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    Wyświetlanie 1-26 z 26
    Tytuł:
    Solitary wave solution to the nonlinear evolution equation in cascaded quadratic media beyond the slowly varying envelope approximations
    Autorzy:
    Sarma, A K
    Biswas, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/174484.pdf
    Data publikacji:
    2014
    Wydawca:
    Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
    Tematy:
    solitons
    integrability
    exact solution
    cascaded quadratic media
    Opis:
    We report an exact bright and dark soliton solution to the nonlinear evolution equation derived by MOSES and WISE (Phys. Rev. Lett. 97, 2006, 073903) for cascaded quadratic media beyond the slowly varying envelope approximations. The integrability aspects of the model are addressed. The travelling wave hypothesis as well as the ansatz method are employed to obtain an exact 1-soliton solution. Both bright and dark soliton solutions are obtained. The corresponding constraint conditions are obtained in order for the soliton solutions to exist.
    Źródło:
    Optica Applicata; 2014, 44, 2; 205-212
    0078-5466
    1899-7015
    Pojawia się w:
    Optica Applicata
    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:
    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
    Tytuł:
    Green’s function for a multifield material with a heat source
    Autorzy:
    Rogowski, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/279505.pdf
    Data publikacji:
    2016
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    Green's functions
    point heat source
    multifield material
    magneto-electro-thermo-elastic fundamental solution
    multifield composites
    exact solution
    Opis:
    Green’s functions for a multifield material subjected to a point heat source are presented in an explicit analytical form. The study concerns the steady-state thermal loading infi- nite region, half-space region and two-constituent magneto-electro-thermo-elastic material region. The new mono-harmonic potential functions, obtained by the author, are used in the analysis. The elastic displacement, electric potential, magnetic potential and induced by those coupled multifield physical quantities, caused by internal or external heat sources, are limited and presented in a very useful form, exactly and explicitly.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2016, 54, 3; 743-755
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Exact Analytical Solutions of Nonlinear Differential Equation of a Large Amplitude Simple Pendulum
    Autorzy:
    Sobamowo, M. G.
    Powiązania:
    https://bibliotekanauki.pl/articles/1030465.pdf
    Data publikacji:
    2020
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Exact Analytical solution
    Large amplitude
    Oscillation system
    Strong nonlinearity
    Opis:
    The governing equation of large amplitude simple pendulum is a nonlinear equation which is very difficult to be solved exactly and analytically. However, the classical way for finding analytical solution is obviously still very much important. This is because an exact analytical solution serves as an accurate benchmark for numerical solution and provides a better insight into the significance of various system parameters affecting the phenomena than the numerical solution. Therefore, in this present work, exact analytical solutions for nonlinear differential equation of large amplitude simple pendulum is presented. Also, with the aid of the exact analytical solutions, parametric studies are carried out to study the effects of the model parameters on the dynamic behavior of the large-amplitude nonlinear oscillation system. The solutions can serve as benchmarks for the numerical solution or approximate analytical solution.
    Źródło:
    World Scientific News; 2020, 144; 70-88
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A simplified elliptical function solution for coupled nonlinear vibration of multilayer graphene sheets
    Autorzy:
    Venkatraman, G.
    Suji, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/2086951.pdf
    Data publikacji:
    2022
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    nonlinear coupled vibration
    nonlinear van der Waals force
    Multilayer Graphene Sheets
    elliptical function
    exact solution
    Opis:
    This paper presents a simple exact solution for coupled nonlinear free vibration analysis of Multilayer Graphene Sheets (MLGS) using elliptical functions. Though elliptical functions are used in nonlinear dynamics, they are employed to find the exact solution of a coupled system for the first time. The nonlinear dynamic equation including geometric nonlinearity and Eringen nonlocal theory is uncoupled by elliptical functions, and exact solutions for simply supported boundary conditions are obtained. The results are compared with the harmonic balance method. The nonlinear frequency of MLGS is studied for its effects with a small scale parameter, and the linear and nonlinear van der Waals force.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2022, 60, 1; 3--16
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    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:
    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 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:
    Mathematical modelling of heat transfer in liquid flat-plate solar collector tubes
    Autorzy:
    Zima, W.
