Wyniki wyszukiwania - Biblioteka Nauki

1

Analytical solution of Cattaneo equation

100%

Lupa M.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2007

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tom Vol. 6, nr 1

127-132

EN

The Cattaneo equation supplemented by adequate boundary and initial conditions is considered. The solution of this equation is found in analytic way. In the final part of the paper the computations basing on the solution presented are shown.

2

An interface crack with mixed electro-magnetic conditions at it faces in a piezoelectric / piezomagnetic bimaterial under anti-plane mechanical and in-plane electric loadings

100%

Onopriienko O. , Loboda V. , Sheveleva A. , Lapusta Y.

Acta Mechanica et Automatica

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2018

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tom Vol. 12, no. 4

301--310

EN

An interface crack between two semi-infinite piezoelectric/piezomagnetic spaces under out-of-plane mechanical load and in-plane electrical and magnetic fields parallel to the crack faces is considered. Some part of the crack faces is assumed to be electrically conductive and having uniform distribution of magnetic potential whilst the remaining part of the crack faces is electrically and magnetically permeable. The mechanical, electrical, and magnetic factors are presented via functions which are analytic in the whole plane except the crack region. Due to these representations the combined Dirichlet-Riemann and Hilbert boundary value problems are formulated and solved in rather simple analytical form for any relation between conductive and permeable zone lengths. Resulting from this solution the analytical expressions for stress, electric and magnetic fields as well as for the crack faces displacement jump are presented. The singularities of the obtained solution at the crack tips and at the separation point of the mention zones are investigated and the formulas for the corresponding intensity factors are presented. The influence of external electric and magnetic fields upon the mechanic, electric and magnetic quantities at the crack region are illustrated in graph and table forms.

3

Behavior of the single-pulse operation switched reluctance motors

100%

Zaskalicky P.

Prace Naukowe Instytutu Maszyn, Napędów i Pomiarów Elektrycznych Politechniki Wrocławskiej. Studia i Materiały

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2000

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tom Vol. 48, nr 20

245-251

EN

The paper deals with analytic solution of currents and torque of Switched Reluctance Motor resulting in calculation of switching angles of the power transistors in supplying converter. The course of the inductance is replaced by a Fourier series.

PL

Przedstawiono dla założonych kątów załączenia tranzystorów mocy w przekształtniku zasilającym analityczne zależności dla prądów i momentu w silniku reluktancyjnym przełączalnym (SRM). Przebiegi indukcyjności zastąpiono szeregami Fouriera.

4

Analytical solution for certain nonlinear electromagnetic field problems

100%

Sowa M. , Spałek D.

Poznan University of Technology Academic Journals. Electrical Engineering

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2012

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tom No. 69

49--56

EN

The paper presents a nonlinear electromagnetic field problem with cylindrical symmetry. A time-sinusoidal boundary condition is applied, which yields non-sinusoidal steady-state fields. The problem is brought forth to test an analytical-numerical method based on the method of small parameter. A distinctive feature of this method is that it requires symbolic calculations to be performed. These allow to reduce the problem to a system of nonlinear equations. In order to check the accuracy of the solution, several error criteria are introduced. Moreover, the power balance of a nonlinear conductive region is verified.

5

Heat Conduction in Grinding

100%

De Payrebrune K. M. , Kuhnert M. , Kroger M.

Machine Dynamics Research

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2011

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tom Vol. 35, No. 4

92-104

EN

Grinding is used as finishing process to increase surface quality but also as main manufacturing operation to generate workpiece geometries. Within the contact area of workpiece and grinding wheel the material removal takes place by irregular abrasive grain engagements. The sliding movement of the grinding wheel and the tangential force component lead to rising temperatures within the workpiece. Due to that, burning or structural changes of the material can occur. This decreases the quality of the manufactured workpiece. To find stable process parameters with high efficiency, models are needed to predict the heat distribution. In this work especially the heat conduction of simple grinding processes are analyzed and predicted by an analytical solution. Temperature measurements at special points and measurements of the heat distribution are used to verify the calculations.

6

A simple trajectory model for the near and far field of a jet in a cross flow

100%

Toften T. H. , Holdo A. E. , Bullen P. R.

