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Tytuł:
Numerical and analytical calculations of the free surface flow between two semi-infinite straights
Autorzy:
Chedala, Fatma Zohra
Amara, Abdelkader
Meflah, Mabrouk
Powiązania:
https://bibliotekanauki.pl/articles/1839736.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
free surface
flow
surface tension
free streamline theory
exact solution
series truncation
Weber number
numer Webera
napięcie powierzchniowe
dokładne rozwiązanie
przepływ swobodny
Opis:
The problem of two-dimensional flow with the free surface of the jet in a region between two semi-infinite straights intersections at point O is calculated analytically for each angle Beta and numerically for each of the various values of the Weber number and angle Beta. By assuming that the flow is potential, irrotational and that the fluid is incompressible and inviscid, and by taking account only the surface tension for a numerical method using the series truncation, and without the effect of gravity and surface tension for the analytic method utilize the hodograph transformation. The obtained results confirmed a good agreement between them when the Weber number tends to infinity, and the comparison of these surface shapes is illustrated.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 21-32
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical and analytical calculations of the free surface flow between two semi-infinite straights
Autorzy:
Chedala, Fatma Zohra
Amara, Abdelkader
Meflah, Mabrouk
Powiązania:
https://bibliotekanauki.pl/articles/1839739.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
free surface
flow
surface tension
free streamline theory
exact solution
series truncation
Weber number
numer Webera
napięcie powierzchniowe
dokładne rozwiązanie
przepływ swobodny
Opis:
The problem of two-dimensional flow with the free surface of the jet in a region between two semi-infinite straights intersections at point O is calculated analytically for each angle Beta and numerically for each of the various values of the Weber number and angle Beta. By assuming that the flow is potential, irrotational and that the fluid is incompressible and inviscid, and by taking account only the surface tension for a numerical method using the series truncation, and without the effect of gravity and surface tension for the analytic method utilize the hodograph transformation. The obtained results confirmed a good agreement between them when the Weber number tends to infinity, and the comparison of these surface shapes is illustrated.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 21-32
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical and numerical solutions of not exact differential equations with interpretation in Mathematica program
Analityczno-numeryczne rozwiązania równań różniczkowych niezupełnych z interpretacją w programie Mathematica
Autorzy:
Czajkowski, A. A.
Mazur-Chrzanowska, B.
Chrzanowski, R.
Udała, R.
Powiązania:
https://bibliotekanauki.pl/articles/135746.pdf
Data publikacji:
2013
Wydawca:
Wyższa Szkoła Techniczno-Ekonomiczna w Szczecinie
Tematy:
not exact differential equation
integrating factor
general integral
particular integral
analytical method
numerical method
graphical interpretation of solution
Mathematica
równanie różniczkowe niezupełne
czynnik całkujący
całka ogólna
całka szczególna
metoda analityczna
metoda numeryczna
interpretacja graficzna rozwiązania
Opis:
Introduction and aim: This paper shows the analytical and numerical solutions of some not exact differential equations. Some short description of a search procedure for integral factor in all three cases has been shown in the considerations. The main aim of this paper is to use Mathematica program to solve the not exact differential equations. Material and methods: In the paper have been analyzed exact differential equation and four not exact differential equations. In order to solve not exact differential equations and create some graphs of obtained solutions has been applied Mathematica program. Analytical and numerical methods have been used in the paper. Results: In the case of integrating factor which dependent on two variables has been shown the way of its searching by using some expectation method. In particular case, when integrating factor has form μ(x,y)=xayb the quantities a and b we can find by solving a system of two linear equations with unknown values a and b. Conclusion: Program Mathematica allows us to look, for more difficult cases, some integrating factor dependent on two variables x and y by using a expectation method.
Wstęp i cele: W pracy pokazano rozwiązania analityczne dla równań różniczkowych niezupełnych. Przestawiono krótki opis procedury szukania czynnika całkującego we wszystkich trzech przypadkach. Głównych celem pracy jest zastosowanie programu Mathematica do rozwiązywania równań różniczkowych niezupełnych. Materiał i metody: Zanalizowano równanie różniczkowe zupełne oraz cztery równania różniczkowe niezupełne. W celu wykonania wykresów otrzymanych rozwiązań szczególnych zastosowano program numeryczny Mathematica. W pracy zastosowano zarówno metodę analityczną jak i numeryczną. Wyniki: W przypadku czynnika całkującego zależnego od dwóch zmiennych pokazano sposób jego wyznaczania stosując metodę przewidywań. W szczególności gdy czynnik całkujący ma postać μ(x,y)=xayb wykładniki a oraz b znajduje się rozwiązując układ dwóch równań linowych o zmiennych a i b. Wnioski: Program Mathematica pozwala na analizę, dla bardziej trudniejszych przypadków, czynnika całkującego zależnego od dwóch zmiennych x oraz y stosując metodę przewidywań.
