delay difference equation with the negative coefficient in the neutral term is obtained. Where are positive sequences.
PL
W artykule opisano nowe kryteria oscylacji, które poprawiają dotychczasowe wyniki dla równania różnicy opóźnienia neutralnego trzeciego rzędu z ujemnym współczynnikiem w członie neutralnym. Gdzie są sekwencje dodatnie.
2
Content available remote Fourth order qualitative inspection of nonlinear neutral delay difference equation
EN
This paper aim is to investigate the nonlinear neutral fourth order difference equation in the form. We establish some conditions to assure that all solutions to this equation are oscillatory or nonoscillatory. We derived this using summation averaging technique and comparison principle. The main outcomes are illustrated using examples.
PL
W artykule badano nieliniowe równanie różnicowe czwartego rzędu. Ustalamy pewne warunki, aby zapewnić, że wszystkie rozwiązania tego równania są oscylacyjne lub nieoscylacyjne. Wyprowadziliśmy to za pomocą techniki uśredniania sumowania i zasady porównania. Główne wyniki zilustrowano na przykładach.
EN
A Heat Exchanger is a secondary process unit that is widely needed in the chemical process industry. This equipment is used to exchange heat between two types of fluids that have different temperatures. The existence of several physical events that change the characteristics of the process causes the stability of the system to be disturbed that necessitates to control the changes in the process parameters. PID controllers are actually conventional controllers which, due to their relatively good condition and easy operation, are still widely used. Many methods have been introduced to analyze PID control parameters, including the Rungge-Kutta method. However, the controlling operators in an industrial process, in order to get good control performance in every industrial process in the event of overshoot or oscillation, adjust the control parameters manually through the trial and error method. For this reason, we need a technique that is able to adapt to changes in process parameters that occur, and at the same time perform automatic re-tuning of controlling parameters. This paper describes a program designed to form an oscillation and reduction curve with a PID controller on a heat exchanger. The design of this program must at least be in accordance with the dynamics of the actual events in the field. the results of the oscillation curve reduction program design which are quite good are the one with the 'PI' controller type as compared to those with the 'P' and 'PID' controller types. The results of the one with the control type 'P' are not good because the process variable (process temperature) is not close to the set. o be used for operator training in industrial processes in the event of disturbances in the form of oscillations.
PL
Wymiennik ciepła jest drugorzędną jednostką procesową, która jest powszechnie potrzebna w przemyśle chemicznym. To urządzenie służy do wymiany ciepła między dwoma rodzajami płynów, które mają różne temperatury. Istnienie kilku zdarzeń fizycznych zmieniających charakterystykę procesu powoduje zaburzenie stabilności systemu, co wymusza kontrolowanie zmian parametrów procesu. Regulatory PID to właściwie regulatory konwencjonalne, które ze względu na stosunkowo dobry stan techniczny i łatwą obsługę nadal znajdują szerokie zastosowanie. Wprowadzono wiele metod analizy parametrów regulacji PID, w tym metodę Rungge-Kutty. Jednak operatorzy kontrolujący w procesie przemysłowym, w celu uzyskania dobrej wydajności sterowania w każdym procesie przemysłowym w przypadku przeregulowania lub oscylacji, dostosowują parametry sterowania ręcznie metodą prób i błędów. Z tego powodu potrzebujemy techniki, która jest w stanie dostosować się do zachodzących zmian parametrów procesu, a jednocześnie wykonać automatyczne przestrojenie parametrów sterujących. W artykule opisano program przeznaczony do tworzenia krzywej oscylacji i redukcji z regulatorem PID na wymienniku ciepła. Projekt tego programu musi być przynajmniej zgodny z dynamiką rzeczywistych wydarzeń w terenie. wyniki projektu programu redukcji krzywej oscylacji, które są dość dobre, to te z regulatorem typu „PI” w porównaniu z tymi z regulatorami typu „P” i „PID”. Wyniki tego ze sterowaniem typu „P” nie są dobre, ponieważ zmienna procesowa (temperatura procesu) nie jest zbliżona do zadanej. o być używany do szkolenia operatorów w procesach przemysłowych w przypadku zakłóceń w postaci oscylacji.
EN
The article provides an analysis of the physical processes underlying the operation of the measuring transducer, with a time based information presentation. A mathematical model is developed that describes the process of free oscillation attenuation excited in the LC-contour of primary measuring transducer, and analyzes and evaluates the influence of external factors that influence the measurement results. The ways of elimination of their influence on the results of measuring control are offered.
PL
Artykuł zawiera analizę procesów fizycznych leżących u podstaw pracy przetwornika pomiarowego wraz z prezentacją informacji w czasie. Opracowano model matematyczny opisujący proces tłumienia drgań swobodnych wzbudzanych w obwodzie LC głównego przetwornika pomiarowego, analizujący i oceniający wpływ czynników zewnętrznych na wyniki pomiarów. Proponowane są sposoby wyeliminowania ich wpływu na wyniki kontroli pomiarów.
