2018
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Transient Natural Convection in an Enclosure with Variable Thermal Expansion Coefficient and Nanofluid Properties
2
2
Transient natural convection is numerically investigated in an enclosure using variable thermal conductivity, viscosity, and the thermal expansion coefficient of Al2O3water nanofluid. The study has been conducted for a wide range of Rayleigh numbers (103≤ Ra ≤ 106), concentrations of nanoparticles (0% ≤ ϕ ≤ 7%), the enclosure aspect ratio (AR =1), and temperature differences between the cold and hot walls (∆T= 30). Transient parameters such as development time and timeaverage Nusselt number along the cold wall are also presented as a nondimensional form. Increasing the Rayleigh number shortens the nondimensional time of the initializing stage. By increasing the volume fraction of nanoparticles, the flow development time shows different behaviors for various Rayleigh numbers. The nondimensional development time decreases by enhancing the concentration of nanoparticles.
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133
139


Esmaeil
Ghahremani
Department of Energy Engineering and Physics, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Islamic Republic of Iran
Department of Energy Engineering and Physics,
Iran
eghahremani86@gmail.com
Nanofluid
natural convection
variable property
transient natural convection
[[1] Ghahremani, E., Ghaffari, R., Ghadjari, H., Mokhtari, J., Effect of variable thermal expansion coefficient and nanofluid properties on steady natural convection in an enclosure, Journal of Applied and Computational Mechanics, 3(4), 2017, pp. 240250. ##[2] Xuan, Y., Roetzel, W., Conceptions for heat transfer correlation of nanofluids, International Journal of Heat and Mass Transfer,43, 2000, pp. 3701–3707. ##[3] Khanafer, K., Vafai, K., Lightstone, M., Buoyancydriven heat transfer enhancement in a twodimensional enclosure utilizing nanofluids, International Journal of Heat and Mass Transfer,46, 2003, pp. 3639–3653. ##[4] Gosselin, L., da Silva, A. K., Combined heat transfer and power dissipation optimization of nanofluid flows”, Applied Physics Letters, 85, 2004, pp. 4160–4162. ##[5] Brinkman, H. C., The viscosity of concentrated suspensions and solutions, Journal of Chemical Physics, 20, 1952, pp. 571–581. ##[6] Polidori, G., Fohanno, S., Nguyen, C. T., A note on heat transfer modeling of Newtonian nanofluids in laminar free convection, International Journal of Thermal Sciences,46, 2007, pp. 739–744. ##[7] Ho, C. J., Chen, M. W., Li, Z. W., Numerical simulation of natural convection of nanofluid in a square enclosure: Effects due to uncertainties of viscosity and thermal conductivity, International Journal of Heat and Mass Transfer, 51, 2008, pp. 4506–4516. ##[8] Maiga, S. E. B., Nguyen, C. T., Galanis, N., Roy, G., Heat transfer behaviors of nanofluids in a uniformly heated tube, Superlattices and Microstructures,35, 2004, pp. 543–557. ##[9] Aminossadati, S. M., Ghasemi, B., Natural convection of water–CuO nanofluid in a cavity with two pairs of heat source–sink, International Communications in Heat and Mass Transfer,38, 2011, pp. 672–678. ##[10] Koo, J., Kleinstreuer, C., A new thermal conductivity model for nanofluids, Journal of Nanoparticle Research,6(6), 2004, pp. 577–588. ##[11] Koo, J., Kleinstreuer, C., Laminar nanofluid flow in micro heatsinks, International Journal of Heat and Mass Transfer,48(13), 2005, pp. 2652–2661. ##[12] AbuNada., E., Chamkha, A. J., Effect of nanofluid variable properties on natural convection in enclosures filled with a CuO–EG–water nanofluid, International Journal of Thermal Sciences, 49(12), 2010, pp. 23392352. ##[13] Sheikholeslami, M., Ellahi, R., Hassan, M., Soleimani, S., A study of natural convection heat transfer in a nanofluid filled enclosure with elliptic inner cylinder, International Journal of Numerical Methods for Heat & Fluid Flow, 24(8), 2014, pp. 19061927. ##[14] Leal, M. A., Machado, H. A., Cotta, R. M., Integral transform solutions of transient natural convection in enclosures with variable fluid properties, International Journal of Heat and Mass Transfer, 43(21), 2000, pp. 39773990. ##[15] Yu, Z. T., Wang, W., Xu, X., Fan, L. W., Hu, Y. C., Cen, K. F., A numerical investigation of transient natural convection heat transfer of aqueous nanofluids in a differentially heated square cavity, International Communications in Heat and Mass Transfer, 38, 2011, pp. 585–589. ##[16] Yu, Z. T., Xu, X., Hu, Y. C., Fan, L. W., Cen, K. F., A numerical investigation of transient natural convection heat transfer of aqueous nanofluids in a horizontal concentric annulus, International Journal of Heat and Mass Transfer, 55, 2012, pp. 1141–1148. ##[17] Rahman, M. M., Oztop, H. F., Mekhilef, S., Saidur, R., AlSalem, K., Unsteady natural convection in Al2O3–water nanoliquid filled in isosceles triangular enclosure with sinusoidal thermal boundary condition on bottom wall, Superlattices and Microstructures, 67, 2014, pp. 181–196. ##[18] Alsabery, A. I., Saleh, H., Hashim, I., Siddheshwar, P.G., NanoliquidSaturated Porous Oblique Cavity using Thermal NonEquilibrium Model, International Journal of Mechanical Sciences, 114, 2016, pp. 233245. ##[19] Nguyen, M. T., Aly, A. M., Lee, S.W., Unsteady natural convection heat transfer in a nanofluidfilled square cavity with various heat source conditions, Advances in Mechanical Engineering, 8(5), 2016, pp. 1–18. ##[20] Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, Taylor and Francis Group, New York, 1980. ##[21] Versteeg, H. K., Malalasekera, W., An Introduction to Computational Fluid Dynamic: The Finite Volume Method, John Wiley & Sons Inc., New York, 1995.##]
Buckling Analysis of Embedded Nanosize FG Beams Based on a Refined Hyperbolic Shear Deformation Theory
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2
In this study, the mechanical buckling response of refined hyperbolic shear deformable (FG) functionally graded nanobeams embedded in an elastic foundation is investigated based on the refined hyperbolic shear deformation theory. Material properties of the FG nanobeam change continuously in the thickness direction based on the powerlaw model. To capture small size effects, Eringen’s nonlocal elasticity theory is adopted. Employing Hamilton’s principle, the nonlocal governing equations of FG nanobeams embedded in the elastic foundation are obtained. To predict the buckling behavior of embedded FG nanobeams, the Naviertype analytical solution is applied to solve the governing equations. Numerical results demonstrate the influences of various parameters such as elastic foundation, powerlaw index, nonlocal parameter, and slenderness ratio on the critical buckling loads of size dependent FG nanobeams.
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140
146


