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Tytuł:
Global linearization of nonlinear systems - A survey
Autorzy:
Čelikovský, Sergej
Powiązania:
https://bibliotekanauki.pl/articles/1359660.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
exact linearization
nonlinear control
global linearization
Opis:
A survey of the global linearization problem is presented. Known results are divided into two groups: results for general affine nonlinear systems and for bilinear systems. In the latter case stronger results are available. A comparision of various linearizing transformations is performed. Numerous illustrative examples are included.
Źródło:
Banach Center Publications; 1995, 32, 1; 123-137
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Statistical and equivalent linearization techniques with probability density criteria
Autorzy:
Socha, L.
Powiązania:
https://bibliotekanauki.pl/articles/280239.pdf
Data publikacji:
1999
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
random vibration
linearization techniques
Duffing oscillator
Opis:
The concept of statistical and equvalent linearization with probability density criteria for dynamic systems under Gaussian excitation is considered in the paper. New criteria of linearization and two approximate approaches are proposed. In the first one (statistical linearization) in order to establish the linearization coefficients and response characteristics the output probability density functions of statistic nonlinear element and the corresponding static linearized element are used in an iterative procedure. In the second approach (equivalent linearization) the direct minimization of a criterion based on output probability density functions of dynamic nonlinear system is proposed. The detailed analysis and numerical results are given for the Duffing oscillator.
W pracy zaproponowano metodę statystycznej i równoważnej linearyzacji dla układów dynamicznych z wymuszeniami o charakterze białych szumów Gaussowskich i kryteriami w przestrzeni funkcji gęstości prawdopodobieństw. Przy wyznaczaniu współczynników linearyzacji i charakterystyk rozwiązań układu dynamicznego za pomocą metody statystycznej linearyzacji korzysta się z minimalizacji kryterium uwzględniającego różnicę wyjściowych funkcji gęstości prawdopodobieństw odpowiednio elementu nieliniowego zlinearyzowanego oraz pewnej procedury iteracyjnej. W przypadku równoważnej linearyzacji przeprowadza się bezpośrednią minimalizację kryterium uwzględniającego różnicę wyjściowych funkcji gęstości prawdopodobieństw odpowiednio układów dynamicznych nieliniowego i zlinearyzowanego. Szczegółową analizę i obliczenia numeryczne przeprowadzono dla oscylatora Duffinga.
Źródło:
Journal of Theoretical and Applied Mechanics; 1999, 2; 369-382
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An analysis of influence of SMA material on dynamic properties of a spring taking into account constructional friction
Autorzy:
Gałkowski, Z.
Powiązania:
https://bibliotekanauki.pl/articles/1986962.pdf
Data publikacji:
2002
Wydawca:
Politechnika Gdańska
Tematy:
control
SMA
constructional friction
connection
linearization
Opis:
In this paper, an analysis of forced transverse harmonic vibration with constant changes of the exciting force in a dynamic system consisting of two beams is presented together with a model of a leaf spring. In this junction both beams are made of shape memory material (SMA). The constructional friction is also taken into account. For the purpose of the analysis an equivalent linearization of the elasticity-damping features of the beams was conducted. As an effect of linearization a junction was acquired with both stiffness of elements and viscosity damping. The obtained differential equations were solved using the asymptotic Bogolubov-Krylov-Mitropolski method. The results of the conducted simulation are presented on graphs, showing the influence of unitary pressure on the system's damping properties.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2002, 6, 3; 351-361
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weakly nonlinear regression model with constraints I: nonlinear hypothesis
Autorzy:
Kubácek, Lubomír
Tesaríková, Eva
Powiązania:
https://bibliotekanauki.pl/articles/729706.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
regression model with constraints
nonlinear hypothesis
linearization
Opis:
The problem considered is under which conditions in weakly nonlinear regression model with constraints I a weakly nonlinear hypothesis can be tested by linear methods. The aim of the paper is to find a region around the approximate value of the regression parameter with the following property. If we are certain that the actual value of the regression parameter is in this region, then the linear method of testing can be used without any significant deterioration of the inference.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2005, 25, 1; 115-133
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The design of ship autopilot by applying observer – based feedback linearization
Autorzy:
Zwierzewicz, Z.
