Wyniki wyszukiwania - Biblioteka Nauki

1

Jednoznaczność rozwiązań zadań brzegowych liniowej teorii termopiezoelektryczności

100%

Jędrzejczyk-Kubik J.

Zeszyty Naukowe. Budownictwo / Politechnika Śląska

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1999

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tom z. 86

87-93

PL

W pracy dowodzi się twierdzenia o jednoznaczności problemu początkowo - brzegowego w liniowej teorii termopiezopolimerów. Dowód przeprowadza się na podstawie transformaty Laplace'a.

EN

In this paper the theorem about uniqueness of the solution of the boundary - initial value problems in linear theory of thermopiezopolymer is proved. The proof is based ou the use t

2

Cardinality and Probability Under Intuitionistic and Interval-Valued Fuzzy Sets

75%

Mańko J. , Niewiadomski A.

Journal of Applied Computer Science

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2006

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tom Vol. 14, nr 1

31-41

EN

The paper focuses on probability and cardinalities in terms of intuitionistic and interval-valued fuzzy sets under classic Laplace's approach. We use the necessity and possibility operators for intuitionistic fuzzy sets, and the type-reduction operations for interval-valued fuzzy sets. In both cases, formulae for the classic probability of an intuitionistic and interval-valued fuzzy event are discussed.

3

Wyznaczanie niestacjonarnych pól temperatury : porownanie metod numerycznych w obszarach 2D

75%

Fraska A.

Zeszyty Naukowe Politechniki Poznańskiej. Budowa Maszyn i Zarządzanie Produkcją

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2005

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tom Nr 2

5-16

PL

W artykule porównano dokładność metod numerycznych. Jako przykłady testowe wykorzystano dwuwymiarowe zagadnienia początkowo-brzegowc mające dokładne rozwiązania. Porównano dwie różne wersje metody kolokacji brzegowej. Pierwsza z nich to metoda źródeł pozornych, w której jest wykorzystana metoda kolokacji brzegowej i metoda rozwiązań podstawowych. Druga jest oparta na transformacji Laplace'a oraz na metodzie rozwiązań podstawowych. Na podstawie otrzymanych wyników można stwierdzić, że metoda oparta na transformacji Laplace'a jest lepsza pod względem dokładności niż metoda źródeł pozornych.

4

Disturbance due to inclined load in generalized thermoelastic medium with two temperatures

75%

Kumar R. , Kaushal S.

International Journal of Applied Mechanics and Engineering

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2008

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tom Vol. 13, no 3

695-706

EN

The present investigation is concerned with the deformation in a homogeneous, isotropic thermoelastic half-space with two temperatures as a result of an inclined load. The inclined load is assumed to be a linear combination of a normal load and a tangential load. The integral transform technique is used to solve the problem. As an application of the approach concentrated and uniformly distributed loads have been considered. The transformed components of displacement, stress, conductive temperature and temperature distribution are inverted by using the numerical inversion technique. The effect of two temperatures and response of two generalized theories of thermoelasticity (Lord and Shulman (L-S), Green and Lindsay (G-L) theories) on the resulting quantities have been depicted graphically for a particular model. Some particular cases of interest have been deduced from the present investigation.

5

Laplace-Carson integral transform for exact solutions of non-integer order initial value problems with Caputo operator

75%

Kumar P. , Qureshi S.

Journal of Applied Mathematics and Computational Mechanics

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2020

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tom Vol. 19, nr 1

57--66

EN

Finding the exact solution to dynamical systems in the field of mathematical modeling is extremely important and to achieve this goal, various integral transforms have been developed. In this research analysis, non-integer order ordinary differential equations are analytically solved via the Laplace-Carson integral transform technique, which is a technique that has not been previously employed to test the non-integer order differential systems. Firstly, it has proved that the Laplace-Carson transform for n-times repeated classical integrals can be computed by dividing the Laplace-Carson transform of the underlying function by n-th power of a real number p which later helped us to present a new result for getting the Laplace-Carson transform for d-derivative of a function under the Caputo operator. Some initial value problems based upon Caputo type fractional operator have been precisely solved using the results obtained thereof.

6

Axisymmetric deformation of an isotropic elastic liquid-saturated porous medium using an eigenvalue approach

75%

Kumar R. , Miglani A. , Garg N. R.