Aicha
Bessaim
Département de génie civil, Faculté des Sciences et Technologie, Université Mustapha Stambouli de Mascara, 29000, Algérie  Laboratoire des Structures et Matériaux Avancés dans le Génie
Département de génie civil,
Iran
aicha.bessaim@gmail.com


Mohammed Sid
Ahmed Houari
Département de génie civil, Faculté des Sciences et Technologie, Université Mustapha Stambouli de Mascara, 29000, Algérie  Laboratoire des Structures et Matériaux Avancés dans le Génie
Département de génie civil,
Iran
houarimsa@yahoo.fr


Bousahla
Abdelmoumen Anis
Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie  Laboratoire de Modélisation et Simulation Multiéchelle, Université de Sidi Bel Abbés, Algeria  Centre
Laboratoire des Matériaux et Hydrologie,
Iran
bousahla.anis@gmail.com


Abdelhakim
Kaci
Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, 22000, Algérie
Laboratoire des Matériaux et Hydrologie,
Iran
abdelhakim.kaci@gmail.com


Abdelouahed
Tounsi
Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Sidi Bel Abbes, 22000, Algérie  Laboratoire des Matériaux et Hydrologie, Université de Sidi
Laboratoire des Structures et Matériaux
Iran
tou_abdel@yahoo.com


