Wyniki wyszukiwania - BazTech

1

Control of chaos in the burke-shaw system of fractal-fractional order in the sense of Caputo-Fabrizio

Saber Sayed

Journal of Applied Mathematics and Computational Mechanics

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2024

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Vol. 23, nr 1

83-96

EN

For the Burke-Shaw system, we propose a fractal-fractional order in the sense of the Caputo-Fabrizio derivative. The proposed system is solved by utilizing the fractal-fractional derivative operator with an exponential decay kernel. Time-fractional Caputo-Fabrizio fractal fractional derivatives are applied to the Burke-Shaw-type nonlinear chaotic systems.Based on fixed point theory, it has been demonstrated that a fractal-fractional-order model under the Caputo-Fabrizio operator exists and is unique. Using a numerical power series method, we solve the fractional Burke-Shaw model. Using Newton’s interpolation polynomial, we solve the equation numerically by implementing a novel numerical scheme based on an efficient polynomial.

2

Unified fractional derivative models of magneto-thermo-viscoelasticity theory

Ezzat M. A., El-Bary A. A.

Archives of Mechanics

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2016

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Vol. 68, nr 4

285--308

EN

A unified mathematical model of fractional magneto-thermo-viscoelasticty for isotropic perfectly conducting media involving fractional relaxation operator is given. Some essential theorems on the linear coupled and generalized theories of thermoviscoelasticity can be easily obtained. The new fractional model is applied to a halfspace subjected to two different forms of time-dependent thermal shock in, the presence of a transverse magnetic field. The Laplace transform techniques are used. Numerical computation is performed by using a numerical inversion technique and the resulting quantities are shown graphically. The effects of the fractional orders on viscoelastic material are discussed.

3

Investigation of traffic flow dynamic processes using discrete model

Bogdevicius M., Junevicius R.

Journal of KONES

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2014

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Vol. 21, No. 4

15--19

EN

Modelling the process of traffic flow was previously studied from different points of view and different mathematical methods where used to describe the same process. All authors have an agreement on basic traffic flow parameters like, traffic flow density, traffic flow rate or the average speed of traffic flow. Besides, a lot of different investigations into the use of traffic flow models to deal with various problems of engineering are carried out. A comparison of different continuum models has drawn that a number of scientific works were based on fluid dynamic theory and gas - kinetic traffic flow theory. The kinetic traffic flow theory is used in ‘microscopic’ or “macroscopic”, traffic flow models. The kinetic traffic flow theory is used in Flötteröd G., Nagel K., Ging A., Li L., Li-qun X., Prigogine I., Herman R. works where various approaches to the similar method are discussed. The ‘macroscopic’ theory of traffic flows also can be developed as the hydrodynamic theory of fluids that was first introduced by Lighthill-Whitham and Richards’s model. Plenty of traffic flow models are based on car–following theories supported by the analogues to Newton’s equation for each individual vehicle interacting in a system of vehicles on the road. Different forms of the equation of motion give different versions of car–following models. This work presents research of traffic flow dynamic processes, as nonlinear dynamic system, by using a discrete model of traffic flow (DMTF). The main variables in DMTF are traffic flow density and speed. DMTF can be used to describe various traffic flow situations in the roads. The mathematical simulation of traffic flow is made when constant value of traffic flow speed and traffic flow rate is entered. Numerical results of traffic flow dynamics are obtained.

4

Przewidywanie momentu pękania i analiza kształtu wyrobu w procesie cięcia z wykorzystaniem metody doświadczalnej i numerycznej

Świłło S., Czyżewski P.

Prace Naukowe Politechniki Warszawskiej. Mechanika

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2013

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z. 253

33--38

PL

Przedstawione zostały przez autorów wyniki pomiarów doświadczalnych i obliczeń numerycznych dla ciętej aluminiowej blachy o grubości 1 mm. W pracy przedstawiono wyniki dla jednej wartości luzu. Pomiary doświadczalne zrealizowane zostały na w pełni automatycznym stanowisku pomiarowym. Zaproponowane zostało rozwiązanie dotyczące wykorzystania metody obróbki obrazu (optical flow) do rozpoznania pól przemieszczeń. Zaprezentowana została kinematyka procesu w odniesieniu do pomiaru odkształceń oraz identyfikacja zjawisk ograniczających tj.: zadzior, ugięcie, tworzenie się stref rozdzielenia materiału. W badaniach doświadczalnych wykorzystano układ wizyjny umożliwiający monitorowanie przebiegu procesu cięcia. Zaprezentowano wyniki odkształceń i wielkości geometryczne pomiarów próbki w trakcie pękania i po rozdzieleniu dla doświadczenia i MES.

EN

The authors presents an experimental and numerical (FEM) results of 1 mm thick sheet metal aluminium at the planar blanking process, where specific clearance was used in the designed, fully automated apparatus. A new approach for the crack propagation visualization based on digital image processin technique (optical flow method) has been proposed. The presented results for the eperiment includes strain measurment, as well as geometrical investigation for the limiting factors. In the experimental approach a vision based apparatus were utilized. Finally, the experimental and numerical results has been combined and presented.