International Journal of Applied Mechanics and Engineering

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2007

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tom Vol. 12, no 4

1009-1025

EN

A deformation problem of an isotropic elastic liquid-saturated porous medium has been discussed by finding a general solution to the field equations of poroelasticity under axisymmetric conditions. An eigenvalue approach using the Laplace and the Hankel transforms is applied to get the solution. To show the utility of the solution obtained, an application of an infinite space with a concentrated point force acting at some interior point of the medium has been considered. The transformed solutions are inverted numerically, using a numerical inversion technique to invert the Laplace and the Hankel transforms. The results in the form of displacement and stress components have been obtained numerically and discussed graphically for a particular model.

7

Magneto-mechanical interactions in micropolar elastic medium

75%

Kumar R. , Rupender

International Journal of Applied Mechanics and Engineering

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2008

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tom Vol. 13, no 2

399-413

EN

The present investigation is concerned with a two-dimensional problem in electromagnetic micropolar elasticity for a half-space whose surface is subjected to mechanical sources in the presence of a transverse magnetic field. As an application of the approach concentrated or uniformly distributed normal force has been taken. Laplace and Fourier transforms techniques are used to solve the problem. The numerical inversion technique has been used to obtain the components of displacement, microrotation, force stress and couple stress. Magnetic effects are shown in the resulting quantity graphically for a specific model. Some special cases of interest are also deduced from the present investigation.

8

Inverse Laplace transforms using convolution integral

75%

Jha B. K. , Ajibade A. O.

International Journal of Applied Mechanics and Engineering

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2008

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tom Vol. 13, no 4

1119-1123

EN

In the present article, the convolution theorem is used to obtain the inverse Laplace-transforms of some Laplace-transforms functions. Although the inverse Laplace-transforms of these functions are available in the works of Abramowitz and Stegun (1965), Carlslaw and Jaeger (1952), Churchill (1972), Miles (1971) and Özisik (1980), they require integration of complementary-error-function for computational purposes. The results presented in this article are directly applicable in many branches of science where time-dependent initial and boundary conditions are frequently occurring.

9

Natural frequency and critical velocities of heated inclined pinned PP-R pipe conveying fluid

75%

Mohmmed J. H. , Tawfik M. A. , Atiyah Q. A.

Journal of Achievements in Materials and Manufacturing Engineering

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2021

|

tom Vol. 107, nr 1

15--27

EN

Purpose: The flow velocity and pressure of fluid flowing through a pipeline can cause the vibration of pipes, and consequently result in the modification in natural frequency via fluid-structure interaction. The value of the natural frequency of a component when approaches the excitation force to a certain degree, a severe resonance failure may occur. Hence, avoiding the resonance failure of a pipe subjected to complex conditions is an essential issue that requires to be solved urgently in the engineering field. This work treats the transverse vibration for flexible inclined heated pipe, made of polypropylene randomcopolymer (PP-R), conveying fluid assuming pinned connections at the ends. The pipe was placed at different support angles and subjected to variant temperatures. Design/methodology/approach: The inclined pipe is modelled as Euler-Bernoulli beam taking into account its self-weight, temperature variation, inclination angle, aspect ratio, and internal fluid velocity. The integral transforms method, which includes the finite Fourier sine and the Laplace transforms, was used to develop an analytic solution to the modified equation of motion and the analytical expressions for dual natural frequencies of the pipefluid interaction system were computed. Findings: The proposed solution technique via finite Fourier sine and Laplace transforms offers a more convenient alternative to calculate the dynamic characteristic of pipes conveying fluid. The obtained results showed that the dynamical behaviour of pipe–fluid system is strongly affected by fluid flow velocity, degree of inclination, temperature variation, and aspect ratio of the pipe in transverse modes. Research limitations/implications: This work focuses on fundamental (first) mode in the most discussions. Practical implications: It was revealed that the thermal effects in the pipe are a very important factor and more significant in comparison with the internal fluid velocity and the inclination angle has a larger impact on vibration characteristics at a higher aspect ratio. The findings can be useful for the design of engineering components. Originality/value: Determining the combining effect of inclination angle, aspect ratio, and thermal loading on vibration characteristic of the pipes conveying fluid by using an improved analytic solution to the modified equation of motion via mixed of finite Fourier sine and Laplace transforms.