El Abbes
Adda Bedia
Laboratoire de Modelisation et Simulation Multiechelle, Universite de Sidi Bel Abbes, Algeria
Laboratoire de Modelisation et Simulation
Iran
adda.bedia@gmail.com
FG nanobeam
Elastic foundation
Buckling
nonlocal elasticity theory
Shear deformation beam theory
[[1] Bedjilili, Y., Tounsi, A., Berrabah, H.M., Mechab, I., Adda Bedia, E.A., Benaissa, S., Natural frequencies of composite beams with a variable fiber volume fraction including rotary inertia and shear deformation, Applied Mathematics and Mechanics, 30(6), 2009, 717726. ##[2] Ghugal, Y.M., Shimpi, R.P., A review of refined shear deformation theories for isotropic and anisotropic laminated beams, Journal of Reinforced Plastics and Composites, 20(3), 2001, 255272. ##[3] Sayyad, A.S., Ghugal, Y.M., A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates, International Journal of Applied Mechanics, 9(1), 2017, 1750007. ##[4] Peddieson, J., Buchanan, G.R., Mc Nitt, R.P., Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science, 41, 2003, 305–312. ##[5] Ebrahimi, F., Barati, M.R., Electromechanical buckling behavior of smart piezoelectrically actuated higher order sizedependent graded nanoscale beams in thermal environment, International Journal of Smart and Nano Materials, 7, 2016, 69–90. ##[6] Eringen, A.C., Nonlocal polar elastic continua, International Journal of Engineering Science, 10(1), 1972, 116. ##[7] Eringen, A.C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54(9), 1983, 47034710. ##[8] Yang, F.A.C.M., Chong, A.C.M., Lam, D.C., Tong, P., Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39(10), 2002, 27312743. ##[9] Zemri, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A., A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory, Structural Engineering and Mechanics, 54(4), 2015, 693710. ##[10] Ebrahimi, F., Barati, M.R., Buckling analysis of nonlocal thirdorder shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39(3), 2017, 937952. ##[11] Aydogdu, M., A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration, Physica E: Lowdimensional Systems and Nanostructures, 41, 2009, 1651–1655. ##[12] Rahmani ,O., Jandaghian ,A.A., Buckling analysis of functionally graded nanobeams based on a nonlocal thirdorder shear deformation theory, Applied Physics A, 119(3), 2015, 1019–1032. ##[13] Tounsi, A, Semmah, A., Bousahla, A.A., Thermal buckling behavior of nanobeams using an efficient higherorder nonlocal beam theory, Journal of Nanomechanics and Micromechanics, 3, 2013, 37–42. ##[14] Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Bég, O., Mahmoud, S.R., Bending and buckling analyses of functionally graded material (FGM) sizedependent nanoscale beams including the thickness stretching effect, Steel and Composite Structures, 18(2), 2015, 425442. ##[15] Pisano, A.A., Sofi, A., Fuschi, P., Finite element solutions for nonhomogeneous nonlocal elastic problems, Mechanics Research Communications, 36, 2009, 755–761. ##[16] Pisano, A.A., Sofi, A., Fuschi, P., Nonlocal integral elasticity: 2D finite element based solutions, International Journal of Solids and Structures, 46, 2009, 3836–3849. ##[17] Janghorban, M., Zare, A., Free vibration analysis of functionally graded carbon nanotubes with variable thickness by differential quadrature method, Physica E: Lowdimensional Systems and Nanostructures, 43, 2011, 1602–1604. ##[18] Eltaher, M.A., Emam, S.A., Mahmoud, F.F., Free vibration analysis of functionally graded sizedependent nanobeams, Applied Mathematics and Computation, 218, 2012, 74067420. ##[19] Lim, C.W., Zhang, G., Reddy, J.N., A higherorder nonlocal elasticity and strain gradient theory and its applications in wave propagation, Journal of the Mechanics and Physics of Solids, 78, 2015, 298–313. ##[20] Ebrahimi, F, Barati, M.R, Dabbagh, A., A nonlocal strain gradient theory for wave propagation analysis in temperaturedependent inhomogeneous nanoplates, International Journal of Engineering Science, 107, 2016, 169–182. ##[21] Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A., Tounsi, A., A nonlocal quasi3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams, Smart Structures and Systems, 19(2), 2017, 115126. ##[22] Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A., Mahmoud, S.R., A nonlocal zerothorder shear deformation theory for nonlinear postbuckling of nanobeams, Structural Engineering and Mechanics, 62(6), 2017, 695702.##]
Differential Quadrature Method for Dynamic Buckling of Graphene Sheet Coupled by a Viscoelastic Medium Using Neperian Frequency Based on Nonlocal Elasticity Theory
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2
In the present study, the dynamic buckling of the graphene sheet coupled by a viscoelastic matrix was studied. In light of the simplicity of Eringen's nonlocal continuum theory to considering the nanoscale influences, this theory was employed. Equations of motion and boundary conditions were obtained using Mindlin plate theory by taking nonlinear strains of von Kármán and Hamilton's principle into account. On the other hand, a viscoelastic matrix was modeled as a threeparameter foundation. Furthermore, the differential quadrature method was applied by which the critical load was obtained. Finally, since there was no research available for the dynamic buckling of a nanoplate, the static buckling was taken into consideration to compare the results and explain some significant and novel findings. One of these results showed that for greater values of the nanoscale parameter, the small scale had further influences on the dynamic buckling.
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147
160