Applied Mechanics and Engineering

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2000

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tom Vol. 5, no 2

471-483

EN

Even with the present day extensive use of Computational Fluid Dynamics (CFD), simplified analytical expressions for Fluid Dynamic phenomena have their applications in highlighting significant mechanisms and aiding initial engineering estimates. The present work shows that experimental data for the trajectory of the centre line of jets exposed to a cross-flow can be found from a single expression. The expression is derived from first principles and unlike most other power law formulas the exponents are not empirically determined from measurements. In comparison with other single expressions based on dimensional analysis, which results in differing expressions for differing parts of the flow field, the equation presented here combines the asymptotic assumptions into a single expression.

7

New analysis of natural convection boundary layer flow on a horizontal plate with variable wall temperature

100%

Mehrizi A. A. , Vazifeshenas Y. , Domairry G.

Journal of Theoretical and Applied Mechanics

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2012

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tom Vol. 50 nr 4

1001-1010

EN

In this study, steady laminar free convection boundary layer flow on a horizontal plate is investigated through analytical solutions. By transforming the governing non-dimensional boundary layer equations into an ordinary differential equation, the application of the Homotopy Analysis Method can be practical. So in this case, the analytical results for different Prandtl numbers and constant M values which portray the power index are achieved. The trend goes on large amounts of (M ��>> 1) and the results are compared with other efforts. Furthermore, the effects of different values of Prandtl number and M values on temperature and velocity profiles are verified.

PL

W pracy zajęto się swobodnym, laminarnym opływem konwekcyjnej warstwy przyściennej na poziomej płycie w ujęciu czysto analitycznym. Bezwymiarowe równania warstwy przekształcono do postaci różniczkowej zwyczajnej, co pozwoliło na zastosowanie metody homotopii. Otrzymano analityczne wyniki określające wykładnik potęgowy opływu dla różnych wartości liczby Prandtla oraz stałej M. Badania rozszerzono na �>> 1, a rezultaty porównano z opracowaniami innych badaczy. Zweryfikowano również wpływ liczby Prandtla oraz stałej M na rozkład temperatury i prędkości opływu w rozważanej warstwie.

8

Analytical solution for one-dimensional consolidation of unsaturated soils under dynamic load

88%

Liu Z.-Y. , Song Y. , Zhou F.-X. , Wang L.-Y.

Journal of Theoretical and Applied Mechanics

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2023

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tom Vol. 61 nr 1

11--22

EN

Firstly, in this paper, based on the theory of the porous elastic medium and combined with the effective stress principle of unsaturated soil, a set of governing equations is established to describe consolidation of the unsaturated soil. Secondly, an analytical expression under any dynamic loads is obtained with the help of Laplace integral transformation. Finally, analysis of numerical examples under specific boundary conditions is made to discuss one-dimensional consolidation characteristics under harmonic loads and the influence of factors on the consolidation characteristics of unsaturated soil, such as excitation frequency and initial saturation.

9

Screw dislocations in piezoelectric laminates with four or more phases

88%

Wang X. , Chen L. , Schiavone P.

Archives of Mechanics

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2019

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tom Vol. 71, nr 3

239--262

EN

We present an analytical solution to the problem of a screw dislocation in a four-phase piezoelectric laminate composed of two piezoelectric layers of equal thickness sandwiched between two semi-infinite piezoelectric media. A new version of the complex variable formulation is proposed such that the 2 × 2 real symmetric matrix appearing in the formulation becomes dimensionless. Using analytic continuation, the original boundary value problem is reduced to the identification of a single 2D analytic vector function which is completely determined following rigorous solution of the resulting linear recurrence relations in matrix form. An explicit expression for the image force acting on the piezoelectric screw dislocation is obtained once the single 2 × 2 real matrix function is identified. We also discuss the solution for a screw dislocation in an N-phase piezoelectric laminate composed of N − 2 piezoelectric layers of equal thickness sandwiched between two semi-infinite piezoelectric media.

10

Shape of dispersion curves in the Rayleigh--Lamb spectrum

88%

Ahmad F.

Archives of Mechanics

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2004

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tom Vol. 56, nr 2

157-165

EN

The following features of the symmetric Lamb modes in an elastic waveguide are well known: 1. There exists no mode with phase speed less than cR. 2. There is only one mode whose speed asymptotically approaches cR. 3. A horizontal line above c = cT (including the line c = cL) cannot be an asymptote to any of the modes. 4. Phase speed of all modes, except the lowest mode, approaches cT as the frequency becomes very large. The above features characterize the spectrum which is obtained numerically or experimentally but are not fully understood analytically. We analyze the Rayleigh-Lamb equation and provide analytical explanation for the above features.