10

Deformation in a generalized thermoelastic material with voids under the dependence of modulus of elasticity and thermal conductivity on reference temperature

63%

Kumar R. , Devi S.

International Journal of Applied Mechanics and Engineering

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2009

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tom Vol. 14, no 3

747-767

EN

The present investigation is to determine the displacement component, change in the volume fraction field and temperature distribution in a generalized thermoelastic half space with voids with a variable modulus of elasticity and thermal conductivity subjected to mechanical and thermal boundary conditions. The formulation is applied to the coupled as well as the generalized theories of thermoelasticity: the Lord-Shulman theory (with one relaxation time), Green-Lindsay theory (with two relaxation times), and Chandrasekhariah-Tzou theory (with dual phase lag). The Laplace transform technique has been used to solve the problem. An application of concentrated (mechanical/thermal) and continuous (mechanical/thermal) sources has been considered to illustrate the utility of the approach. The transformed solutions are inverted using a numerical inversion technique to obtain the displacement component, change in the volume fraction field and temperature distribution in the physical domain and illustrated graphically for a particular model. Various special cases of interest have been deduced from the present investigation.

11

Analyzing fuid fow characteristics in a dual porosity reservoir with an elastic outer boundary

63%

Kim S. C. , Han C. G. , Rim M. W. , Kim J. S. , Ryang M. J.

Acta Geophysica

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2021

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tom Vol. 69, no. 5

1843--1853

EN

When we develop petroleum and natural gas reservoirs, we can see a lot of dual-porosity reservoirs with both pores and fractures. Many researchers have studied characteristics of fluid flow in dual-porosity reservoirs with the ideal outer boundary (infinite boundary, closed boundary or constant pressure boundary) but nobody has considered dual-porosity model with the elastic outer boundary (EOB) reflecting the real condition. So there could be large errors in analyzing well-test data for dual-porosity model. In this paper, we establish a percolation model for dual-porosity reservoirs with the EOB and consider the skin factor and wellbore storage. And we obtain its solution in Laplace space by introducing the effective well radius and applying the Laplace transformation. An approximation in Laplace space is also derived by using an asymptotic formula of I0(x) and I1(x). By using Stehfest numerical inversion of Laplace transformation, the solution in the real space is obtained. We compare this model to homogeneous model with the EOB and conventional dual-porosity model, respectively. Comparison results show that the conventional outer boundary conditions are three special cases of the EOB and homogeneous model with the EOB is a special case of dual-porosity model with the EOB. Flow characteristics are analyzed and it is shown that the EOB affects analysis of well-test data through simulation. This study may improve the accuracy of well-test analysis for dual-porosity reservoir.

12

Properties of transient states in electrical circuits : transformation of F(s) in to the Maclaurin series f(t)

63%

Piwowarczyk T.

Czasopismo Techniczne. Elektrotechnika

|

2005

|

tom R. 102, z. 5-E

45--52

EN

Transients in linear electrical circuits can be expressed as functions f(t), or as their Laplace transform F(s). The relation between them takes the form of a well known integral transform. The Laplace transform F(s) can also be computed from some finite subset of derivatives of f(t). In this approach the appropriate formulas take the form of the matrix transformation. It contains four arithmetic operations exclusively. Thus it is easy to be implemented in the assembly language. It also delivers a new interpretation of transients. A set of interesting theorems has been proved in the article. One of theorems states that some approximation of f(t) can contain all the information about a transient which is coded in a special way. This unexpected fact provides a basis for a new method of finding transients in linear electrical circuits.

PL

Stany nieustalone w liniowych obwodach elektrycznych mogą być wyrażone jako transformaty Laplace'a F(s) oryginału f(t). Jeżeli funkcja F(s) jest dana, to oryginał f(t) jest obliczany z zastosowaniem odwrotnej transformacji Laplace'a. W tym celu należy znać wszystkie zera mianownika wy.miernej funkcji F(s). Dla wyższych stopni funkcji F(s) rozkład na ułamki proste staje się poważnym problemem ze względu na twierdzenie Abela. W szczególności jest to zasadniczy problem, gdy elementy obwodu elektrycznego są podane w formie parametrycznej, tak jak to jest w przypadku syntezy obwodu. Możemy ominąć ten problem używając uogólnionych ciągów Fibonacciego. Co więcej, można do obliczeń użyć pewnego skończonego podciągu będącego częścią uogólnionego ciągu Fibonacciego bez straty informacji potrzebnej do odtworzenia dokładnego rozwiązania. Takie skończone podciągi tworzą podstawę nowej teorii rozwiązywania i analizowania stanów nieustalonych w obwodach elektrycznych.