Mohammad
Malikan
Department of Mechanical engineering, faculty of engineering, Islamic Azad University, Mashhad branch, Iran
Department of Mechanical engineering, faculty
Iran
mohammad.malikan@yahoo.com


Mohammad Naser
Sadraee Far
Department of mechanical engineering, Islamic Azad university, Mashhad
Department of mechanical engineering, Islamic
Iran
sadrayifar_m@yahoo.com
Dynamic buckling
Graphene sheet
Viscoelastic matrix
differential quadrature method
[[1] Shijie, C., Hong, H., Hee Kiat, Ch., Numerical analysis of dynamic buckling of rectangular plates subjected to intermediatevelocity impact, International Journal of Impact Engineering, 25(2), 2001, 147167. ##[2] HosseiniAra, R., Mirdamadi, H.R., Khademyzadeh, H., Salimi, H., Thermal effect on dynamic stability of singlewalled Carbon Nanotubes in low and high temperatures based on Nonlocal shell theory, Advanced Materials Research, 622623, 2013, 959964. ##[3] Haftchenari, H., Darvizeh, M., Darvizeh, A., Ansari, R., Sharma, C.B., Dynamic analysis of composite cylindrical shells using differential quadrature method (DQM), Composite Structures, 78(2), 2007, 292–298. ##[4] Tamura, Y.S., Babcock, C.D., Dynamic stability of cylindrical shells under step loading, Journal of Applied Mechanics, 42(1), 1975, 190194 ##[5] Jabareen, M., Sheinman, I., Dynamic buckling of a beam on a nonlinear elastic foundation under step loading, Journal of Mechanics of Materials and Structures, 4, 2009, 78. ##[6] Ramezannezhad Azarboni, H., Darvizeh, M., Darvizeh, A., Ansari, R., Nonlinear dynamic buckling of imperfect rectangular plates with different boundary conditions subjected to various pulse functions using the Galerkin method, ThinWalled Structures, 94, 2015, 577–584. ##[7] Wang, X., Yang, W.D., Yang, S., Dynamic stability of carbon nanotubes reinforced composites, Applied Mathematical Modelling, 38(1112), 2014, 29342945. ##[8] Petry, D., Fahlbusch, G., Dynamic buckling of thin isotropic plates subjected to inplane impact, ThinWalled Structures, 38(3), 2000, 267–283. ##[9] Kubiak, T., Criteria of dynamic buckling estimation of thinwalled structures, ThinWalled Structures, 45(1011), 2007, 888–892. ##[10] Reddy, J.N., Srinivasa, A.R., Nonlinear theories of beams and plates accounting for moderate rotations and material length scales, International Journal of NonLinear Mechanics, 66, 2014, 4353. ##[11] Ghorbanpour Arani, A., Shiravand, A., Rahi, M., Kolahchi, R., Nonlocal vibration of coupled DLGS systems embedded on ViscoPasternak foundation, Physica B, 407, 2012, 4123–4131. ##[12] Eringen, A.C., Nonlocal Continuum Field Theories, SpringerVerlag, New York, 2002. ##[13] Eringen, A.C., Linear theory of nonlocal elasticity and dispersion of plane waves, International Journal of Engineering Science, 10(5), 1972, 425435. ##[14] Duan, W.H., Wang, C.M., Zhang, Y.Y., Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics, Journal of Applied Physics, 101(2), 2007, 2430524311. ##[15] Duan, W.H., Wang, C.M., Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory, Nanotechnology, 18(38), 2007, 385704. ##[16] https://www.slideshare.net/zead28/conceptofcomplexfrequency. ##[17] Franco, S., Electric Circuits Fundamentals, Oxford University Press, Inc., 1995. ##[18] Bellman, R., Kashef, B.G., Casti, J., Differential Quadrature: A Technique for the Rapid Solution of Nonlinear Partial Differential Equation, Journal of Computational Physics, 10(1), 1972, 40–52. ##[19] Shu, C., Differential Quadrature and Its Application in Engineering, Springer, Berlin, 2000. ##[20] Bellman, R., Casti, J., Differential