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  1. 16 International Journal of Applied Mechanics and Engineering
  2. 5 Journal of Applied Mathematics and Computational Mechanics
  3. 2 Demonstratio Mathematica
  4. 1 Acta Mechanica et Automatica
  5. 1 Archives of Civil and Mechanical Engineering
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  1. 4 Kumar R.
  2. 2 Muthucumaraswamy R.
  3. 2 Povstenko Y.
  4. 2 Singh R.
  5. 1 Aasoori S. K.
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  1. 5 2022
  2. 3 2021
  3. 1 2020
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1
Content available Exact solution for heat conduction inside a sphere with heat absorption using the regularized Hilfer-Prabhakar derivative
Elhadedy Hager, Latif Mohamed S. Abdel, Nour Hamed M., Kader Abbas H. Abdel
Journal of Applied Mathematics and Computational Mechanics
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2022
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Vol. 21, nr 2
27--37
EN
In this article, we utilize the finite Sine-Fourier transform and the Laplace transform for solving fractional partial differential equations with regularized Hilfer-Prabhakar derivative. These transforms are used to get analytical solutions for the time fractional heat conduction equation (TFHCE) with the regularized Hilfer-Prabhakar derivative associated with heat absorption in spherical coordinates. Two cases of Dirichlet boundary conditions are considered by obtaining an analytical solution in each case. The effect of the parameters of the regularized Hilfer-Prabhakar derivative on the heat transfer inside the sphere is discussed using some figures.
2
Content available Approximate analytical solution to the Cattaneo heat conduction model with various laser sources
Nuruddeen Rahmatullah Ibrahim
Journal of Applied Mathematics and Computational Mechanics
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2022
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Vol. 21, nr 1
67--78
EN
The present manuscript investigates the role being played by various laser short heating sources in a conduction process of a metallic substrate. The Cattaneo heat conduction model is considered in favour of its finiteness of conduction speed. The analytical solutions for the temperature fields are determined via the application of the Laplace integral transform. Finally, we sought a numerical Laplace inversion scheme where the analytical inversion failed and graphically examined the significance of the heating parameters on the temperature fields.
3
Content available The influence of thermal expansion on flow past an inclined accelerated sectional plate with persistent mass diffusion
Nagarajan G., Sundar Raj M., Muthucumaraswamy R.
International Journal of Applied Mechanics and Engineering
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2022
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Vol. 27, no. 4
105--116
EN
In this article, we examined the solution of a homogeneously intensified isothermal inclined infinite plate with constant temperature. The plate is elevated to Tw, and the species accumulation is enhanced at a consistent speed. Under appropriate boundary conditions, the non-dimensional guiding formulae are remedied using the Laplace transform procedure. The effect of velocity, temperature, and concentration on various factors, including thermal and mass Grashof numbers, Schmidt numbers, and duration, is discussed. The velocity increases proportionally to the thermal and mass Grashof numbers, but decreases as the inclined angle, Schmidt numbers and time increase.
4
Content available Analysis of deflection in visco-thermoelastic beam resonators subjected to harmonic loading
Chopra Deepti, Singh Prince
International Journal of Applied Mechanics and Engineering
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2022
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Vol. 27, no. 2
35--52
EN
This paper analyses the transverse deflection in a homogeneous, isotropic, visco-thermoelastic beam when subjected to harmonic load. The ends of the beam are considered at different boundary conditions (both axial ends clamped, both axial ends simply supported and left end clamped and right end free). The deflection has been studied by using the Laplace transform. Numerical computation of analytical expression of deflection obtained after Inverse Laplace transform has been done using MATLAB software. The graphical observations have been discussed under various boundary conditions for different values of time and length. The above work has applications in design of resonators.
5
Content available remote Mesomechanical model for concrete creep with viscoelastic interface transition zone
Xu Zehua, Zhao Qingxin, Guo Weichao
Archives of Civil and Mechanical Engineering
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2022
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Vol. 22, no. 2
art. no. e65, 1--15
EN
The interface transition zone (ITZ) effect on concrete creep performance was analyzed in this study. The ITZ was treated as a weakened matrix, which mechanical behavior could be described by the Burgers model. The proposed prediction model of concrete creep took account of the ITZ's viscoelasticity by combining the generalized self-consistent Mori–Tanaka method with the Laplace transformation principle. The model's experimental validation confirmed that it accurately simulated the creep behavior of concrete specimens with various fly ash and ground slag ratios. The existence of viscoelastic ITZ promotes the creep of concrete, and the maximum creep growth rate was attained in the concrete specimen with 60% ratio of fly ash. The effects of ITZ thickness and other parameters, the volume fraction of aggregates, and particularly ITZ contribution to concrete creep in the concrete specimens with five mix proportions at different loading ages were clarified and discussed in detail.