11

Analytical solutions for the unsteady MHD rotating flow over a rotating sphere near the equator

88%

Sweet E. , Vajravelu K. , Gorder R.

Open Physics

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2011

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tom 9

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nr 1

167-175

EN

In this paper we investigate the three-dimensional magnetohydrodynamic (MHD) rotating flow of a viscous fluid over a rotating sphere near the equator. The Navier-Stokes equations in spherical polar coordinates are reduced to a coupled system of nonlinear partial differential equations. Self-similar solutions are obtained for the steady state system, resulting from a coupled system of nonlinear ordinary differential equations. Analytical solutions are obtained and are used to study the effects of the magnetic field and the suction/injection parameter on the flow characteristics. The analytical solutions agree well with the numerical solutions of Chamkha et al. [31]. Moreover, the obtained analytical solutions for the steady state are used to obtain the unsteady state results. Furthermore, for various values of the temporal variable, we obtain analytical solutions for the flow field and present through figures.

12

An analytical solution for dynamic response of water barrier subjected to strong shock waves caused by an underwater explosion to dams

88%

Lu L. , Zou D. , Zhu Y. , Dong Y. , Zuo C. , Wu Y.

Polish Maritime Research

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2017

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tom S 2

111--117

EN

Shock waves arriving at a dam site are close to plane waves when the center of an underwater explosion is far from the dam site. In general, the wave pressure is calculated with COLE empirical formula. The COLE formula is a negative exponential function with respect to time. In this paper, a new analytical solution algorithm is proposed, which does not require the use of step-by-step time integration. In Comparison with the step-by-step time integration, the proposed algorithm requires relatively less calculation and avoids high-frequency oscillation. Furthermore, the vertical upstream surface and the sloping upstream surface in two types of the dams are analyzed in this paper. The research results indicate that the analytical solution can be applied for a dam with a vertical upstream surface. However, because the upstream face of a dam is inclined, the analytical solution can be obtained only for dams that are at lower height. Whenever the height of a dam is higher, then no analytical solution can be obtained, and only the use of step-by-step time integration can obtain a solution.

13

Analysis of delamination in two-dimensional functionally graded multilayered beam with non-linear behaviour of material

88%

Rizov V. I.

Engineering Transactions

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2018

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tom Vol. 66, iss. 1

61--78

EN

An analytical study of delamination fracture in a two-dimensional functionally graded multilayered beam exhibiting material non-linearity is carried-out. The beam is made of adhesively bonded horizontal layers. The material is two-dimensional functionally graded in the cross-section of each layer. A delamination crack is located symmetrically with respect to the beam mid-span. The delamination is studied in terms of the strain energy release rate. The solution derived is compared with the J-integral for verification. The effects of material gradients, the crack location along the beam height and the material non-linearity on the delamination fracture are investigated. The distribution of the J-integral value along the crack front is analysed too.

14

Analytical solutions of heat transfer for laminar flow in rectangular channels

88%

Mikielewicz J. , Rybiński W.

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nr 4

15

Nonlinear dispersion of a pollutant ejected into a channel flow

88%

Gorder R. , Vajravelu K.

Open Physics

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2011

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tom 9

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nr 5

1182-1194

EN

In this paper, we study the nonlinear coupled boundary value problem arising from the nonlinear dispersion of a pollutant ejected by an external source into a channel flow. We obtain exact solutions for the steady flow for some special cases and an implicit exact solution for the unsteady flow. Additionally, we obtain analytical solutions for the transient flow. From the obtained solutions, we are able to deduce the qualitative influence of the model parameters on the solutions. Furthermore, we are able to give both exact and analytical expressions for the skin friction and wall mass transfer rate as functions of the model parameters. The model considered can be useful for understanding the polluting situations of an improper discharge incident and evaluating the effects of decontaminating measures for the water bodies.

16

Effectiveness factor of two-dimensional ring-shaped catalyst pellets

88%

Asif M. , Ibrahim A. A. , Mohammed Y. A. , Al-Ghurabi E. H.