    Dziewa, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/240431.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    kolektor słoneczny
    model matematyczny
    rozwiązanie dokładne
    stan przejściowy
    exact solution
    mathematical model
    solar collector
    transient state
    Opis:
    The paper presents a one-dimensional mathematical model for simulating the transient processes which occur in the liquid flat-plate solar collector tubes. The proposed method considers the model of collector tube as one with distributed parameters. In the suggested method one tube of the collector is taken into consideration. In this model the boundary conditions can be time-dependent. The proposed model is based on solving the equation describing the energy conservation on the fluid side. The temperature of the collector tube wall is determined from the equation of transient heat conduction. The derived differential equations are solved using the implicit finite difference method of iterative character. All thermo-physical properties of the operating fluid and the material of the tube wall can be computed in real time. The time-spatial heat transfer coefficient at the working fluid side can be also computed on-line. The proposed model is suitable for collectors working in a parallel or serpentine tube arrangement. As an illustration of accuracy and effectiveness of the suggested method the computational verification was carried out. It consists in comparing the results found using the presented method with results of available analytic solutions for transient operating conditions. Two numerical analyses were performed: for the tube with temperature step function of the fluid at the inlet and for the tube with heat flux step function on the outer surface. In both cases the conformity of results was very good. It should be noted, that in real conditions such rapid changes of the fluid temperature and the heat flux of solar radiation, as it was assumed in the presented computational verification, do not occur. The paper presents the first part of the study, which aim is to develop a mathematical model for simulating the transient processes which occur in liquid flat-plate solar collectors. The experimental verification of the method is a second part of the study is not presented in this paper. In order to perform this verification, the mathematical model would be completed with additional energy conservation equations. The experimental verification will be carry out in the close future.
    Źródło:
    Archives of Thermodynamics; 2010, 31, 2; 45-62
    1231-0956
    2083-6023
    Pojawia się w:
    Archives of Thermodynamics
    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:
    Contact problem of conducting and heated punch on a multifield foundation
    Autorzy:
    Rogowski, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/264461.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    magneto-electro-thermo-elastic medium
    conducting and heated punch
    contact problem
    exact solution
    sprężystość materiałów
    potencjał elektryczny
    potencjał magnetyczny
    Opis:
    The solution for a multifield material subjected to temperature loading in a circular region is presented in an explicit analytical form. The study concerns the steady – state thermal loading infinite region (heated embedded inclusion), half – space region and two – constituent magneto – electro – thermo – elastic material region. The new mono – harmonic potential functions, obtained by the author, are used in the analysis of punch problem. The more interested case in which the contact region is annular is analyzed. By using the methods of triple integraf equations and series solution technique the solution for an indentured multifield substrate over an annular contact region is given. The sensitivity analysis of obtained indentation parameters shows some interesting points. In particular, it shows that the increasing of the applied electric and magnetic potentials reduces the indentation depth in multifield materials.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2015, 20, 3; 531-564
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of mode I conducting crack in piezo-electro-magneto-elastic layer
    Autorzy:
    Rogowski, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/264519.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    warstwa elastyczna
    szczelina dielektryczna
    natężenie pola
    magneto electro-elastic layer
    penny-shaped crack
    dielectric crack
    field intensity factors
    exact solution
    Opis:
    Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto - electrically dielectric crack embedded in a magnetoelectroelastic layer is investigated. The prescribed displacement, electric potential and magnetic potential boundary conditions on the layer surfaces are adopted. Applying the Hankel transform technique, the boundary - value problem is reduced to solving three coupling Fredholm integral equations of second kind. These equations are solved exactly. The corresponding semi - permeable crack - face magnetoelectric boundary conditions are adopted and the electric displacement and magnetic induction of crack interior are obtained explicitly. This field inside the crack is dependent on the material properties, applied loadings, the dielectric permittivity and magnetic permeability of crack interior, and the ratio of the crack length and the layer thickness. Field intensity factors are obtained as explicit expressions.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2013, 18, 1; 153-176
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    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:
    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:
    Application of Rank Controlled Differential Quadrature Method for Solving an Infinite Steel Plate Cooling Problem
    Autorzy:
    Żak, P. L.
    Suchy, J. S.
    Lelito, J.