13

Properties of transient states in electrical circuits : transformation of f(t) in F(s)

63%

Piwowarczyk T.

Czasopismo Techniczne. Elektrotechnika

|

2005

|

tom R. 102, z. 5-E

53--59

EN

Transients in linear electrical circuits can be expressed as functions f(t), or as their Laplace transform F(s). The relation between them takes the form of a well known integral transform. The Laplace transform F(s) can also be computed from some finite subset of derivatives of f(t). In this approach the appropriate formulas take the form of the matrix transformation. It contains four arithmetic operations exclusively. Thus it is easy to be implemented in the assembly language. It also delivers a new interpretation of transients. A set of interesting theorems has been proved in the article. One of theorems states that some approximation of f(t) can contain all the information about a transient which is coded in a special way. This unexpected fact provides a basis for a new method of finding transients in linear electrical circuits.

PL

Stany nieustalone w liniowych obwodach elektrycznych RLC wyrażane są za pomocą funkcji czasowych f(t) lub ich transformat Laplace'a F(s). Relacje między nimi przybierają postać znanych transformacji całkowych. Transformacja Laplace'a F(s) może być wyznaczona z pewnego podzbioru pochodnych funkcji f(t). W takim podejściu odpowiednie wzory przyjmują postać zapisów macierzowych zawierających cztery arytmetyczne działania. Wzory te są łatwe w implementacji komputerowej, na przykład w asemblerze. Są również podstawą nowej interpretacji stanów nieustalonych. W teorii został dowiedziony pewien zbiór twierdzeń. Jedno z nich stwierdza, że pewna aproksymacja funkcji f(t) może zawierać całą informację o stanie przejściowym zakodowaną w specyficzny sposób. Ten nieoczekiwany fakt jest podstawą nowej metody znajdowania stanów nieustalonych w liniowych obwodach elektrycznych RLC.

14

Anti-plane strain problem of micropolar viscoelastic medium

63%

Kumar R. , Singh R.

International Journal of Applied Mechanics and Engineering

|

2008

|

tom Vol. 13, no 1

175-191

EN

The eigen value approach, following Laplace and Fourier transforms, has been employed to find the general solution to the field equation in a micropolar viscoelasitc medium for the anti- plane strain problem. An infinite space with concentrated force at the origin has been applied to illustrate the application of the approach. The integral transforms have been inverted by using a numerical inversion technique to get the results in the physical domain. The results in the form of normal microrotation, tangential displacement, tangential force stress and normal couple stress components have been obtained numerically and illustrated graphically to depict the effects of viscosity. A particular case of a micropolar elastic solid has also been deduced.

15

Generalized thermoelasticity model of nonlocal strain gradient Timoshenko nanobeams

63%

Yue X. , Yue X. , Borjalilou V.

Archives of Civil and Mechanical Engineering

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2021

|

tom Vol. 21, no. 3

655--674

EN

The aim of this study is to establish a thorough model for appraisal of size-dependent thermoelastic vibrations of Timoshenko nanobeams by capturing small-scale effect on both structural and thermal fields. With the intention of incorporating size effect within motion and heat conduction equations, nonlocal strain gradient theory (NSGT) as well as nonclassical heat conduction model of Guyer and Krumhansl (GK model) are exploited. For the sake of generalization and clarifying the impact of nonclassical scale parameters on results, by introducing some nondimensional quantities, the size-dependent coupled thermoelastic equations are written in dimensionless form. By applying the Laplace transform to this system of differential equations, thermoelastic responses of a simply supported Timoshenko nanobeam under dynamic load are extracted in closed forms. In order to highlight the influence of scale parameters on thermoelastic behavior of Timoshenko nanobeams, a variety of numerical results is provided. The discrepancy between classical and nonclassical outcomes betokens the salient role of structural and thermal scale parameters in accurate analysis of nanobeams. In addition, findings reveal that utilization of NSGT gives the means to capture both stiffness softening and stiffness enhancement characteristic of small-sized structures, so that according to the relative values of two scale parameters of NSGT, the nonclassical model of Timoshenko nanobeam can exhibit either softening or hardening behavior in comparison with the classical one.