Polish Journal of Chemical Technology

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2017

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tom Vol. 19, nr 3

99--105

EN

The use of hollow catalytic support improves the utilization of the catalytic material because of the absence of the pellet core, and moreover ensures low reactor pressure drop owing to enhanced bed voidage. In this study, the expressions for the efficient computation of the effectiveness factor are derived for a ring-shaped catalyst pellet undergoing first-order irreversible reaction. The methodology consists of using solutions of one-dimensional problems to remove non-homogeneous boundary conditions. The expressions obtained exhibit significantly faster convergence behavior than those reported in literature. The shape parameters, namely, the height-to-diameter ratio and the inner-to-outer radii ratio, significantly affect the catalyst utilization, such that several-fold improvement in the effectiveness factor is achievable.

17

Indentation theory on orthotropic materials subjected to a frictional moving punch

88%

Zhou Y. T. , Lee K. Y. , Jang Y. H.

Archives of Mechanics

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2014

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tom Vol. 66, nr 2

71--94

EN

The present article establishes a general theory of frictional moving contact of orthotropic materials indented by a moving rigid punch with various punch profiles. The punch moves to the right or left at a constant speed with the shear stress arising inside the contact region. The motion should be subsonic. By using Galilean transformation and Fourier transform, a singular integral equation of the second kind is obtained, solution of which has a non-square-root or unconventional singularity. Numerical results are presented to show the influences of relative moving velocity and the friction coefficient on surface in-plane stress for each case of the four types of punches, which demonstrates that the surface crack initiation and propagation in load transfer components more likely occur at the trailing edge. The present theory provides a basis for explaining the surface damage mechanism of orthotropic materials under an indentation loading and for exploiting the physics behind the different punch profiles.

18

MHD flow of Walters’ liquid B over a nonlinearly stretching sheet

75%

Siddheshwar P. G. , Mahabaleshwar U. S. , Chan A.

International Journal of Applied Mechanics and Engineering

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2015

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tom Vol. 20, no. 3

589--603

EN

The paper discusses the boundary layer flow of a weak electrically conducting viscoelastic Walters’ liquid B over a nonlinearly stretching sheet subjected to an applied transverse magnetic field, when the liquid far awal from the surface is at rest. The stretching is assumed to be a quadratic function of the coordinate along the direction of stretching. An analytical expression is obtained for the stream function and velocity components as a function of the viscoelastic parameter, the Chandrasekhar number and stretching related parameters. The results have possible technological applications in liquid based systems involving stretchable materials.

19

Analytical solution of equations describing slow axonal transport based on the stop-and-go hypothesis

75%

Kuznetsov A.

Open Physics

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2011

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tom 9

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nr 3

662-673

EN

This paper presents an analytical solution for slow axonal transport in an axon. The governing equations for slow axonal transport are based on the stop-and-go hypothesis which assumes that organelles alternate between short periods of rapid movement on microtubules (MTs), short on-track pauses, and prolonged off-track pauses, when they temporarily disengage from MTs. The model includes six kinetic states for organelles: two for off-track organelles (anterograde and retrograde), two for running organelles, and two for pausing organelles. An analytical solution is obtained for a steady-state situation. To obtain the analytical solution, the governing equations are uncoupled by using a perturbation method. The solution is validated by comparing it with a high-accuracy numerical solution. Results are presented for neurofilaments (NFs), which are characterized by small diffusivity, and for tubulin oligomers, which are characterized by large diffusivity. The difference in transport modes between these two types of organelles in a short axon is discussed. A comparison between zero-order and first-order approximations makes it possible to obtain a physical insight into the effects of organelle reversals (when organelles change the type of a molecular motor they are attached to, an anterograde versus retrograde motor).

20

Displacement potential solution of short stiffened flat composite bars under axial loading

75%

Deb Nath S. K. , Reaz Ahmed S. , Afsar A. M.

International Journal of Applied Mechanics and Engineering

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2006

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tom Vol. 11, no 3

557-575

EN

The present paper describes a new approach to analytical solution of two-dimensional stress problems of orthotropic composite materials. In this approach, the elastic problem is formulated in terms of a single potential function, defined in terms of the displacement components, which satisfies a single differential equation of equilibrium. The new mathematical model, namely, the displacement potential formulation is especially suitable for the solution of mixed-boundary-value elastic problems of orthotropic composite materials. This paper presents the solution of stresses and displacements at different sections of short stiffened flat composite bars under axial loading, where a number of bar aspect ratios are considered together with different materials of interest. The solutions are obtained in the form of infinite series and the results are presented mainly in the form of graphs. The results appear to be quite reasonable and accurate, and thus establish the soundness as well as reliability of the present displacement potential approach.