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1

Eigen value approach to two dimensional problem in generalized magneto micropolar thermoelastic medium with rotation effect

Singh R., Kumar V.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 1

205--219

EN

In this study an eigen value approach has been employed to examine the mechanical force applied along with a transverse magnetic field in a two dimensional generalized magneto micropolar thermoelastic infinite space. Results have been obtained by treating rotational velocity to be invariant. Integral transforms have been applied to solve the system of partial differential equations. Components of displacement, normal stress, tangential couple stress, temperature distribution, electric field and magnetic field have been obtained in the transformed domain. Finally numerical inversion technique has been used to invert the result in the physical domain. Graphical analysis has been done to described the study.

2

Regularization using truncated singular value decomposition for estimating the Fourier spectrum of a noised space distribution over an extended support

Al Hadad W., Maillet D., André S., Rémy B.

Computer Assisted Methods in Engineering and Science

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2014

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Vol. 21, no. 3-4

211--222

EN

This paper is devoted to a theoretical and numerical study of different ways of calculating the Fourier transform of a noisy signal where the boundary conditions at the lateral boundaries of the measurement interval are not precisely known. This happens in different characterization problems where infrared camera is used for temperature measurements. In order to overcome this difficulty, the interval where the Fourier transform (its support) is supposed to be larger than the measurement domain is defined. Thus, this virtual interval larger than the measurement interval is used. We show that regularization by truncated singular value decomposition is able to yield good estimates to this very ill-posed inverse problem.

3

Surface wave generation due to glacier calving

Massel S.R., Przyborska A.

Oceanologia

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2013

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No. 55 (1)

101-127

EN

Coastal glaciers reach the ocean in a spectacular process called "calving". Immediately after calving, the impulsive surface waves are generated, sometimes of large height. These waves are particularly dangerous for vessels sailing close to the glacier fronts. The paper presents a theoretical model of surface wave generation due to glacier calving. To explain the wave generation process, four case studies of ice blocks falling into water are discussed: a cylindrical ice block of small thickness impacting on water, an ice column sliding into water without impact, a large ice block falling on to water with a pressure impulse, and an ice column becoming detached from the glacier wall and falling on to the sea surface. These case studies encompass simplified, selected modes of the glacier calving, which can be treated in a theoretical way. Example calculations illustrate the predicted time series of surface elevations for each mode of glacier calving.

4

Forced vibrations due to mechanical loads in piezothermoelastic half-space

Sharma J. N., Thakur A. D., Sharma Y. D.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 2

535-557

EN

The article studies disturbances in a homogeneous, transversely isotropic, generalized piezothermoelastic half-space due to impact/continuous strip mechanical loads acting on a thermally insulated/isothermal and electrically shorted (closed circuit) surface. Combinations of the Laplace transform with respect to time and Fourier transform with respect to a space variable are employed to solve the boundary value problem in the transformed domain, in the context of classical and non-classical theories of thermoelasticity. The systems of equations are solved by using the Gauss elimination process for the unknowns. The values of these unknowns are used in the formal solution which leads to the expressions of displacements, temperature change, electric potential, electric displacement and stresses in the transformed domain. In order to obtain solution in the physical domain the inverse transform integrals are evaluated by using the Romberg integration and Fourier series approximations numerically. Temperature change, stresses and electric displacement so obtained in the physical domain, are computed numerically from the relevant expressions and relations for PZT-5A material. The illustrations and comparisons of the results for classical and non-classical theories of thermoelasticity are presented graphically. This may find applications in buzzers inside pagers and cell phones, shakers inside ultrasonic cleaners and strain sensors inside pressure gages.

5

Disturbance due to thermomechanical sources in a thermoviscoelastic medium with rotation

Kumar R., Garg S. K., Ahuja S.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 1

127-141

EN

A dynamic problem in a thermoviscoelastic material with rotation is investigated for the disturbance due to thermomechanical sources. To solve the problem the Laplace and Fourier transform techniques are applied. Concentrated and uniformly distributed sources are taken as an application of the approach. A numerical inversion technique is used to invert the integral transform and to obtain the components of displacement, stress and temperature distribution in the physical domain. The effect of rotation and viscosity is examined on the resulting quantities and depicted graphically for a specific model .Some special case are also deduced from the present investigation.

6

Weight function for a crack in an orthotropic medium under normal impact loading

Mukherjee S., Das S.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 4

915-928

EN

The paper deals with the investigation of an elastodynamic response of an infinite orthotropic medium containing a central crack under normal impact loading. Laplace and Fourier integral transforms are employed to reduce the dimensional wave propagation problem to the solution of a pair of dual integral equations in the Laplace transform plane. These integral equations are then reduced to integral differential equations which have been solved in the low frequency domain by method of iteration. To determine time dependence of the parameters, these equations are inverted to yield the dynamic stress intensity factor (SIF) for normal point force loading. These results have been used to obtain the SIF at the crack tip which corresponds to the weight function for the crack under normal loading. Analytical expressions of the weight function are used to derive SIF for polynomial loading. Numerical results of normalized SIF for a large normalized time variable and for different concentrated point force loading at an arbitrary location of the crack surface have been calculated for different orthotropic materials. In the present paper, a numerical Laplace inversion technique is used to recover the time dependence of the solution. Finally, the results obtained are displayed graphically.