quadrature and longterm integration, Journal of Mathematical Analysis and Applications, 34(2), 1971, 235–238. ##[21] Chen, W., Differential Quadrature Method and its Applications in Engineering, Shanghai Jiao Tong University, 1996. ##[22] Golmakani, M.E., Rezatalab, J., Non uniform biaxial buckling of orthotropic Nanoplates embedded in an elastic medium based on nonlocal Mindlin plate theory, Composite Structures, 119, 2015, 238250. ##[23] Murmu, T., Pradhan, S.C., Buckling analysis of a singlewalled carbon nanotubes embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Physica E, 41(7), 2009, 1232–9. ##[24] Golmakani, M.E., Sadraee Far, M.N., Buckling analysis of biaxially compressed double‑layered graphene sheets with various boundary conditions based on nonlocal elasticity theory, Microsystem Technologies, 23(6), 2017, 21452161. ##[25] Ansari, R., Sahmani, S., Prediction of biaxial buckling behavior of singlelayered graphene sheets based on nonlocal plate models and molecular dynamics simulations, Applied Mathematical Modelling, 37(1213), 2013, 7338–7351. ##[26] Malikan, M., Jabbarzadeh, M., Sh. Dastjerdi, Nonlinear Static stability of bilayer carbon nanosheets resting on an elastic matrix under various types of inplane shearing loads in thermoelasticity using nonlocal continuum, Microsystem Technologies, 23(7), 2017, 29732991. ##[27] Malikan, M., Electromechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory, Applied Mathematical Modelling, 48, 2017, 196–207. ##[28] Malikan, M., Analytical predictions for the buckling of a nanoplate subjected to nonuniform compression based on the fourvariable plate theory, Journal of Applied and Computational Mechanics, 3(3), 2017, 218–228. ##[29] Malikan, M., Buckling analysis of micro sandwich plate with nano coating using modified couple stress theory, Journal of Applied and Computational Mechanics, 4(1), 2018, 115. ##[30] Civalek, Ö., Korkmaz, A., Demir, Ç., Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on twoopposite edges, Advances in Engineering Software, 41(4), 2010, 557560. ##[31] Dastjerdi, S., Jabbarzadeh, M., Nonlinear bending analysis of bilayer orthotropic graphene sheets resting on Winkler–Pasternak elastic foundation based on nonlocal continuum mechanics, Composites Part B: Engineering, 87, 2016, 161175. ##[32] Karličić, D., Adhikari, S., Murmu, T., Cajić, M., Exact closedform solution for nonlocal vibration and biaxial buckling of bonded multi nanoplate system, Composites Part B, 66, 2014, 328339.##]
Moving Mesh Nonstandard Finite Difference Method for Nonlinear Heat Transfer in a Thin Finite Rod
2
2
In this paper, a moving mesh technique and a nonstandard finite difference method are combined, and a moving mesh nonstandard finite difference (MMNSFD) method is developed to solve an initial boundary value problem involving a quartic nonlinearity that arises in heat transfer with thermal radiation. In this method, the moving spatial grid is obtained by a simple geometric adaptive algorithm to preserve stability. Moreover, it uses variable time steps to protect the positivity condition of the solution. The results of this computational technique are compared with the corresponding uniform mesh nonstandard finite difference scheme. The simulations show that the presented method is efficient and applicable, and approximates the solutions well, while because of producing unreal solution, the corresponding uniform mesh nonstandard finite difference fails.
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161
166