Źródło:
Problemy Nauk Stosowanych; 2013, 1; 5-30
2300-6110
Pojawia się w:
Problemy Nauk Stosowanych
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact controllability of a string to rest with a moving boundary
Autorzy:
Gugat, Martin
Powiązania:
https://bibliotekanauki.pl/articles/970107.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
pde constrained optimization
optimal control of pdes
optimal boundary control
wave equation
analytic solution
exact controllability
moving boundaries
mining elevator
Opis:
We consider the problem of steering a finite string to the zero state in finite time from a given initial state by controlling the state at one boundary point while the other boundary point moves. As a possible application we have in mind the optimal control of a mining elevator, where the length of the string changes during the transportation process. During the transportation process, oscillations of the elevator-cable can occur that can be damped in this way. We present an exact controllability result for Dirichlet boundary control at the fixed end of the string that states that there exist exact controls for which the oscillations vanish after finite time. For the result we assume that the movements are Lipschitz continuous with a Lipschitz constant, whose absolute value is smaller than the wave speed. In the result, we present the minimal time, for which exact controllability holds, this time depending on the movement of the boundary point. Our results are based upon travelling wave solutions. We present a representation of the set of successful controls that steer the system to rest after finite time as the solution set of two point-wise equalities. This allows for a transformation of the optimal control problem to a form where no partial differential equation appears. This representation enables interesting insights into the structure of the successful controls. For example, exact bang-bang controls can only exist if the initial state is a simple function and the initial velocity is zero.
Źródło:
Control and Cybernetics; 2019, 48, 1; 69-87
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Thermal analysis of longitudinal a porous fin with temperature-dependent internal heat generation using the variation of parameters method
Autorzy:
Güngör, Osman
Arslantürk, Cihat
Powiązania:
https://bibliotekanauki.pl/articles/1839762.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
variation of parameters method
porous fin
heat generation
exact solution
metoda wariacji parametrów
żebro porowate
wytwarzanie ciepła
dokładne rozwiązanie
Opis:
The present study investigates the thermal performance of longitudinal a porous fin with temperature-dependent internal heat generation. The Darcy model is utilized to obtain the differential form of the governing equation that solves the nonlinear temperature distribution equation using the method of variation of parameters. Although this method is applied to solve both linear and nonlinear differential equations, there exist rare applications of this method to solve nonlinear heat transfer problems. In the present study, we applied the method to estimate the thermal analysis of the porous fin exposed to convection. The heat generation is assumed as a function of temperature. The effects of the convection parameter Nc, internal heat generation ɛ, porosity Sh, and generation number G parameter on the dimensionless temperature distribution are discussed in detail. The accuracy of the variation of parameters method is verified through comparison with homotopy perturbation method and the Matlab bvp4c solver (NUM). The results have disclosed that the variation of parameters method can be used as a very effective and practical approach for further studies of the porous medium.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 3; 5-16
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Active Transient Sound Radiation Control from a Smart Piezocomposite Hollow Cylinder
Autorzy:
Hasheminejad, S. M.
Rabbani, V.
Powiązania:
https://bibliotekanauki.pl/articles/177572.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
active structural acoustic control (ASAC) thick cylindrical shells
exact elasto-acoustic analysis
time-domain solution
intelligent system
sound field attenuation
Opis:
The linear 3D piezoelasticity theory along with active damping control (ADC) strategy are applied for non-stationary vibroacoustic response suppression of a doubly fluid-loaded functionally graded piezolaminated (FGPM) composite hollow cylinder of infinite length under general time-varying excitations. The control gain parameters are identified and tuned using Genetic Algorithm (GA) with a multi-objective performance index that constrains the key elasto-acoustic system parameters and control voltage. The uncontrolled and controlled time response histories due to a pair of equal and opposite impulsive external point loads are calculated by means of Durbin’s numerical inverse Laplace transform algorithm. Numerical simulations demonstrate the superior (good) performance of the GA-optimized distributed active damping control system in effective attenuation of sound pressure transients radiated into the internal (external) acoustic space for two basic control configurations. Also, some interesting features of the transient fluid-structure interaction control problem are illustrated via proper 2D time domain images and animations of the 3D sound field. Limiting cases are considered and accuracy of the formulation is established with the aid of a commercial finite element package as well as comparisons with the current literature.