Powiązania:
https://bibliotekanauki.pl/articles/259972.pdf
Data publikacji:
2015
Wydawca:
Politechnika Gdańska. Wydział Inżynierii Mechanicznej i Okrętownictwa
Tematy:
ship autopilot design
feedback linearization
nonlinear observer
Opis:
The paper considers the problem of ship autopilot design based on Bech’s model of the vessel. Since the model is highly nonlinear and some of the state vector coordinates are unavailable, the control system synthesis is performed by means of an output feedback linearization method combined with a nonlinear observer. The asymptotic stability of the overall system has been proven, including the asymptotic stability of the system internal dynamics. The performed simulations of the ship course-changing process have confirmed a high performance of the proposed controller. It has been emphasized that for its practical usability the system robustification is necessary.
Źródło:
Polish Maritime Research; 2015, 1; 16-21
1233-2585
Pojawia się w:
Polish Maritime Research
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Linearisierungsmöglichkeiten und Kasuszuweisung in deverbalen Nominalphrasen. Ein deutsch-polnischer Vergleich
Linearization and case assignment in deverbal noun phrases. A comparison of German and Polisch
Autorzy:
Aptacy, Jarosław
Powiązania:
https://bibliotekanauki.pl/articles/916994.pdf
Data publikacji:
2018-11-05
Wydawca:
Uniwersytet im. Adama Mickiewicza w Poznaniu
Tematy:
noun phrase
adjacency
Genitive
Linearization of DPs
Opis:
In the following paper German and Polish deverbal noun phrases will be examined in respect to the linearization of their constituents. The point of departure will be the adjacency condition which is obligatory in the Genitive DPs in German, but optional in Polish. In other words, Polish displays more linearization possibilities than German. In addition to adjacency which is conditioned by grammar also communicative factors and text grammar condition the linearization of DPs. Constituents with a higher comment value tend to appear as far to the right of the deverbal noun as possible, while topic constituents stand closer to the noun.
Źródło:
Glottodidactica. An International Journal of Applied Linguistics; 2010, 36, 1; 9-19
0072-4769
Pojawia się w:
Glottodidactica. An International Journal of Applied Linguistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of atatistical linearization techniques to design of quqsi-optimal active control of nonlinear system
Autorzy:
Socha, L.
Powiązania:
https://bibliotekanauki.pl/articles/279701.pdf
Data publikacji:
2000
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
statistical linearization
stochastic optimal control
active suspensions
Opis:
A comparison between the applicability of statistical linearizationmethods with moment criteria and criteria in probability density space to the determination of quasi-optimal external control for the nonlinear dynamic system excited by a coloured Gaussian noise and the mean square criterion is discussed in this paper. To determine the quasi-optimal control two modified versions of a standard iterative procedure are proposed, where three versions of statistical linearization with moment criteriaand two versions with criteria in the probability density space were combined with the optimal control method for linear systems with the mean square criterion. The detailed considerations are given for a nonlinear 2-degree-of-freedom system with external control force excited by a coloured Gaussian noise which is treated as an outputof 2D linear filter. The control is assumed as a linear feedback. The obtained results are illustrated by a numerical example.Zastosowanie sta
zastosowanie statystycznej linearyzacji w nieliniowych układach do wyznaczania kwazi-optymalnego aktywnego sterowania. W pracy przedstawiono porównanie zastosowania kilku metod statystycznej linearyzacji z kryteriami momentowymi oraz z przestrzeni gęstości prawdopodobieństw do wyznaczania kwazi-optymalnego, addytywnego sterowaniaw układach nieliniowych z wymuszeniem w postaci kolorowego Gaussowskiego szumu i ze średnio kwadratowym kryterium optymalizacji. W celu wyznaczenia kwazi-optymalnego sterowania zaproponowano dwie zmodyfikowane wersje standardowej procedury iteracyjnej, gdzie trzy wersje statystycznej linearyzacji z momentowymi kryteriami i dwie wersje z kryteriami w przestrzeni gęstości prawdopodobieństw wykorzystano łącznie ze standardowym algorytmem wyznaczania sterowania optymalnego w układach liniowych ze średniokwadratowym wskaźnikiem jakości. Szczegółowa analiza została przedstawiona dla układów o dwu stopniach swobody z zewnętrznym wymuszeniem w postaci Gaussowskiego szumu kolorowego traktowanego jako wyjście z dwuwymiarowego filtru liniowego. Sterowanie przyjęto jako liniowe sprzężenie zwrotne. Otrzymane wyniki zilustrowano na przykładzie numerycznym.