Morteza
BishehNiasar
Department of Applied Mathematics, Faculty of Mathematical Science, University of
Kashan, Kashan, Iran.
Department of Applied Mathematics, Faculty
Iran
mbisheh@kashanu.ac.ir


Maryam
Arab Ameri
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
Department of Mathematics, University of
Iran
arabameri@math.usb.ac.ir
Nonstandard finite difference
positivity
moving mesh
heat conduction equation
[[1] Jordan, P.M., A nonstandard finite difference scheme for a nonlinear heat transfer in a thin finite rod, Journal of Difference Equations and Applications, 9(11), 2003, 1015102. ##[2] Dai ,W., Su, S., A nonstandard finite difference scheme for solving one dimensional nonlinear heat transfer, Journal of Difference Equations and Applications,10(11), 2004, 10251032. ##[3] Mohammadi, A., Malek, A., Stable nonstandard implicit finite difference schemes for nonlinear heat transfer in a thin finite rod, Journal of Difference Equations and Applications, 15(7), 2009, 719728. ##[4] Qin, W., Wang, L., Ding, X., A nonstandard finite difference method for a hepatitis B virus infection model with spatial diffusion, Journal of Difference Equations and Applications, 20(12), 2014, 16411651. ##[5] Elsheikh, S., Ouifki, R., Patidar, K.C., A nonstandard finite difference method to solve a model of HIVMalaria coinfection, Journal of Difference Equations and Applications, 20(3), 2014, 354378. ##[6] Mickens, R.E., Nonstandard finite difference schemes for differential equations, Journal of Difference Equations and Applications, 8(9), 2002, 823847. ##[7] Ehrhardt, M., Mickens, R.E., A nonstandard finite difference scheme for convection diffusion equations having constant coefficients, Applied Mathematics and Computation, 219(12), 2013, 65916604. ##[8] Mickens, R.E., Nonstandard finite difference schemes for reactiondiffusion equations, Numerical Methods for Partial Differential Equation, 15(2), 1999, 2012014. ##[9] Mickens, R.E., Gumel, A.B., Construction and analysis of a nonstandard finite difference scheme for the BurgersFisher equation, Journal of Sound and Vibration, 257(4), 2002, 791797. ##[10] SanzSerna, J.M., Christie, I., A Simple Adaptive Technique for Nonlinear Wave Problems, Journal of Computational Physics, 67(2), 1986, 348360. ##[11] Mickens, R.E., Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994.##]
Inherent Irreversibility of Exothermic Chemical Reactive ThirdGrade Poiseuille Flow of a Variable Viscosity with Convective Cooling
2
2
In this study, the analysis of inherent irreversibility of chemical reactive thirdgrade poiseuille flow of a variable viscosity with convective cooling is investigated. The dissipative heat in a reactive exothermic chemical moves over liquid in an irreversible way and the entropy is produced unceasingly in the system within the fixed walls. The heat convective exchange with the surrounding temperature at the plate surface follows Newton’s law of cooling. The solutions of the dimensionless nonlinear equations are obtained using weighted residual method (WRM). The solutions are used to obtain the Bejan number and the entropy generation rate for the system. The influence of some pertinent parameters on the entropy generation and the Bejan number are illustrated graphically and discussed with respect to the parameters.
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167
174


S.O.
Salawu
Department of Mathematics, Landmark University, Omuaran, Nigeria
Department of Mathematics, Landmark University,
Iran
kunlesalawu2@gmail.com