6
Content available Analysis of solutions of the 1D fractional Cattaneo heat transfer equation
Siedlecka Urszula, Ciesielski Mariusz
Journal of Applied Mathematics and Computational Mechanics
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2021
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Vol. 20, nr 4
87--98
EN
In this paper, a solution of the single-phase lag heat conduction problem is presented. The research concerns the generalized 1D Cattaneo equation in a whole-space domain, where a second order time derivative is replaced by the fractional Caputo derivative. The Fourier-Laplace transform technique is used to determine a solution of the considered problem. The numerical inversion of the Laplace transforms is applied. The effect of the order of the fractional derivative on the temperature distribution is investigated.
7
Content available Exact solutions for fractionalized second grade fluid flows with boundary slip effects
Dehraj S., Malookani R. A., Aasoori S. K., Bhutto G. M., Arain L.
International Journal of Applied Mechanics and Engineering
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2021
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Vol. 26, no. 1
88--103
EN
In this paper, an exact analytical solution for the motion of fractionalized second grade fluid flows moving over accelerating plate under the influence of slip has been obtained. A coupled system of partial differential equations representing the equation of motion has been re-written in terms of fractional derivatives form by using the Caputo fractional operator. The Discrete Laplace transform method has been employed for computing the expressions for the velocity field […] and the corresponding shear stress […]. The obtained solutions for the velocity field and the shear stress have been written in terms of Wright generalized hypergeometric function pqψ and are expressed as a sum of the slip contribution and the corresponding no-slip contribution. In addition, the solutions for a fractionalized, ordinary second grade fluid and Newtonian fluid in the absence of slip effect have also been obtained as special case. Finally, the effect of different physical parameters has been demonstrated through graphical illustrations.
8
Content available Queueing systems with random volume customers and a sectorized unlimited memory buffer
Tikhonenko Oleg, Ziółkowski Marcin, Kempa Wojciech M.
International Journal of Applied Mathematics and Computer Science
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2021
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Vol. 31, no. 3
471--486
EN
In the present paper, we concentrate on basic concepts connected with the theory of queueing systems with random volume customers and a sectorized unlimited memory buffer. In such systems, the arriving customers are additionally characterized by a non-negative random volume vector. The vector’s indications can be understood as the sizes of portions of information of a different type that are located in the sectors of memory space of the system during customers’ sojourn in it. This information does not change while a customer is present in the system. After service termination, information immediately leaves the buffer, releasing its resources. In analyzed models, the service time of a customer is assumed to be dependent on his volume vector characteristics, which has influence on the total volume vector distribution. We investigate three types of such queueing systems: the Erlang queueing system, the single-server queueing system with unlimited queue and the egalitarian processor sharing system. For these models, we obtain a joint distribution function of the total volume vector in terms of Laplace (or Laplace-Stieltjes) transforms and formulae for steady-state initial mixed moments of the analyzed random vector, in the case when the memory buffer is composed of two sectors. We also calculate these characteristics for some practical case in which the service time of a customer is proportional to the customer’s length (understood as the sum of the volume vector’s indications). Moreover, we present some numerical computations illustrating theoretical results.
9
Content available A study on fractional order thermoelastic half space
Roy Sourov, Lahiri Abhijit
International Journal of Applied Mechanics and Engineering
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2020
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Vol. 25, no. 4
191--202
EN
In this paper, we consider a one dimensional problem on a fractional order generalized thermoelasticity in half space subjected to an instantaneous heat source. The Laplace transform as well as eigen value approach techniques are applied to solve the governing equations of motion and heat conduction. Closed form solutions for displacement, temperature and stress are obtained and presented graphically.
10
Content available Using Shehu integral transform to solve fractional order Caputo type initial value problems
Qureshi Sania, Kumar Prem
Journal of Applied Mathematics and Computational Mechanics
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2019
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Vol. 18, nr 2
75--83
EN
In the present research analysis, linear fractional order ordinary differential equations with some defined condition (s) have been solved under the Caputo differential operator having order α > 0 via the Shehu integral transform technique. In this regard, we have presented the proof of finding the Shehu transform for a classical nth order integral of a piecewise continuous with an exponential nt h order function which leads towards devising a theorem to yield exact analytical solutions of the problems under investigation. Varying fractional types of problems are solved whose exact solutions can be compared with solutions obtained through existing transformation techniques including Laplace and Natural transforms.