Źródło:
Journal of Theoretical and Applied Mechanics; 2000, 38, 3; 591-605
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Linearyzacja modelu matematycznego siłownika hydraulicznego połączonego z ramieniem manipulatora
Linearization of the mathematical model of a hydraulic actuator connected to a manipulator arm
Autorzy:
Cedro, L.
Janecki, D.
Powiązania:
https://bibliotekanauki.pl/articles/151701.pdf
Data publikacji:
2009
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
linearyzacja
układ hydrauliczny
linearization
hydraulic actuator system
Opis:
Streszczenie W pracy przedstawiono metodę linearyzacji modelu matematycznego układu hydraulicznego połączonego z ramieniem manipulatora. Układ zamodelowano w dwóch postaciach: w postaci równań różniczkowych, oraz modelu quasi-liniowego. Uzyskany model uproszczony poddano weryfikacji z modelem dokładnym. Model taki może być wykorzystany w procesach identyfikacji metodą najmniejszych kwadratów, która jest jedną z najbardziej efektywnych metod identyfikacji. Drugim obszarem zastosowań może być projektowanie układów regulacji.
The paper presents the method of linearization of a hydraulic actuator system connected to a manipulator arm. Fig. 1 shows a drive system supplied with constant pressure . The flow controller (2) acts as a throttling valve, while the hydraulic actuator (1) is a receiver. The constant pressure is provided by the pump (3). The arm-actuator system presented in Fig. 2 is a one-dimensional model. In the analysis, the elements connecting the actuator to the arm are not taken into consideration. This way it is easier to determine the system dynamic properties. The method used in this study requires expanding the linear function in a Taylor series around the operating point and considering linear terms only. After linearization of the mathematical model of a manipulator connected to a hydraulic actuator, there was obtained a simplified model (7) representing well the real system model behaviour (1). The simplified model was compared with the accurate one. In the case of the second-order, quasi-linear model and the mathematical model of the hydraulic actuator system, both signals fully coincide (Fig. 6). That is why the simplification to such a form is justified. The hydraulic actuator system was designed in two forms: as differential equations(1) (accurate model), and as a quasi-linear model (10) (simplified one). The simplified model can be used for identification purposes using the least squares method, which is one of the most effective identification method. Another area of application can be design of control systems.
Źródło:
Pomiary Automatyka Kontrola; 2009, R. 55, nr 2, 2; 126-130
0032-4140
Pojawia się w:
Pomiary Automatyka Kontrola
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Control of an Induction Motor Using Sliding Mode Linearization
Autorzy:
Etien, E.
Cauet, E.
Rambault, L.
Champenois, G.