7

Deformations due to mechanical sources in elastic solid with voids

Kumar R., Ailawalia P.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 4

865-880

EN

Void effects of a load applied normal to the boundary and moving at a constant velocity along one of the coordinate axis in an elastic half space is studied. The analytic expressions for displacement, force stress and volume fraction field for concentrated normal point force, uniformly distributed force, linearly distributed force and moving concentrated normal force are obtained by employing the eigen value approach after applying the integral transforms. A numerical inversion technique has been applied to obtain the solution in the physical domain. The numerical results are presented graphically. Some particular cases have been deduced.

8

The Abel summation of the Kontorovich-Lebedev integral representation

Cojuhari P.A., Gomilko A.M.

Opuscula Mathematica

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2005

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Vol. 25, no. 1

101-107

EN

A new result on the summation of the Kontorovich-Lebedev integral representation in the sense of Abel mean is given.

9

A simple phenomenological model of lixivitation of active substances dispersed in a porous material. Part I: progressive conversion approach

Sławomirski M.

Archives of Mining Sciences

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2005

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Vol. 50, no 2

161-174

EN

In this paper the lixivitation of small solid particles of an active substance dispersed in a porous material has been considered. The model has been formulated in order to describe the phenomenon of lixivitation of toxic substances contained in industrial waste material located in an undergound depository. In the depository the lixivitation process is implied by the steady horizontal flow of subsurface water which is able to dissolve active substances. It has been assumed that the dissolution phenomenon depends on the reaction kinetics. The progressive conversion, unreacted core, and shrinking core models of the heterogeneous liquid - solid reaction have briefly been described. The system of differential equations which describe the lixivitation process for the progressive conversion dissolution pattern has been solved applying the Carson-Laplace integral transform method. The adequacy of the discontinuous solution of the boundary value problem for the description of the genuine lixivitation process has briefly been discussed.

PL

W artykule rozważono proces ługowania drobnych cząstek substancji aktywnej rozproszonych w ośrodku porowatym. Model został sformułowany w celu opisu zjawiska ługowania substancji szkodliwych zawartych w odpadach przemysłowych umieszczonych w podziemnym składowisku odpadów. Proces ługowania substancji ze składowiska spowodowany jest przez ustalony poziomy przepływ wód podziemnych zdolnych do roztwarzania substancji aktywnych. W artykule założono, że proces roztwarzania zależy od kinetyki odpowiedniej reakcji chemicznej. Przedstawiono w zarysie trzy modele przebiegu heterogenicznych reakcji chemicznych w układzie płyn - ciało stałe: model stopniowego przekształcania, model nieprzereagowanego rdzenia oraz model kurczącego się rdzenia. Jako podstawowe parametry modelu opisującego proces roztwarzania przyjęto koncentrację substancji aktywnej w przepływającym płynie F oraz koncentrację substancji aktywnej rozproszonej w odpadach [...]. Obydwa te parametry traktowane są jako funkcje położenia x i czasu t. Układ równań różniczkowych cząstkowych opisujący proces ługowania przebiegający zgodnie z modelem stopniowego przekształcania rozwiązano metodą transformacji całkowych Carsona-Laplace'a. Otrzymane rozwiązanie ma postać przesuwającej się z prędkością adwekcji u pojedynczej fali zmian koncentracji, reprezentującej wypieranie wody skażonej, znajdującej się początkowo w przestrzeni porowej odpadów przez wodę czystą, dopływającą przez brzeg składowiska x = O. Przedyskutowano zagadnienie adekwatności nieciągłego rozwiązania sformułowanego zagadnienia początkowo-brzegowego do opisu rzeczywistego procesu roztwarzania.

10

Axi-Symmetric Migration of Active Substances which Are Involved in a Sequential Reaction, and Transferred from the Underground Depository of Waste Materials

Sławomirski M.

Bulletin of the Polish Academy of Sciences. Earth Sciences

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2003

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Vol. 51, nr 1

43-63

EN

In this paper one-dimensional migration of the chemically active substances transferred from the underground depository of waste materials by technical water has been considered. It has been assumed that active substances dissolved in water flowing through rocks are subjected simultaneously to the advection, sorption, and chemical reactions. The author has taken into account the situation in which the substance A flowing out the depository is transformed chemically into substance B, and substance B is afterwards transformed chemically into substance E. The author assumed that from the standpoint of chemical kinetics the sequential reaction A -› B -› E is of the first order. For the description of the propagation problem the system of partial differential transport equations have been applied. In the transport equations, the concentrations FA, FB,FE of substances A, B, E were handled to be the primary dependent variables. The cylindrical symmetry of the problem has been assumed. The system of differential equations describing the propagation process has been solved applying the Carson-Laplace integral transform method. Rational considerations have been completed with a brief discussion concerning the adequacy of the model for the genuine migration phenomenon.

11

Linear-invariant order for integral transform of univalent functions

Lewandowski Z., Prokhorov D., Szynal A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

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1999

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z. 23 [175]

71-74

EN

For alpha is an element of R, we find the linear-invariant order for functions g(z) = integralz/0 f'(t)(f(t)/t)alpha dt where f(z) = z+.... are holomorphic and univalent in the unit disk.