    Gracz, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/381994.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    information technology
    foundry industry
    solidification process
    exact solution
    rank controlled differential quadrature
    numerical modelling
    technologia informatyczna
    przemysł odlewniczy
    proces krzepnięcia
    dokładne rozwiązanie
    kwadratura różniczkowa sterowanego rzędu
    modelowanie numeryczne
    Opis:
    Rank Controlled Differential Quadrature method is a numerical method that allows to approximate the partial derivatives that appears in partial differential equations. Those equations with proper geometrical, physical, initial and boundary conditions make mathematical models of physical process. The heat transfer process is governed by Fourier–Kirchhoff equation, which is parabolic Partial Differential Equation. In this paper authors present the steel plate cooling problem. At the beginning of the process plate is heated up to 450 °C and is cooled to ambient temperature. The cooling of the plate is basic heat transfer problem. If the plates dimensions has proper proportions such problem may be described as one dimensional and solved exactly. The mathematical model and exact solution is given in the work. Authors apply the Rank Controlled Differential Quadrature to approximate derivatives in Fourier–Kirchhoff equation and in boundary conditions. After changing derivatives into quadrature formulation set of algebraic equations is obtained. Substituting thermo-physical parameters numerical model is obtained. The computer program was prepared to solve the problem numerically. Results of simulation are confronted with the exact ones. Error value at each time step as well as error value increase rate for examined numerical method is analyzed.
    Źródło:
    Archives of Foundry Engineering; 2013, 13, 3 spec.; 201-206
    1897-3310
    2299-2944
    Pojawia się w:
    Archives of Foundry Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Anti – plane crack emanating from the interface in a bounded smart PEMO- elastic structure
    Autorzy:
    Rogowski, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/955285.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    interfejs
    natężenie pola
    transformacja Fouriera
    równanie Cauchy'ego
    interface
    anti-plane shear crack
    singularity of power law
    field intensity factors
    magnetoelectroelastic behaviour
    Fourier transform
    Cauchy singular integral equation
    exact solution
    Opis:
    The magnetoelectroelastic analysis of two bonded dissimilar piezo-electro-magneto-elastic ceramics with a crack perpendicular to and terminating at the interface is made. By using the Fourier integral transform (in perpendicular directions in each materials), the mixed boundary conditions and continuity conditions are transformed to a singular integral equation with generalized Cauchy kernel, the solution of which has been well studied, and classical methods are directly applicable here to obtain the closed form solution. The results are presented for a permeable crack under anti-plane shear loading and in-plane electric and magnetic loadings, as prescribed electric displacement and magnetic inductions or electric and magnetic fields. The results indicate that the magnetoelectroelastic field near the crack tip in the homogeneous PEMO- elastic ceramic is dominated by a traditional inverse square-root singularity, while the coupled field near the crack tip at the interface exhibits the singularity of the power law r--α , r being the distance from the interface crack tip and α depending on the material constants of a bimaterial. In particular, electric and magnetic fields have no singularity at the crack tip in a homogeneous solid, whereas they are singular around the interface crack tip. Numerical results are given graphically to show the effects of the material properties on the singularity order, field intensity factors and energy release rates. The results presented in this paper should have potential applications to the design of multilayered magnetoelectroelastic structures.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2013, 18, 4; 1165-1199
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    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:
    On the multisummability of WKB solutions of certain singularly perturbed linear ordinary differential equations
    Autorzy:
    Takei, Y.
    Powiązania:
    https://bibliotekanauki.pl/articles/255041.pdf
    Data publikacji:
    2015
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    exact WKB analysis
    WKB solution
    multisummability
    Opis:
    Using two concrete examples, we discuss the multisummability of WKB solutions of singularly perturbed linear ordinary differential equations. Integral representations of solutions and a criterion for the multisummability based on the Cauchy-Heine transform play an important role in the proof.
    Źródło:
    Opuscula Mathematica; 2015, 35, 5; 775-802
    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:
    Open tandem networks with blocking analysis – two approaches
    Autorzy:
    Oniszczuk, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/205602.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    two-node network with blocking
    multi-server tandem queues
    exact algorithm
    product form solution
    Opis:
    The paper describes an analytical study of open twonode (tandem) network models with blocking. Here, a specific tandem configuration is chosen: the first node is treated as an infinite server (IS - often referred to as the ample-server), meaning that any incoming task can find at least one empty line for service in this node, and the second node has several parallel lines that can serve input task streams simultaneously. Between these two nodes there is a buffer with finite capacity. In this type of network, if the buffer is full, the accumulation of new tasks by the second node is temporarily suspended (blocking factor) and tasks must wait at the first node until the transmission process is resumed. In this paper, the two-node model is investigated using two different methods. The first is the multi-step exact algorithm, involving a numerical part for solving a set of linear equations, and the second is an approximate algorithm using a product form solution. The numerical part is used for solving a system of linear equations and for calculating the state probability vector. Finally, after comparing both algorithms, some recommendations as to when each method can be used are given.
    Źródło:
    Control and Cybernetics; 2014, 43, 1; 111-132
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    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:
    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:
    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
      Wyświetlanie 1-26 z 26

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