Powiązania:
https://bibliotekanauki.pl/articles/908504.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
automatyka
induction motor
sliding mode control
linearization
Opis:
Nonlinear control of the squirrel induction motor is designed using sliding mode theory. The developed approach leads to the design of a sliding mode controller in order to linearize the behaviour of an induction motor. The second problem described in the paper is decoupling between two physical outputs: the rotor speed and the rotor flux modulus. The sliding mode tools allow us to separate the control from these two outputs. To take account of parametric variations, a model-based approach is used to improve the robustness of the control law despite these perturbations. Experimental results obtained with a laboratory setup illustrate the good performance of this technique.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2002, 12, 4; 523-531
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
How to deal with regression models with a weak nonlinearity
Autorzy:
Tesaríková, Eva
Kubáček, Lubomír
Powiązania:
https://bibliotekanauki.pl/articles/729868.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
nonlinear regression model
criteria of linearization
demo program
Opis:
If a nonlinear regression model is linearized in a non-sufficient small neighbourhood of the actual parameter, then all statistical inferences may be deteriorated. Some criteria how to recognize this are already developed. The aim of the paper is to demonstrate the behaviour of the program for utilization of these criteria.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2001, 21, 1; 21-48
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Finite-time stability and stabilization of singular state-delay systems using improved estimation of a lower bound on a Lyapunov-like functional
Autorzy:
Stojanovic, S. B.
Debeljkovic, D. Lj.
Antic, D. S.
Powiązania:
https://bibliotekanauki.pl/articles/200145.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
singular systems
time-delay
LMIs
finite-time stability
stabilizing controllers
cone complementarity
linearization
cone complementarity linearization algorithm
systemy pojedyńcze
czas opóźnienia
stabilność w czasie skończonym
kontrolery stabilizujące
komplementarność
linearyzacja
algorytm cone complementarity linearization
Opis:
In this paper, the problems of finite-time stability and stabilization for a class of singular time-delay systems are studied. Using the Lyapunov-like functional (LLF) with (exponential or power) weighting function and a new estimation method for the lower bound on LLF, some sufficient stability conditions are introduced. It is shown that the weighting function significantly reduces the conservatism of the stability criteria in comparison to estimation of the lower bound on LLF without this function. To solve the finite-time stabilization problem, a stabilizing linear state controller is designed by exploiting the cone complementarity linearization algorithm. Two numerical examples are given to illustrate the effectiveness of the proposed method.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2015, 63, 2; 479-487
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The linearization of mooring load distribution problem
Autorzy:
Artyszuk, J.
Powiązania:
https://bibliotekanauki.pl/articles/135702.pdf
Data publikacji:
2016
Wydawca:
Akademia Morska w Szczecinie. Wydawnictwo AMSz
Tematy:
ship manoeuvring
mooring
berthing
hydrodynamics
loads
linear model
linearization
Opis:
This paper presents a novel step forward in finding the loads of particular mooring ropes that balance the steady environmental excitations for a ship staying at berth. The industrial static equilibrium method for a rough assessment of ship mooring safety is considered to be well-established. The static loads are directly related to the rope’s MBLs (minimum breaking loads) while applying a certain safety margin (usually 50%). The problem is reduced to a set of linear equations that may be solved analytically. The generality in terms of arbitrary horizontal and vertical angles of mooring ropes is preserved. All derivations are provided to enhance trust in the very simple yet absolutely accurate and fast linear solution. The accuracy is studied both analytically, throughout all the development stages, and finally by comparison to the exact numerical solution of the original nonlinear equilibrium equations for an exemplary mooring pattern. A discussion of selected effects in load distribution is also given. Using the approach presented, for instance, we can efficiently test mooring safety when any mooring rope of the set is accidentally broken.
Źródło:
Zeszyty Naukowe Akademii Morskiej w Szczecinie; 2016, 46 (118); 9-16
1733-8670
2392-0378
Pojawia się w:
Zeszyty Naukowe Akademii Morskiej w Szczecinie
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the ship course-keeping control system design by using robust feedback linearization
Autorzy:
Zwierzewicz, Z.