5

Izolacyjność akustyczna budowlanych płyt kompozytowych – doświadczenia i obliczenia MES

Wawrzynowicz A.

Zeszyty Naukowe Politechniki Gdańskiej. Inżynieria Lądowa i Wodna

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2012

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Nr 1 (625)

153--161

PL

Artykuł zajmuje się problemem izolacyjności akustycznej nowych płyt kompozytowych stosowanych w budownictwie mieszkaniowym. Płyty składają się z okładzin magnezjowych oraz styropianowego rdzenia. Izolacyjność akustyczną wyznaczono doświadczalnie w zespole komór pogłosowych zgodnie z wymaganiami normowymi. Wykonane doświadczenie modelowano następnie numerycznie metodą elementów skończonych w przestrzeni dwuwymiarowej. Otrzymano zadawalającą zgodność wyników numerycznych z doświadczalnymi.

EN

This paper describes results of laboratory measurements of the airborne sound insulation of composite panels applied in residential buildings in the frequency range of 100-5000 Hz. The panels consist of an expanded polystyrene layer and two facesheets of glass fibre-cement-magnesium boards. An acoustic laboratory composed of the source and receiving chambers was used according to basic requirements of the PN-EN ISO 140-1 standard. The experiment was numerically modelled using the finite element method based on the equation of compressible, inviscid and linear fluid and a simplified fluid-structure interface. A satisfactory agreement was achieved between numerical and experimental results.

6

An advanced aeroelastic model for horizontal axis wind turbines

Dumitrescu H., Dumitrache A., Cardos V., Frunzulica A.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 3

683-702

EN

In this paper, an advanced aeroelastic numerical tool for horizontal axis wind turbines (HAWT) is presented. The tool is created by coupling an unsteady aerodynamic model based on the lifting-line approximation with an elastodynamic model based on the beam approximation. The coupling is non-linear in the sense that at every time step the two models interact through data transfer from the one to the other. Two interfaces assure a constant communication between the two parts of the complete model. The aero-to-elastic interface defines the loads exercised on the structure, whereas the elastic-to-aero interface transmits the rates of deformations. The aeroelastic model is evaluated through comparisons of its predictions with experimental data as well as with predictions obtained by simpler models.

7

Dynamics of the complex system with elastic and visco-elastic inertial interlayers

Cabańska-Płaczkiewicz K.

Engineering Transactions

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2007

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Vol. 55, iss. 4

317-333

EN

In this paper is given the dynamic analysis of the free and forced vibration problems of a complex system with elastic and visco-elastic inertial interlayers. The analytical method of solving the free and forced vibrations problem of the system is presented in the paper. The external layer of the complex system is treated as the plate made from elastic materials, coupled by visco-elastic inertial interlayers. The plate is described by the Kirchhoff-Love model. The visco-elastic, inertial interlayer possesses the characteristics of a continuous inertial Winkler foundation arid has been described by the Voigt-Kelvin model. Snlall transverse displarernents of the complex system are excited by the stationary and non-stationary dynamical loadings. The phenomenon of free and forced vibrations problems has been described using a non-homogeneous system of conjugate, partial differential equations. After separation of variables in the homogeneous system, the boundary value problem has been solved and two sequences have been obtained: the sequences of frequencies and the sequences of free vibrations modes. Then, the property of orthogonality of complex free vibrations has been presented. The free vibrations problem has been solved for some arbitrarily assumed initial conditions. The forced vibrations problem has been considered for different modes of dynamical loading The solution of the ecological safety problem and protection from exposure to dust, depended much on the equipment and techniques used in quarrying the brown coal. Thus, dynamics of loading the open coast colliery dump trucks which have a load-carrying capacity of hundreds of tons, mass of tens of tons and dimensions of tens of meters, is a very important problem. The numerical results of free and forced vibrations problems of the complex system with the elastic arid visco-elastic inertial interlayer, for various parameters and different modes of dynamical loading, are given in this paper.

8

Similiarity solutions for the unsteady boundary layer flow and heat transfer due to a stretching sheet

Sharidan S., Mahmood T., Pop I.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 3

647-654

EN

A similarity analysis is presented to investigate the unsteady boundary layers over a stretching sheet for special distributions of the stretching velocity and surface temperature or surface heat flux. The governing unsteady boundary layer equations are reduced to ordinary differential equations with two parameters, the Prandtl number and the unsteadiness parameter. These equations are solved numerically for some values of the governing parameters using the Keller-box method. Some flow and heat transfer characteristics are determined and discussed in detail.

9

Vibrations of the three-layer shell with damping

Cabańska-Płaczkiewicz K.

Engineering Transactions

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2006

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Vol. 54, iss. 4

329-351

EN

In this paper the analytical method [17, 18] has been used for solving the problem of vibrations of the three-layer shell with damping. External layers are modelled as the MINDLIN shells and the internal layer possesses the characteristics of a viscoelastic one-directional WINKLER foundation. Small transverse vibrations of the three-layer shell with damping is excited by the dynamical non-uniform loading moving at the constant velocity v*. Numerical results are presented in the diagrams.

