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1
Content available Some closed form series solutions for the time-fractional diffusion-wave equation in polar coordinates with a generalized Caputo fractional derivative
Elkott Ibrahim, Abdel-Latif Mohamed S., El-Kalla Ibrahim L., Abdel Kader Abass H.
Journal of Applied Mathematics and Computational Mechanics
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2023
|
Vol. 22, nr 2
5--14
EN
In this paper, we obtain some closed form series solutions for the time fractional diffusion-wave equation (TFDWE) with the generalized time-fractional Caputo derivative (GTFCD) associated with a source term in polar coordinates. These solutions are found using generalized Laplace and Hankel transforms. We obtained the closed form series solutions in the form of the Polygamma function. The effect of the fractional order derivative on the diffusion-wave variable is illustrated graphically.
2
Content available remote Inequalities for second-order Riesz transforms associated with Bessel expansions
Osękowski Adam
Bulletin of the Polish Academy of Sciences. Mathematics
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2020
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Vol. 68, no. 1
75--88
EN
The paper contains the proofs of Lp, logarithmic and weak-type estimates for the second-order Riesz transforms arising in the context of multidimensional Bessel expansions. Using a novel probabilistic approach, which rests on martingale methods and the representation of Riesz transforms via associated Bessel-heat processes, we show that these estimates hold with constants independent of the dimension.
3
Content available Frictionless contact between a rigid indentor and a transversely isotropic functionally graded layer
Patra R., Barik S. P., Chaudhuri P. K.
International Journal of Applied Mechanics and Engineering
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2018
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Vol. 23, no. 3
655--671
EN
This article is concerned with the study of frictionless contact between a rigid punch and a transversely isotropic functionally graded layer. The rigid punch is assumed to be axially symmetric and is supposed to be pressing the layer by an applied concentrated load. The layer is resting on a rigid base and is assumed to be sufficiently thick in comparison with the amount of indentation by the rigid punch. The graded layer is modeled as a non-homogeneous medium. The relationship between the applied load P and the contact area is obtained by solving the mathematically formulated problem through using the Hankel transform of different order. Numerical results have been presented to assess the effects of functional grading of the medium and the applied load on the stress distribution in the layer as well as on the relationship between the applied load and the area of contact.
4
Content available Solutions of vibration problems for thin infinite plates subjected to harmonic loads
Klanner M., Ellermann K.
Journal of Theoretical and Applied Mechanics
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2017
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Vol. 55 nr 3
949—961
EN
New closed form solutions for harmonic vibrations of infinite Kirchhoff plates subjected to a constant harmonic ring load, a constant harmonic circular load and an alternating harmonic circular load are derived. Two different approaches are used to define the closed form solutions. The first approach uses the integration of the harmonic point force and the addition theorem for Bessel functions, while the second approach applies the Hankel transform to solve the inhomogeneous partial differential equation of the Kirchhoff plate theory. The new closed form particular solutions can especially be used in Trefftz like methods and extend their field of application.
5
Content available remote Effect of Two Temperatures and Thermal Phase-lags in a Thick Plate due to a Ring Load with Axisymmetric Heat Supply
Kumar J., Sharma N., Lata P.
Computational Methods in Science and Technology
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2016
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Vol. 22, No. 3
153--162
EN
The present investigation concerns thermomechanical interactions in a homogeneous isotropic thick plate in the light of the two-temperature thermoelasticity theory with dual phase lag due to a ring load. The upper and lower ends of the thick plate are traction free and subjected to an axisymmetric heat supply. The solution is obtained by using Laplace and Hankel transform techniques. The analytical expressions of displacement components, stresses, conductive temperature, temperature change and cubic dilatation are computed in a transformed domain. The numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect of thermal phase-lags and two temperatures are shown on the various components. Some particular cases of the result are also deduced from the present investigation.
6
Content available remote Analysis of micropolar porous thermoelastic circular plate by eigenvalue approach
Kumar R., Miglani A., Rani R.
Archives of Mechanics
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2016
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Vol. 68, nr 6
423--439
EN
The present paper examined a two-dimensional axi-symmetric problem of thick circular plate in a micropolar porous thermoelastic medium due to thermomechanical sources. An eigenvalue approach has been employed after applying the Laplace and Hankel transforms to investigate the problem. The expressions of displacements, stresses, microrotation, volume fraction field and temperature distribution are obtained in the transformed domain. A numerical inversion technique has been used to obtain the resulting quantities in the physical domain. The numerical simulated resulting quantities are shown graphically to depict the effects of thermal forces and porosity. Particular cases of interest are also studied and presented.
7
Content available Sound Radiation from a Surface Source Located at the Bottom of the Wedge Region
Szemela K.