Powiązania:
https://bibliotekanauki.pl/articles/260552.pdf
Data publikacji:
2013
Wydawca:
Politechnika Gdańska. Wydział Inżynierii Mechanicznej i Okrętownictwa
Tematy:
feedback linearization
robust control
differential games
ship autopilot design
Opis:
In the paper the problem of ship autopilot design based on feedback linearization method combined with the robust control approach, is considered. At first the nonlinear ship model (of Norrbin type) is linearized with the use of the simple system nonlinearity cancellation. Next, bearing in mind that exact values of the model parameters are not known, the ensuing inaccuracies are taken as disturbances acting on the system. Thereby is obtained a linear system with an extra term representing the uncertainty which can be treated by using robust, H∞optimal control techniques. The performed simulations of ship course-changing process confirmed a high performance of the proposed controller despite the assumed significant errors of its parameters.
Źródło:
Polish Maritime Research; 2013, 1; 70-76
1233-2585
Pojawia się w:
Polish Maritime Research
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oscillatory criteria via linearization of half-linear second order delay differential equations
Autorzy:
Baculikova, Blanka
Dzurina, Jozef
Powiązania:
https://bibliotekanauki.pl/articles/255725.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
second order differential equations
delay
monotonic properties
linearization
oscillation
Opis:
In the paper, we study oscillation of the half-linear second order delay differential equations of the form [formula]. We introduce new monotonic properties of its nonoscillatory solutions and use them for linearization of considered equation which leads to new oscillatory criteria. The presented results essentially improve existing ones.
Źródło:
Opuscula Mathematica; 2020, 40, 5; 523-536
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Test bench and simulation research on hydrodynamic torque converter for different input signals
Autorzy:
Wozniak, M.
Siczek, K.
Pawelski, Z.
Powiązania:
https://bibliotekanauki.pl/articles/247933.pdf
Data publikacji:
2016
Wydawca:
Instytut Techniczny Wojsk Lotniczych
Tematy:
torque converter
torque
Matlab/Simulink
linearization
nonlinear model
ARX
OE
Opis:
This paper presents the experimental research and simulating results of a ZM130 hydrodynamic torque converter under steady and unsteady working conditions with an external step signal and sinus on turbine’s shaft on a modified test bench. The mathematical model of torque converter was described by the one-dimensional flow theory with variable loss coefficients. The character of received equations from test bend showed by linearized transmittance functions with variable coefficients. For test bend object identification researches will be used an Identification Toolbox from a mathematical code in Matlab, which enables to create transfer functions as a linear model from measurements data as they got the highest correctness level with input signal (as they get the best correction level with input signal on the pump´s shaft). This mathematical model for dynamic loads will be verified by experimental tests. The aim of the carried out studies was determination the effect of sampling time decreasing on the quality of measured parameters. Results of present investigations were compared with those obtained earlier, but for the same input signals .It is possible to affirm that proposed theoretical model imitates the change of dynamic parameters, and the same the property of the torque converter. Researches led on the test bend with extortion input torque sinus signal on the turbine’s shaft confirmed correctness of this model.
Źródło:
Journal of KONES; 2016, 23, 4; 561-568
1231-4005
2354-0133
Pojawia się w:
Journal of KONES
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Ship course stabilization by feedback linearization with adaptive object model
Autorzy:
Borkowski, P.
Powiązania:
https://bibliotekanauki.pl/articles/259940.pdf
Data publikacji:
2014
Wydawca:
Politechnika Gdańska. Wydział Inżynierii Mechanicznej i Okrętownictwa
Tematy:
ship course stabilization
feedback linearization controller
GRBF
safety of navigation
Opis:
The algorithm of ship course stabilization herein presented is based on a feedback linearization controller with adaptive object model. The described method, consisting in current approximation of unknown object model functions by neuro-fuzzy approximators, represents a new generation of adaptive control methods. The implementation of this algorithm, which may constitute an executive module of a navigational decision support system, will contribute to a higher degree of automation and navigational safety improvement.