Źródło:
Archives of Acoustics; 2015, 40, 3; 359-381
0137-5075
Pojawia się w:
Archives of Acoustics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Fundamental Study on the Free Vibration of Geometrical Nonlinear Cantlever Beam using an Exact Solution and Experimental Investigation
Autorzy:
Jamal-Omidi, M.
Shayanmehr, M.
Sazesh, S.
Powiązania:
https://bibliotekanauki.pl/articles/139743.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
cantilever beam
geometrical nonlinearity
free vibrations
exact solution
experimental test
belka wspornikowa
nieliniowość geometryczna
drgania swobodne
dokładne rozwiązanie
test doświadczalny
Opis:
Two fundamental challenges in investigation of nonlinear behavior of cantilever beam are the reliability of developed theory in facing with the reality and selecting the proper assumptions for solving the theory-provided equation. In this study, one of the most applicable theory and assumption for analyzing the nonlinear behavior of the cantilever beam is examined analytically and experimentally. The theory is concerned with the slender inextensible cantilever beam with large deformation nonlinearity, and the assumption is using the first-mode discretization in dealing with the partial differential equation provided by the theory. In the analytical study, firstly the equation of motion is derived based on the theory of large deformable inextensible beam. Then, the partial differential equation of motion is discretized using the Galerkin method via the assumption of the first mode. An exact solution to the obtained nonlinear ordinary differential equation is developed, because the available semi analytical and approximated methods, due to their limitations, are not always sufficiently reliable. Finally, an experiment set-up is developed to measure the nonlinear frequency of oscillations of an aluminum beam within a domain of initial displacement. The results show that the proposed analytical method has excellent convergence with experimental data.
Źródło:
Archive of Mechanical Engineering; 2018, LXV, 1; 65-82
0004-0738
Pojawia się w:
Archive of Mechanical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact solution of fin problem with linear temperature-dependent thermal conductivity
Autorzy:
Kader, A. H. A.
Latif, A. S. A.
Nour, H. M.
Powiązania:
https://bibliotekanauki.pl/articles/122709.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
exact solution
fin equation
fin efficiency
thermal conductivity
żebro prostokątne
sprawność żebra
wymiana ciepła
przewodność cieplna
Opis:
In this paper, we obtain the general exact solution of a nonlinear fin equation which governs heat transfer in a rectangular fin with linear temperature-dependent thermal conductivity using the partial Noether method. The relationship between the fin efficiency and the thermo-geometric fin parameter is obtained. Additionally, we obtained the relationship among the fin effectiveness, the thermo-geometric fin parameter and the Biot number.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 4; 51-61
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized characteristic singular integral equation with Hilbert kernel
Autorzy:
Karczmarek, P.
Powiązania:
https://bibliotekanauki.pl/articles/255057.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
singular integral equation
characteristic equation
exact solution
Hilbert kernel
Opis:
In this paper an explicit solution of a generalized singular integral equation with a Hilbert kernel depending on indices of characteristic operators is presented.
Źródło:
Opuscula Mathematica; 2008, 28, 3; 287-294
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Singular integral equation with a multiplicative Cauchy kernel in the half-plane
Autorzy:
Karczmarek, P.
Powiązania:
https://bibliotekanauki.pl/articles/255089.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
singular integral equation
exact solution
Cauchy kernel
multiplicative kernel
Opis:
In this paper the explicit solutions of singular integral equation with a multiplicative Cauchy kernel in the half-plane are presented.
Źródło:
Opuscula Mathematica; 2008, 28, 1; 63-72
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Controllability of semilinear systems with fixed delay in control
Autorzy:
Kumar, S.
Sukavanam, N.