Archives of Acoustics
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2015
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Vol. 40, No. 2
223--234
EN
Applying rigorous analytical methods, formulas describing the sound radiation have been obtained for the wedge region bounded by two transverse baffles with a common edge and bottom. It has been assumed that the surface sound source is located at the bottom. The presented formulas can be used to calculate the sound pressure and power inside the wedge region. They are valid for any value of the wedge angle and represent a generalization of the formulas describing the sound radiation inside the two and three-wall corner region. Moreover, the presented formulas can be easily adapted for any case when more than one sound source is located at the bottom. To demonstrate their practical application, the distribution of the sound pressure modulus and the sound power have been analyzed in the case of a rectangular piston located at the wedge’s bottom. The influence of the transverse baffle on the sound power has been investigated. Based on the obtained formulas, the behaviour of acoustic fields inside a wedge can be predicted.
8
Content available Interaction due to mechanical source in generalized thermo microstretch elastic medium
Singh R., Kumar V.
International Journal of Applied Mechanics and Engineering
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2014
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Vol. 19, no. 2
347--363
EN
The eigen value approach, following the Laplace and Hankel transformation has been employed to find a general solution of the field equations in a generalized thermo microstretch elastic medium for an axisymmetric problem. An infinite space with the mechanical source has been applied to illustrate the utility of the approach. The integral transformations have been inverted by using a numerical inversion technique to obtain normal displacement, normal force stress, couple stress and microstress in the physical domain. Numerical results are shown graphically.
9
Content available Influence of heat sources and relaxation time on temperature distribution in tissues
Sharma S., Sharma K.
International Journal of Applied Mechanics and Engineering
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2014
|
Vol. 19, no. 2
427--433
EN
In the present study, the temperature fluctuations in tissues based on Penne’s bio-heat transfer equation is investigated by applying the Laplace and Hankel transforms. To get the solution in a physical form, a numerical inversion technique has been applied. The temporal and spatial distribution of temperature is investigated with the effect of relaxation time and is presented graphically.
10
Content available Eigen value approach in micropolar elastic medium with voids
Singh R., Singh K.
International Journal of Applied Mechanics and Engineering
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2013
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Vol. 18, no. 2
521--536
EN
The eigen value approach, following the Laplace and Hankel transformation has been employed to find a general solution of the field equations in a micropolar elastic medium with voids for an axisymmetric problem. An infinite space with the mechanical source has been applied to illustrate the utility of the approach. The integral transformations has been inverted by using a numerical inversion technique to get the result in physical domain. The results in the form of normal displacement, volume fraction, normal force stress, tangential force stress and tangential couple stress components have been obtained numerically and illustrated graphically.
11
Content available remote An analytical model of the power spatial distribution for underwater optical wireless communication
Wei W, Xiao-Hui Z, Yue-Yun C, Xue-Jun Z
Optica Applicata
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2012
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Vol. 42, nr 1
157--166
EN
Employing optical propagation theory in Hankel transform, an analytical model of the optical power spatial distribution is derived for the ideal point optical source and the Gaussian laser, respectively. Experimental measurements of the spatial distribution of a Gaussian laser are presented. The expected results of our analytical model are in good agreement with experimental data.
12
Content available Some exact solutions for Oldroyd-B fluid due to time dependent prescribed shear stress
Jamil M., Fetecau C., Rana M.
Journal of Theoretical and Applied Mechanics
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2012
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Vol. 50 nr 2
549-562
EN
The velocity field and the shear stress corresponding to motion of an Oldroyd-B fluid between two infinite coaxial circular cylinders are established by means of the Hankel transforms. The flow of the fluid is produced due to the time dependent axial shear stress applied on the boundary of the inner cylinder. The exact solutions, presented under a series form, can easily be specialized to give similar solutions for the Maxwell, second grade and Newtonian fluids performing the same motion. Finally, some characteristics of the motion as well as the influence of the material constants on the behavior of the fluid are underlined by graphical illustrations.
PL
Pole prędkości i pole rozkładu naprężeń stycznych wywołanych ruchem cieczy Oldroyda-B umieszczonej między dwoma koncentrycznymi cylindrami wyznaczono za pomocą transformaty Hankela. Przepływ cieczy wywołano zależnym od czasu naprężeniem stycznym od zewnętrznej ściany cylindra wewnętrznego. Uzyskane rozwiązanie dokładne, ujęte w formie rozwinięcia w szereg, może łatwo być zastosowane dla przypadków szczególnych cieczy Maxwella, cieczy drugiego stopnia i nienewtonowskich przy tych samych warunkach przepływu. Na zakończenie rozważań, przedstawiono graficznie charakterystyki ruchu cieczy i wpływ parametrów materiałowych na jej zachowanie.
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