Źródło:
Polish Maritime Research; 2014, 1; 14-19
1233-2585
Pojawia się w:
Polish Maritime Research
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Transistor-based temperature measuring device
Tranzystorowy układ do pomiaru temperatury
Autorzy:
Hotra, Oleksandra
Powiązania:
https://bibliotekanauki.pl/articles/407702.pdf
Data publikacji:
2020
Wydawca:
Politechnika Lubelska. Wydawnictwo Politechniki Lubelskiej
Tematy:
temperature measurement
transistor structure
linearization
pomiar temperatury
struktura tranzystorowa
linearyzacja
Opis:
The schematic diagrams of the temperature measuring device based on transistor structures are presented in the paper. The temperature dependence of collector current without and with linearization of the conversion function is analysed. The linearization method based on compensation current formation is proposed. This allowed to reduce the temperature measurement error up to ± 0.006°C over the temperature ranges 40… 60°C and 60… 80°C and up to 0.08°C over the temperature range 10… 90°C.
W artykule zostały przedstawione schematy miernika temperatury opartego na strukturach tranzystorowych. Została przeanalizowana zależność prądu kolektora od temperatury bez i przy zastosowaniu linearyzacji funkcji przetwarzania. Zaproponowano metodę linearyzacji opartą na formowaniu prądu kompensacyjnego, która pozwoliła zmniejszyć błąd pomiaru temperatury do ± 0,006°C w zakresach temperatury 40… 60°C i 60… 80°C oraz do ±0,08°C w zakresie 10… 90°C.
Źródło:
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska; 2020, 10, 2; 4-7
2083-0157
2391-6761
Pojawia się w:
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Collocation method based on barycentric interpolation iteration for analysis of nonlinear microbeams
Autorzy:
Zhuang, M.
Miao, C.
Wang, Z.
Powiązania:
https://bibliotekanauki.pl/articles/279890.pdf
Data publikacji:
2018
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
nonlinear microbeams
barycentric Lagrange interpolation
collocation method
linearization method
iteration method
Opis:
A powerful computational methodology, named the barycentric Lagrange interpolation iteration collocation method (BLIICM), for solving nonlinear bending problems of a doubly clamped microbeam under electrostatic loads is presented. The nonlinear governing equation of the microbeam is converted into a linear differential equation by assuming the initial function. The barycentric Lagrange interpolation collocation method (BLICM) is used to solve the linear differential equation. The direct linearization formulations and Newton linearization calculation formulations for the nonlinear differential equation have been given. The calculation method and formulation of the nonlinear integral term have been discussed in details. By applying a barycentric Lagrange interpolation differential matrix, a matrix-vector calculation formula of BLIICM has been established. Numerical results of calculation examples show that the advantages of the proposed methodology are efficient, simple and of high precision.
Źródło:
Journal of Theoretical and Applied Mechanics; 2018, 56, 3; 741-749
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Investigation of the dynamics of singular protected systems
Autorzy:
Naumeyko, I.
Alja'afreh, M.
Powiązania:
https://bibliotekanauki.pl/articles/411040.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Oddział w Lublinie PAN
Tematy:
"Man-Machine-Environment" model
non-linear system
singular equations
asymptotic
linearization
Opis:
The analysis of asymptotic representations of the systems protected from harmful influences is carried out. Various types of general models of the "manmachineenvironment" with protection are considered. Each of them adequately describes some of the practically important qualities of the object, and they all together describe the object in terms of its safe operation. The dynamic properties of complex ergonomic systems, presented in the form of systems of differential equations with a small parameter at the derivative are investigated The methods of reducing the impact on the person of harmful factors are theoretically substantiated. The dynamic protection response speed is considered to be significantly greater than the harmful factor production rate. Numerical solution of the general problem and the analytical solution for autonomous case is obtained for harmful effects. By using asymptotic the system of equations has been solved in closed form not only for autonomous case, but also for parameters smoothly changing in time. The estimates of the cost of protection was obtained for the various cost-functionals and for different functions in the right-hand side of the equation describing the dynamics of protection. To assess the accuracy of model calculations and for graphic representation of the results mathematical package MAXIMA is used.