Powiązania:
https://bibliotekanauki.pl/articles/952777.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
first order delay system
mild solution
fixed point
exact controllability
Opis:
In this paper, different sufficient conditions for exact controllability of semilinear systems with a single constant point delay in control are established in infinite dimensional space. The existence and uniqueness of mild solution is also proved under suitable assumptions. In particular, local Lipschitz continuity of a nonlinear function is used. To illustrate the developed theory some examples are given.
Źródło:
Opuscula Mathematica; 2015, 35, 1; 71-83
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical models for compact stars with a linear equation of state
Autorzy:
Malaver, Manuel
Powiązania:
https://bibliotekanauki.pl/articles/1191971.pdf
Data publikacji:
2016
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Einstein-Maxwell system
linear equation of state
charge density
MIT-Bag Model
metric function
exact solution
Opis:
In this paper, we found two new classes of solutions to the Einstein-Maxwell system of equations for compact stars assuming an anisotropic pressure and a linear equation of state for the matter distribution within the framework of MIT-Bag Model with a particular form of the metric function. The exact solutions can be written in terms of elementary function in presence of an electromagnetic field. All the obtained models have a singularity in the charge density but not admit singularities in the matter and metric functions at the centre.
Źródło:
World Scientific News; 2016, 50; 64-73
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Group invariant solution of some time fractional evolution equations
Autorzy:
Mandal, H.
Bira, B.
Powiązania:
https://bibliotekanauki.pl/articles/122890.pdf
Data publikacji:
2018
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional coupled Burger’s equation
fractional DSSH equations
Riemann Liouville’s fractional derivative
Erdélyi-Kober operator
symmetry analysis
exact solution
równania ewolucji
ułamkowe równania różniczkowe
ułamkowe równania DSSH
pochodna ułamkowa Riemanna Liouville'a
operator Erdélyi-Kober
Opis:
In this paper, we consider some classes of a system of nonlinear fractional differential equations (FDEs) arising in some important physical phenomena. Using symmetry group of transformations, the given systems of fractional partial differential equations (FPDEs) are reduced to systems of fractional ordinary differential equations (FODEs). Further, using the group invariant condition, we solve the reduced systems of FODEs and exact solutions of the given equations are constructed. Finally, the physical significance of the solutions are investigated graphically based on the exact solutions in order to highlight the importance of the study.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 4; 35-46
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hypothetical analysis for peristaltic transport of metallic nanoparticles in an inclined annulus with variable viscosity
Autorzy:
Nadeem, S.
Sadaf, H.
Powiązania:
https://bibliotekanauki.pl/articles/201426.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
inclined annulus
viscous nanofluid
peristaltic flow
variable viscosity
exact solution
pierścień
nanofluid
przepływ perystaltyczny
dokładne rozwiązanie
Opis:
The main objective of this article is to present a mathematical model for peristaltic transport in an inclined annulus. In this analysis, two-dimensional flow of a viscous nanofluid is observed in an inclined annulus with variable viscosity. Copper as nanoparticle with blood as its base fluid has been considered. The inner tube is unifom or rigid, while the outer tube takes a sinusoidal wave. Governing equations are solved under the well-known assumptions of low Reynolds number and long-wavelength. Exact solutions have been established for both velocity and nanoparticle temperature. The features of the peristaltic motion are explored by plotting graphs and discussed in detail.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2016, 64, 2; 447-454
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact solution for large amplitude flexural vibration of nanobeams using nonlocal Euler-Bernoulli theory
Autorzy:
Nazemnezhad, R.
Hosseini-Hashemi, S.
Powiązania:
https://bibliotekanauki.pl/articles/279261.pdf
Data publikacji:
2017
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
nonlinear free vibration
nonlocal elasticity
nanobeam
exact solution
elliptic integrals
Opis:
In this paper, nonlinear free vibration of nanobeams with various end conditions is studied using the nonlocal elasticity within the frame work of Euler-Bernoulli theory with von K´arm´an nonlinearity. The equation of motion is obtained and the exact solution is established using elliptic integrals. Two comparison studies are carried out to demonstrate accuracy and applicability of the elliptic integrals method for nonlocal nonlinear free vibration analysis of nanobeams. It is observed that the phase plane diagrams of nanobeams in the presence of the small scale effect are symmetric ellipses, and consideration the small scale effect decreases the area of the diagram.
Źródło:
Journal of Theoretical and Applied Mechanics; 2017, 55, 2; 649-658
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
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