10

G-jitter induced free convection near a two-dimensional stagnation point in micropolar fluids

Sharidan S., Amin N., Pop I.

International Journal of Applied Mechanics and Engineering

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2005

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Vol. 10, no 2

311-328

EN

A numerical solution for the effect of a small but fluctuating gravitational field, characteristic of g-jitter, on the free convection boundary layer flow near the forward stagnation point of a two-dimensional symmetric body resulting from a step change in its surface temperature and immersed in a micropolar fluid is presented in this paper. Both the cases when the spin gradient on the wall is zero and non-zero are considered. The transformed non-similar boundary layer equations are solved numerically by a very efficient implicit finite-difference scheme known as the Keller-box method to investigate the effects on the skin friction and on the rate of heat transfer of variations in the forcing amplitude, a, forcing frequency, 'omega', and micropolar parameter, K. The results are given for a value of the Prandt number Pr=0.7. It has been found that these parameters affect considerably the considered flow characteristics. A comparison with earlier results for a Newtonian fluid (K=0) shows a good agreement.

11

Vibrations of the plate with a viscoelastic interlayer

Cabańska-Płaczkiewicz K., Wilczyński M.

Zeszyty Naukowe. Mechanika / Akademia Techniczno-Rolnicza w Bydgoszczy

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2004

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Z. 54(243)

67-74

EN

In this paper the uniform analytical method [11] has been used for solving a problem of vibrations of the plate with a viscoelastic interlayer. External layers are modelled as Kirchhoff-Love's plates, while the internal layer possesses the characteristics of a viscoelastic, one-directional Winkler foundation. In the case small transverse vibrations of the complex system with damping is excited by the dynamical steady force [wzór] at the point [wzór] and varying in time t. Numerical results are presented in the diagrams.

PL

W pracy zastosowano analityczną jednolitą metodę [11] do rozwiązywania zagadnienia drgań płyty z lepkosprężystą przekładką. Zewnętrzne warstwy zamodelowano płytą Kirchhoffa-Love'a, której wewnętrzna warstwa posiada charakter lepkosprężystego, jedno-kierunkowego podłoża Winklera. Małe drgania poprzecznego złożonego układu z tłumieniem są pobudzane dynamiczną ustaloną siłą [wzór] w punkcie [wzór] i zmieniająca się w czasie t. Wyniki numeryczne przedstawiono na rysunkach.

12

Zrozumiałość mowy w pomieszczeniu zamkniętym. Analiza porównawcza wyników numerycznych i symulacyjnych

Nowoświat A.

Zeszyty Naukowe. Budownictwo / Politechnika Śląska

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2004

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z. 102

323-328

PL

W pracy przedstawiono dwie metody analizy pomieszczenia pod względem odbioru dźwięku słownego. Za pomocą programu ODEON uzyskano wyniki wpływu czasu pogłosu na wskaźnik STI (Speech Transmission Index), określający zrozumiałość mowy w pomieszczeniu zamkniętym, a następnie wyniki te porównano z wynikami otrzymanymi na podstawie algorytmu własnego [4] opartego na metodzie Houtgasta i Steenekena [3] i rozważanego za pomocą programu MATLAB.

EN

The paper presents two methods of rooms' analysis in respect of speech reception. Using the ODEON software results of reverberation times influence on the STI (Speech Transmission Index), specifying the speech comprehensibility in rooms, were obtained and then the results were compared with results obtained on the basis of own algorithm [4] based on the Houtgast and Steeneken method [3] and considered using the MATLAB software.

13

Mixed radiation-convection boundary layer flow of an opically dense fluid along a vertical flat plate in a non-Darcy porous medium

Takhar H. S., Beg O. A., Chamkha A. J., Filip D., Pop I.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 3

483-496

EN

The combined effects of thermal radiation flux, thermal conductivity, Reynolds number and non-Darcian (Forcheimmer drag and Brinkman boundary resistance) body forces on steady laminar boundary layer flow along a vertical surface in an idealized geological porous medium are investigated. The classical Rosseland one-dimensional diffusion approximation is implemented in the energy equation to avoid solving the general integro-differential equation for radiative transfer. Pseudo-similarity transformations are invoked and the resulting highly coupled and non-linear set of ordinary differential equations for momentum and energy equations are solved numerically using a well-tested and highly accurate shooting Runge-Kutta quadrature with a Merson-Gill algorithm. It is shown that the dimensionless velocity functions generally increase with rising radiation parameter and the Prandtl number, and the dimensionless temperature functions decrease as the non-Darcian body forces decrease. It is also shown that the dimensionless temperature functions rise in magnitude with rising radiation parameter and the Prandtl number but are depressed by lowered non-Darcian resistance parameter and rising Reynolds number. Generally radiation is seen to substantially boost the overall heat transfer.