Źródło:
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2016, 5, 4; 37-42
2084-5715
Pojawia się w:
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Wavelet-based numerical solution for MHD boundary-layer flow due to stretching sheet
Autorzy:
Karkera, Harinakshi
Katagi, Nagaraj N.
Powiązania:
https://bibliotekanauki.pl/articles/2106444.pdf
Data publikacji:
2021
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
magnetohydrodynamika
przepływ
linearyzacja
MHD flow
boundary layer
quasi-linearization
Haar wavelets
Opis:
In this paper, a two-dimensional steady flow of a viscous fluid due to a stretching sheet in the presence of a magnetic field is considered. We proposed two new numerical schemes based on the Haar wavelet coupled with a collocation approach and quasi-linearization process for solving the Falkner-Skan equation representing the governing problem. The important derived quantities representing the fluid velocity and wall shear stress for various values of flow parameters Mand βare calculated. The proposed methods enable us to obtain the solutions even for negative β, nonlinear stretching parameter, and smaller values of the magnetic parameter ()M1< which was missing in the earlier findings. Numerical and graphical results obtained show an excellent agreement with the available findings and demonstrate the efficiency and accuracy of the developed schemes. Another significant advantage of the present method is that it does not depends on small parameters and initial presumptions unlike in traditional semi-analytical and numerical methods.
Źródło:
International Journal of Applied Mechanics and Engineering; 2021, 26, 3; 84--103
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Impact of Using an Inerter on the Performance of Vehicle Active Suspension
Autorzy:
Alshabatat, Nabeel
Shaqarin, Tamir
Powiązania:
https://bibliotekanauki.pl/articles/2201718.pdf
Data publikacji:
2022
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
inerter
active suspension
nonlinear quarter-car model
ride comfort
feedback linearization
Opis:
This paper investigates the effect of employing an inerter on the performance of active suspension systems. A quarter-car model with cubic-nonlinear spring is considered. The inerter is installed in parallel with the primary suspension spring and damper. First, feedback linearization (FBL) is used to linearize the mathematical model. Then the linear quadratic regulator (LQR) is adopted to control the suspension system. The proposed design is ride comfort-oriented and considers structural constraints. Numerical simulations are executed for passive systems with different values of inertance. Results show that employing an inerter to the passive suspension can improve the ride comfort performance by more than 32%. Employing an inerter to active suspension systems can also improve the ride comfort and reduce actuator force significantly. The actuator force can be reduced by 25%. However, the results also show that the uncaring selection of the inerter can dramatically degrade the performance of the suspension system.
Źródło:
Advances in Science and Technology. Research Journal; 2022, 16, 3; 331--339
2299-8624
Pojawia się w:
Advances in Science and Technology. Research Journal
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dynamic balance research of protected systems
Autorzy:
Naumeyko, I.
Alja'afreh, M.
Powiązania:
https://bibliotekanauki.pl/articles/411213.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Oddział w Lublinie PAN
Tematy:
Non-linear system
singular points
eigenvalues
asymptotic behavior
first approximation
linearization
Opis:
The dynamic models of the complex ergatic objects' behavior, presented in the form of differentia equations and their systems were studied. The stability and other properties are researched. The methods of analysis and reduce of harmful factors and their impact on people were theoretically proved. The methods of analysis and critical points removal in dynamic models of hazards distribution are offered. The object of study is the system of the harmful external factors protection. Subject of research is the system of two nonlinear differential equations as a model of technical systems with protection. The object of protection is described by logistic equation. and defense system - by non-linear differential equation with a security functions of rather general form. This paper describes critical modes analysis and stationary states’ stability of protected systems with harmful influences. Numerical solution of general problem and also the analytical solution for the case of fixed expected harmful effects have been obtained. Various types of general models for "Man-machine-environment" systems were studied. Each of describes some kind of the practically important quality of object in an appropriate way. And All together they describe the object in terms of it’s safe operation. Their further detailing process results to either well-known, or some new subsystems’ models. Systems with "fast" protection at a relatively slow dynamics of the object were studied. This leads to the models with small parameter and asymptotic solutions of differentia equations. Some estimates for protection cost in different price-functional and for different functions in the right part of equation, which describes the dynamics of defense were obtained. For calculations, analysis and graphical representations some of mathematical packages was applied.