11
Content available Phase-lag effects in skin tissue during transient heating
Kumar R., Vashishth A. K., Ghangas S.
International Journal of Applied Mechanics and Engineering
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2019
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Vol. 24, no. 3
603--623
EN
A three-phase-lag (TPL) model is proposed to describe heat transfer in a finite domain skin tissue with temperature dependent metabolic heat generation. The Laplace transform method is applied to solve the problem. Three special types of heat flux are applied to the boundary of skin tissue for thermal therapeutic applications. The depth of tissue is influenced by the different oscillation heat flux. The comparison between the TPL and dual-phase-lag (DPL) models is analyzed and the effects of phase lag parameters […] and material constant […] on the tissue temperature distribution are presented graphically.
12
Content available Generation of surface waves due to initial axisymmetric surface disturbance in water with a porous bottom
Kundu P., Mandal B. N.
International Journal of Applied Mechanics and Engineering
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2019
|
Vol. 24, no. 3
625--644
EN
A two-dimensional Cauchy Poisson problem for water with a porous bottom generated by an axisymmetric initial surface disturbance is investigated here. The problem is formulated as an initial value problem for the velocity potential describing the motion in the fluid. The Laplace and Hankel transform techniques have been used in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is then evaluated asymptotically by the method of stationary phase. The asymptotic form of the free surface is depicted graphically in a number of figures for different values of the porosity parameter and for different types of initial disturbances.
13
Content available remote A two dimensional axisymmetric thermoelastic diffusion problem of micropolar porous circular plate with dual phase lag model
Kumar R., Miglani A., Rani R.
Mechanics and Mechanical Engineering
|
2018
|
Vol. 22, nr 4
1389--1406
EN
In the present work, we consider a two dimensional axisymmetric problem of micropolar porous circular plate with thermal and chemical potential sources in the context of the theory of dual phase lag generalized thermoelastic diffusion. The potential functions are used to analyze the problem. The Laplace and Hankel transforms techniques are used to find the expressions of displacements, microrotation, volume fraction field, temperature distribution, concentration and stresses in the transformed domain. The inversion of transforms based on Fourier expansion techniques is applied to obtain the results in the physical domain. The numerical results for resulting quantities are obtained and depicted graphically. Effect of porosity, LS theory and phase lag are presented on the resulting quantities. Some particular cases are also deduced.
14
Content available remote Certain Laplace transforms of convolution type integrals involving product of two special pFp functions
Milovanović G. V., Parmar R. K., Rathie A. K.
Demonstratio Mathematica
|
2018
|
Vol. 51, nr 1
264--276
EN
Recently the authors obtained several Laplace transforms of convolution type integrals involving Kummer’s function 1F1 [Appl. Anal. Discrete Math., 2018, 12(1), 257–272]. In this paper, the authors aim at presenting several new and interesting Laplace transforms of convolution type integrals involving product of two special generalized hypergeometric functions pFp by employing classical summation theorems for the series 2F1, 3F2, 4F3 and 5F4 available in the literature.
15
Content available The fundamental solutions to the central symmetric time-fractional heat conduction equation with heat absorption
Povstenko Y., Klekot J.
Journal of Applied Mathematics and Computational Mechanics
|
2017
|
Vol. 16, nr 2
101--112
EN
The time-fractional heat conduction equation with heat absorption proportional to temperature is considered in the case of central symmetry. The fundamental solutions to the Cauchy problem and to the source problem are obtained using the integral transform technique. The numerical results are presented graphically.
16
Content available Eigen value approach to generalized thermoelastic interactions in an unbounded body with circular cylindrical cavity without energy dissipation
Chakraborty S.
International Journal of Applied Mechanics and Engineering
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2017
|
Vol. 22, no. 4
811--825
EN
The theory of generalized thermoelasticity in the context of the Green-Naghdi model -II (thermoelasticity without energy dissipation) is studied for an infinite circular cylindrical cavity subjected to two different cases of thermoelastic interactions when the radial stress is zero for (a) maintaining constant temperature and (b) temperature is varying exponentially with time. The Laplace transform from time variable is used to the governing equations to formulate a vector matrix differential equation which is then solved by the eigen value approach. Numerical computations for the displacement component, temperature distribution and components of thermal stress have been made and presented graphically.
17
Content available Axisymmetric vibration for micropolar porous thermoelastic circular plate
Kumar R., Kaushal P., Sharma R.