5
Content available remote Asymptotic behavior of even-order noncanonical neutral differential equations
EN
In this article, we study the asymptotic behavior of even-order neutral delay differential equation (a⋅(u+ρ⋅u∘τ)(n−1))′(ℓ)+h(ℓ)u(g(ℓ))=0,ℓ≥ℓ0, where n≥4, and in noncanonical case, that is, ∞∫a−1(s)ds<∞. To the best of our knowledge, most of the previous studies were concerned only with the study of n-order neutral equations in canonical case. By using comparison principle and Riccati transformation technique, we obtain new criteria which ensure that every solution of the studied equation is either oscillatory or converges to zero. Examples are presented to illustrate our new results.
6
Content available remote Experimental research of oscillation parameters of vibrating-rotor crusher
EN
In article experimental model and specifications Vibrating-Rotor Crusher for grinding feed grain are present. Crusher implements the idea of the combined interaction of vibration and rotational motion of executive bodies, which can significantly increase the power to influence material. To determine the range of the operating parameters of the machine was carried out experimental studies of the amplitude-frequency characteristics of the developed machine depending on the angular velocity of the drive shaft.
PL
Przedstawiono model i badania rozdrabniacza z wibrującym wirnikiem do ziaren paszy. Rozdrabniacz łączy wibrowanie I obracanie co znacząco poprawia jakość pracy. Badano zależność częstotliwości I amplitudy od prędkości kątowej.
EN
The aim of the work is to develop algorithms and a set of programs for studying the dynamic characteristics of viscoelastic thin plates on a deformable base on which it is installed with several dynamic dampers. The theory of thin plates is used to obtain the equation of motion for the plate. The relationship between the efforts and the stirred plate obeys in the hereditary Boltzmann Voltaire integral. With this, a system of integro-differential equations is obtained which is solved by the method of complex amplitudes. As a result, a transcendental algebraic equation was obtained to determine the resonance frequencies, which is solved numerically by the Muller method. To determine the displacement of the point of the plate with periodic oscillations of the base of the plate, a linear inhomogeneous algebraic equation was obtained, which is solved by the Gauss method. The amplitude - frequency response of the midpoint of the plate is constructed with and without regard to the viscosity of the deformed element. The dependence of the stiffness of a deformed element on the frequency of external action is obtained to ensure optimal damping of vibrational vibrations of the plate.
EN
This paper describes a question of evaluation necessity of bridge cranes using the method of limit deformation state and oscillation damping. The solution was performed by means of theoretical analysis and an experimental verification at the selected bridge crane. The final result sounds that in the case of a correct strength computing of given bridge crane, it is not necessary to also check deformation and damping of oscillation as well.
EN
The working process and regularities of the functioning of vibrating and vibro-impact machines based on hydroimpulse drive with a singlestage valve pulser are analyzed. The essential characteristics determining the conditions for the excitation and existence of periodic oscillations of the valve-pulser shut-off valve are determined. Using the criterion of A. Hurwitz, based on the differential equation of motion, the existence of undamped periodic oscillations of the valve-pulser shut-off valve is analytically justified.
PL
Przeanalizowano działanie i regularność pracy maszyn wibracyjnych oraz maszyn poddawanych wibracjom opartych na napędzie hydro-impulsowym z jednostopniowym zaworem impulsowym. Określono podstawowe cechy wpływające na warunki wzbudzenia oraz występowania drgań okresowych zaworu impulsowego. Przy zastosowaniu kryterium A. Hurwitza, opartego na równaniu różniczkowym ruchu, istnienie nietłumionych drgań okresowych zaworu impulsowego jest analitycznie uzasadnione.
EN
This paper deals with the oscillation of a certain class of second order difference equations with a sub-linear neutral term. Using some inequalities and Riccati type transformation, four new oscillation criteria are obtained. Examples are included to illustrate the main results.
11
EN
The springing support in a driver’s seat is a very serious issue, such that manufacturers are increasing their efforts to optimize the dynamic properties of this kind of seat. The main optimization criterion is vibration insulation efficiency with regard to health research and associated health standards and regulations. This article deals with the definition of the optimal driver’s seat properties in relation to two examples of springing systems with different kinds of damping. The first case involves the springing support of a driver’s seat that uses a pneumatic spring and a telescopic hydraulic damper. In the second case, the damping effect is achieved by two pneumatic springs whose forces effect a phase shift due to a throttle valve located in the connecting piping system.
12
Content available remote Oscillation of higher-order half-linear neutral differential equations
EN
In this paper, we establish some new oscillation criteria for the higher-order half-linear neutral differential equation (…). An example is given to illustrate the main results.
EN
An unsteady hydromagnetic Couette flow of class-II of a viscous incompressible electrically conducting fluid in a rotating system is studied. The fluid flow within the channel is induced due to non-torsional oscillations of the upper plate of the channel. An exact solution of the governing equations is obtained by the Laplace transform technique. The numerical solution of the fluid velocity is depicted graphically whereas numerical values of shear stress at the plates are presented in a tabular form for various values of the magnetic parameter, rotation parameter and frequency parameter.