16

Eigenvalue approach to study generalized thermoelastic problem for an infinitely long circular cylinder

63%

Lahiri A. , Sarkar N.

International Journal of Applied Mechanics and Engineering

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2011

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tom Vol. 16, no 3

731-745

EN

In this work, a one-dimensional problem for an infinitely long circular cylinder is solved by an eigenvalue approach. The outer surface of this cylinder is traction free and subjected to a thermal shock. The problem is in the context of the theory of generalized thermoelasticity with one relaxation time parameter. The Laplace transform technuiqe is used. The solution in the transformed domain is obtained by a direct eigenvalue approach. The inversion of the Laplace transform solution is evaluated numerically. Numerical results are obtained and represented graphically for two cases and finally compared with the current results available in the literature.

17

On axisymmetrical boundary problem of unsteady motion of micropolar fluid in the half-space

63%

El-Sirafy I. H. , Aboutahoun A. W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2016

|

tom Vol. 64, nr 1

51--62

EN

The aim of this paper is developing an exact solution for the problem of axisymmetrical flow of unsteady motion of micropolar fluid in the half-space when the shear stresses are given on the boundary. The Laplace-Hankel transform technique is used to solve this problem. Some physical quantities such as velocities, pressure and microrotations are obtained and illustrated numerically.

18

Effects of Hall current on unsteady hydromagnetic free convection flow past an impulsively moving vertical plate with Newtonian heating

63%

Seth G. S. , Sarkar S. , Sharma R.

International Journal of Applied Mechanics and Engineering

|

2016

|

tom Vol. 21, no. 1

187--203

EN

An investigation of unsteady hydromagnetic free convection flow of a viscous, incompressible and electrically conducting fluid past an impulsively moving vertical plate with Newtonian surface heating embedded in a porous medium taking into account the effects of Hall current is carried out. The governing partial differential equations are first subjected to the Laplace transformation and then inverted numerically using INVLAP routine of Matlab. The governing partial differential equations are also solved numerically by the Crank-Nicolson implicit finite difference scheme and a comparison has been provided between the two solutions. The numerical solutions for velocity and temperature are plotted graphically whereas the numerical results of skin friction and the Nusselt number are presented in tabular form for various parameters of interest. The present solution in special case is compared with a previously obtained solution and is found to be in excellent agreement.

19

Resonance of nanoscale beam due to various sources in modified couple stress thermoelastic diffusion with phase lags

63%

Kumar R. , Devi S. , Sharma V.

Mechanics and Mechanical Engineering

|

2019

|

tom Vol. 23, nr 1

36--49

EN

This paper deals with the study of thermoelastic thin beam in a modified couple stress with three-phaselag thermoelastic diffusion model subjected to thermal and chemical potential sources. The governing equations are derived by using the Euler-Bernoulli beam assumption and eigenvalue approach. The Laplace transform technique is employed to obtain the expressions for displacements, lateral deflection, temperature change, axial stress and chemical potential. A particular type of instantaneous and distributed sources is taken to show the utility of the approach. The general algorithm of the inverse Laplace transform is developed to compute the results numerically. The numerical results are depicted graphically to show the effects of phase lags, with and without energy dissipation on the resulting quantities. Some special cases are given.

20

Eigenvalue approach to generalized thermoelastic interactions in an unbounded body with spherical cavity

63%

Lahiri A. , Kar T. K.

International Journal of Applied Mechanics and Engineering

|

2007

|

tom Vol. 12, no 4

1027-1037

EN

Exact expressions for the temperature distribution stress and displacement component are obtained in the Laplace transform domain in the case of an infinite medium with a spherical cavity by using the eigenvalue approach in the context of the theory of thermoelasticity with two relaxation time parameters. The surface of the spherical cavity is stress free and suddenly subjected to a thermal shock. A numerical approach is implemented for the inversion of the Laplace transform in order to obtain the solution in a physical domain. Finally numerical computations of the stress and temperature have been made and represented graphically.