International Journal of Applied Mechanics and Engineering
|
2017
|
Vol. 22, no. 3
583--600
EN
The present investigation is concerned with a two dimensional axisymmetric problem in a homogeneous isotropic micropolar porous thermoelastic circular plate by using the eigen value approach. The Laplace and Hankel transform are used to solve the problem. The expression of displacements, microrotation, volume fraction field, temperature distribution and stresses are obtained in the transformed domain subjected to thermomechanical sources. A computer algorithm is developed for numerical computations. To obtain the resulting quantities in a physical domain, a numerical inversion technique is used. The resulting quantities are depicted graphically for a specific model. Some special cases are also deduced.
18
Content available K-dron, jego matematyczne modelowanie i zastosowanie
Kapusta J., Gawinecki J., Łazuka J., Rafa J.
Biuletyn Wojskowej Akademii Technicznej
|
2016
|
Vol. 65, nr 1
169--202
PL
W pracy przedstawiono pojęcie K-dronu, nowego kształtu geometrycznego odkrytego w 1985 roku w Nowym Jorku przez dr. Janusza Kapustę, historię jego odkrycia, związki z geometrią, symetrią sześcianu. Należy podkreślić, że autorzy wyprowadzili nowy wzór na powierzchnie K-dronu, stosując metodę transformacji Laplace’a do wyznaczenia rozwiązania zagadnienia brzegowo-początkowego do równania drgań struny. Wyprowadzony wzór w swojej naturze jest bardziej czytelny ze wzlgędu na swoją strukturę. Otrzymane przez autorów w pracy rozwiązanie opisuje w sposób najbardziej ogólny powierzchnie K-dronu oraz bardziej ogólne powierzchnie nazwane przez autorów n-K-dronem. Wzór na powierzchnie K-dronu uzyskany metodą transformaty Laplace’a posiada przejrzystą interpretację geometryczną, ponieważ jest przedstawiony w postaci kombinacji liniowej równań płaszczyzn o współczynnikach kierunkowych określonych przez odpowiednie kombinacje funkcje Heaviside’a. Szeroko także przedstawiono różnorodne i wielorakie zastosowanie K-dronu.
EN
In this paper we present the definition of K-dron, new geometrical form discovered by Janusz Kapusta in 1985 in New York, its history and connection between geometry and symmetry of a cube. It is worth to emphasize that the authors have derived new formulae for the surface of K-dron using the Laplacea transform in order to obtain the solution of the boundary-value problem for the partial differential equation describing the vibration of the string. The formula proved by us in this paper is clearer and understandable in view of this structure. The solution obtained in this paper describes in general manner the surface of K-dron and more general surfaces named by us n-K-drons. The formula for the surface of K-dron was derived by the method of Laplacea transform having clear geometrical and physical interpretation because it is presented in linear combination of the equation of planes with the coefficients of directions described by suitable combinations of Heavisides functions. Also wide range and different applications of K-dron are presented.
19
Content available Theoretical study of heat transfer effects on flow past a parabolic started vertical plate in the presence of chemical reaction of first order
Muthucumaraswamy R., Velmurugan S.
International Journal of Applied Mechanics and Engineering
|
2014
|
Vol. 19, no. 2
275--284
EN
An exact solution of an unsteady flow past a parabolic starting motion of an infinite vertical plate with variable temperature and mass diffusion, in the presence of a homogeneous chemical reaction of first order has been studied. The plate temperature as well as concentration level near the plate are raised linearly with time t. The dimensionless governing equations are solved using the Laplace-transform technique. The effects of velocity profiles are studied for different physical parameters such as the chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time. It is observed that the velocity increases with increasing values of the thermal Grashof number or mass Grashof number. The trend is just reversed with respect to the chemical reaction parameter.
20
Content available Construction method of optimal control system of a group of unmanned aerial vehicles
Korobchynsky M., Mashkov O.
Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
|
2014
|
nr 1
41--43
EN
In the following work the authors implement mathematical representation of a control system of complex dynamic system. An example of such system is a group of unmanned aerial vehicles. The sufficiency of controlled object mathematical representation is implemented, using the system approach, which in turn describes system elements, taking into account all the relations between them.
PL
W prezentowanej pracy autorzy wdrażają matematyczny opis systemu kontroli złożonego systemu dynamicznego. Przykładem takiego systemu jest grupa bezzałogowych samolotów. Zaimplementowano odpowiedni opis matematyczny kontrolowanego obiektu stosując podejście systemowe, które opisuje wszystkie elementy systemu uwzględniając wszystkie relacje między nimi.
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