EN
An oscillatory MHD convective and mass transfer flow of an electrically conducting, viscous, incompressible fluid in a rotating porous channel filled with a porous medium has been analyzed. Effects of radiation and chemical reaction are also considered. The two porous plates are subjected to a constant injection and suction. It is considered that the influence of the uniform magnetic field acts normal to the flow. The entire system rotates about an axis normal to the planes of the plates with uniform angular velocity [...]. Expressions for velocity, temperature, concentration, and amplitude and phase angle of skin-friction, the Nusselt number and Sherwood number are obtained. The results obtained for velocity are discussed for small (...) and large (...) rotation of the channel with the help of graphs.
EN
A class of third-order nonlinear neutral differential equation (r(t)(y"(t)) α)' + q(t) f(x(σ (t))) = 0 is investigated in this paper, where y(t) = x(t) + p(t)x(?(t)), and ? > 0 is any quotient of odd integers. Using a new method, we obtain some sufficient conditions for the oscillation of the above equation, and some known oscillation criteria be extended. An example is inserted to illustrate the result.
16
Content available remote Exact solution of an oscillatory MHD flow in a channel filled with porous medium
EN
An exact solution of an oscillatory MHD flow of a viscous, incompressible and electrically conducting fluid in an infinite horizontal channel is presented. The channel is filled with a porous medium and a magnetic field is applied perpendicular to the plates of the channel. During the analysis it is found that the mathematical formulation and the solution obtained of the problem by Makinde and Mhone (2005) are both wrong. Equations (2.1) to (2.4) do not govern the flow problem shown geometrically in their Fig.1. This important flow problem is again formulated mathematically in the present paper and a fresh and a correct closed form analytical solution is obtained. The validity and correctness of the present solution is verified by the limiting case for H=s=0. In this case of oscillatory flow in the absence of a magnetic field and through ordinary medium the solution reduces to the well known result obtained by Schlichting and Gersten (2001). The results are discussed in detail with the help of graphs for the variations of different flow parameters.
EN
Effects of Hall current on an unsteady hydromagnetic Couette flow, induced due to an accelerated movement of the lower plate of the channel in a rotating system when the fluid flow is permeated by an inclined magnetic field is studied. An exact solution for the fluid velocity is obtained by the Laplace transform technique. The expression for the shear stress at the moving plate is also derived. An asymptotic behavior of the solution is analyzed for small and large values of time to gain some physical insight into the flow-pattern. It is found that Hall current, rotation and angle of inclination of the magnetic field tend to accelerate fluid flow in both the primary and secondary flow directions, whereas the magnetic field has a tendency to retard fluid flow in both the primary and secondary flow directions.
EN
This article presents the generation of the oscillation of [alfha, beta, ghama] rhythms which is directly connected with mutual correlations that occur between populations of pyramidal cells and interneurons. The significance of the oscillation of particular rhythms in the universal EEG signal is described. It is especially helpful during creating population models of this signal, which demonstrates its stochastic nature.
19
Content available remote Eliminacja oscylacji w układzie zasilania pojazdu trakcyjnego
PL
W artykule przedstawiona została nowa metoda sterowania układem napędowym z silnikiem indukcyjnym, umożliwiająca eliminację oscylacji napięcia na kondensatorze obwodu pośredniczącego falownika zasilanego z tramwajowej lub trolejbusowej sieci trakcyjnej. Zaburzenia tego typu są charakterystyczne dla układów trakcyjnych, w których jest stosowany wejściowy filtr RLC o słabym tłumieniu. W artykule zostały zamieszczone rozważania teoretyczne i badania symulacyjne potwierdzające skuteczność proponowanej metody.
EN
In this article the new method of power supply voltage oscillation elimination was presented. These types of disturbances are typical in voltage converter fed traction vehicle with low dumped RLC input filter. Analytical approach and simulation results showing efficiency of proposed method was included.
EN
Modern methods of motor drives control are ought to be high precision and quality. This quality is achieved through a rapid and accurate realization of given electromagnetic torque which is insensitive to inverter voltage changes. As a result of using such control methods, a whole system can be considered as an element on constant power for constant angular velocity of the rotor, which leads to occurrence of negative admittance in presence of voltage changes. When an inverter input filter has a high inductance value, negative admittance leads to the excitation of input filter voltage oscillations, whose amplitude often exceeds 50% of nominal voltage. Such a perturbations of inverter voltage can lead to unstable work of electric drive or to damaging one of the inverter elements. The article outlined a method for stabilizing an inverter voltage, through an additional admitance which compensates an unstable component of system. Theoretical considerations and practical algorithm are included. As confirmation of the high efficiency of the proposed algorithm, article contains computer simulation, tests and results.
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