Źródło:
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2015, 4, 3; 85-90
2084-5715
Pojawia się w:
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Linearization of the product of orthogonal polynomials of a discrete variable
Autorzy:
Belmehdi, Saïd
Lewanowicz, Stanisław
Ronveaux, André
Powiązania:
https://bibliotekanauki.pl/articles/1339159.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
linearization coefficients
classical orthogonal polynomials of a discrete variable
recurrence relations
Opis:
Let {$P_k$} be any sequence of classical orthogonal polynomials of a discrete variable. We give explicitly a recurrence relation (in k) for the coefficients in $P_iP_j=\sum_kc(i,j,k)P_k$, in terms of the coefficients σ and τ of the Pearson equation satisfied by the weight function ϱ, and the coefficients of the three-term recurrence relation and of two structure relations obeyed by {$P_k$}.
Źródło:
Applicationes Mathematicae; 1996-1997, 24, 4; 445-455
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Non-linear stochastic dynamics of a cable-mass system with finite bending stiffness via an equivalent linearization technique
Autorzy:
Weber, Hanna
Kaczmarczyk, Stefan
Iwankiewicz, Radosław
Powiązania:
https://bibliotekanauki.pl/articles/1839662.pdf
Data publikacji:
2020
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
stochastic dynamics
nonlinear systems
cable
finite bending stiffness
equivalent
linearization techniques
Opis:
The non-linear stochastic dynamic behaviour of a high-rise vertical transportation system modelled as a concentrated mass and a cable with finite bending stiffness is considered. The slow time scale is defined and lateral cable displacements coupled with transverse motions are expanded in terms of approximating functions. The excitation of the high-rise building is assumed in the form of a narrow-band mean-square process equivalent to the harmonic process. The equivalent linearization technique is used to replace the original non-linear system with a linear approximation whose coefficients are determined from minimization of the mean-square equation difference between both systems.
Źródło:
Journal of Theoretical and Applied Mechanics; 2020, 58, 2; 483-497
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Linearization of Arbitrary products of classical orthogonal polynomials
Autorzy:
Hounkonnou, Mahouton
Belmehdi, Said
Ronveaux, André
Powiązania:
https://bibliotekanauki.pl/articles/1208207.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
classical orthogonal polynomials
Hermite orthogonal polynomials
linearization coefficients
recurrence relations
differential equations
Opis:
A procedure is proposed in order to expand $w=\prod^N_{j=1} P_{i_j}(x)=\sum^M_{k=0} L_ k P_ k(x)$ where $P_i(x)$ belongs to aclassical orthogonal polynomial sequence (Jacobi, Bessel, Laguerre and Hermite) ($M=\sum^N_{j=1} i_j$). We first derive a linear differential equation of order $2^N$ satisfied by w, fromwhich we deduce a recurrence relation in k for the linearizationcoefficients $L_k$. We develop in detail the two cases $[P_i(x)]^N$, $P_ i(x)P_ j(x)P_ k(x)$ and give the recurrencerelation in some cases (N=3,4), when the polynomials $P_i(x)$are monic Hermite orthogonal polynomials.
Źródło:
Applicationes Mathematicae; 2000, 27, 2; 187-196
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
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