S.I.
Oke
Department of Mathematical Sciences, University of Zululand, Zululand, South Africa
Department of Mathematical Sciences, University
Iran
segunoke2016@gmail.com
Exothermic reaction
thirdgrade fluid
Poiseuille flow
Variable viscosity
Convective cooling
[[1] Siddiqui, A.M., Mahmood, R., Ghori, Q.K., Thin film flow of a third grade fluid on a moving belt by He’s homotopy perturbation method, International Journal of Nonlinear Sciences and Numerical Simulation, 7(1), 2006, 18. ##[2] Ellahi, R., Afzal, A., Effects of variable viscosity in a third grade fluid with porous medium: an analytic solution, Communications in Nonlinear Science and Numerical Simulation, 14(5), 2009, 20562072. ##[3] Makinde, O.D., Thermal stability of a reactive third grade fluid in a cylindrical pipe: an exploitation of Hermite–Padé approximation technique, Applied Mathematics and Computation, 189, 2007, 690697. ##[4] Rajagopal, K.R., On Boundary Conditions for Fluids of the Differential Type: Navier–Stokes Equations and Related NonLinear Problems, Plenum Press, New York, 273,1995. ##[5] Fosdick, R.L., Rajagopal, K.R., Thermodynamics and stability of fluids of third grade, Proceedings of the Royal Society of London, Series A, 1980, 339351. ##[6] Kamal, M.R., Ryan, M.E., Reactive polymer processing: techniques and trends, Advanced Polymer Technology, 4, 1984, 323348. ##[7] Datta, R., Henry, M., Lactic acid: recent advances in products, processes and technologies a review, Journal of Chemical Technology and Biotechnology, 81, 2006, 11191129. ##[8] Bapat, S.S., Aichele, C.P., High, K.A., Development of a sustainable process for the production of polymer grade lactic acid, Sustainable Chemical Processes, 2, 2014, 18. ##[9] Halley, P.J., George, G.A., Chemorheology of Polymers: From Fundamental Principles to Reactive Processing, Cambridge University Press, UK, 2009. ##[10] Chinyoka, T., Twodimensional flow of chemically reactive viscoelastic fluids with orwithout the influence of thermal convection, Communications in Nonlinear Science and Numerical Simulation, 16, 2011, 13871395. ##[11] Makinde, O.D., On thermal stability of a reactive thirdgrade fluid in a channel with convective cooling at the walls, Applied Mathematics and Computation, 213, 2009, 170176. ##[12] Makinde, O.D., Thermal ignition in a reactive viscous flow through a channel filled with a porous medium, Journal of Heat Transfer, 128, 2006, 601604. ##[13] Beg, O.A., Motsa, S.S., Islam, M.N., Lockwood, M., Pseudospectral and variational iteration simulation of exothermically reacting RivlinEricksen viscoelastic flow and heat transfer in a rocket propulsion duct, Computational Thermal Sciences, 6, 2014, 91102. ##[14] Chinyoka, T., Makinde, O.D., Analysis of transient Generalized Couette flow of a reactive variable viscosity thirdgrade liquid with asymmetric convective cooling, Mathematical and Computer Modelling, 54, 2011, 160174. ##[15] Makinde, O.D., Ogulu, A., The effect of thermal radiation on the heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field, Chemical Engineering Communications, 195(12), 2008, 15751584. ##[16] Gitima, P., Effect of variable viscosity and thermal conductivity of micropolar fluid in a porous channel in presence of magnetic field, International Journal for Basic Sciences and Social Sciences, 1(3), 2012, 6977. ##[17] Hazarika, G.C., Utpal, S.G.Ch., Effects of variable viscosity and thermal conductivity on MHD flow past a vertical plate, Matematicas Ensenanza Universitaria, 2, 2012, 4554. ##[18] Salawu, S.O., Dada, M.S., Radiative heat transfer of variable viscosity and thermal conductivity effects on inclined magnetic field with dissipation in a nonDarcy medium, Journal of the Nigerian Mathematical Society, 35, 2016, 93106. ##[19] Bejan, A., Entropy Generation through Heat and Fluid Flow, Wiley, New York, 1982. ##[20] Adesanya, S.O., Makinde, O.D., Irreversibility analysis in a couple stress film flow along an inclined heated plate with adiabatic free surface, Physica A, 432, 2015, 222229. ##[21] Pakdemirli, M., Yilbas, B.S., Entropy generation for pipe low of a third grade fluid with Vogel model viscosity, International Journal of NonLinear Mechanics, 41(3), 2006, 432437. ##[22] Hooman, K., Hooman, F., Mohebpour, S.R., Entropy generation for forced convection in a porous channel with isoflux or isothermal walls, International Journal of Exergy, 5(1), 2008, 7896. ##[23] Chauhan, D.S., Kumar, V., Entropy analysis for thirdgrade fluid flow with temperaturedependent viscosity in annulus partially filled with porous medium, Theoretical and Applied Mechanics, 40(3), 2013, 441464. ##[24] Das, S., Jana, R.N., Entropy generation due to MHD flow in a porous channel with Navier slip, Ain Shams Engineering Journal, 5, 2014, 575584. ##[25] Srinivas, J., Ramana Murthy, J.V., Second law analysis of the flow of two immiscible micropolar fluids between two porous beds, Journal of Engineering Thermophysics, 25(1), 2016, 126142. ##[26] Odejide, S.A., Aregbesola, Y.A.S., Applications of method of weighted residuals to problems with semifinite domain, Romanian Journal of Physics, 56(12), 2011, 1424. ##[27] McGrattan, E.R., Application of weighted residual methods to dynamic economics models, Federal Reserve Bank of Minneapolis Research Department Staff Report, 232, 1998.##]
Exact Radial Free Vibration Frequencies of PowerLaw Graded Spheres
2
2
This study concentrates on the free pure radial vibrations of hollow spheres made of hypothetically functionally simple power rule graded materials having identical inhomogeneity indexes for both Young’s modulus and the density in an analytical manner. After offering the exact elements of the free vibration coefficient matrices for freefree, freefixed, and fixedfixed restraints, a parametric study is fulfilled to study the effects of both the aspect ratio and the inhomogeneity parameters on the natural frequencies. The outcomes are presented in both graphical and tabular forms. It was seen that the fundamental frequency is mostly affected by the inhomogeneity parameters rather than the higher ones. However, the natural frequencies except the fundamental ones are dramatically affected by the thickness of the sphere. It is also revealed that there is a linear relationship between the fundamental frequency and others in higher modes of the same sphere under all boundary conditions.
1

175
186


Vebil
Yıldırım
Cukurova University, Department of Mechanical Engineering, Turkey
Cukurova University, Department of Mechanical
Iran
vebil@cu.edu.tr
Free vibration
Functionally graded
Exact solution
Hollow sphere
Thickwalled
[[1] Horace Lamb, M.A., On the Vibrations of an Elastic Sphere, Proceedings of the London Mathematical Society, 13(1), 1881, 189–212. ##[2] Horace Lamb, M.A., On the Vibrations of a Spherical Shell, Proceedings of the London Mathematical Society, 14(1), 1882, 5056. ##[3] Sato, Y., Usami T., Basic Study on the oscillation of Homogeneous Elastic SpherePart I. Frequency of the Free Oscillations, Geophysics Magazine, 31(1), 1962, 1524. ##[4] Sato, Y., Usami, T., Basic Study on the oscillation of Homogeneous Elastics SpherePart II. Distribution of Displacement, Geophysics Magazine, 31(1), 1962, 2547. ##[5] Eason, G., On the Vibration of Anisotropic Cylinders and Spheres, Applied Scientific Research, 12, 1963, 81–85. ##[6] Seide, P., Radial Vibrations of Spherical Shells, Journal of Applied Mechanics, 37(2), 1970, 528530. ##[7] Gosh, K., Agrawal, M.K., Radial Vibrations of Spheres, Journal of Sound and Vibration, 171(3), 1994, 315–322. ##[8] Sharma, J.N., Sharma, N., Free Vibration Analysis of Homogeneous Thermoelastic Solid Sphere, Journal of Applied Mechanics, 77(2), 2010, 021004. ##[9] Scafbuch, P.J., Rizzo, F.J., Thomson, R.B., Eigen Frequencies of an Elastic Sphere with Fixed Boundary Conditions, Journal of Applied Mechanics, 59(2), 1992, 458–459. ##[10] Shah, H., Ramkrishana, C.V., Datta, S.K., Three Dimensional and Shell Theory Analysis of Elastic Waves in a Hollow SpherePart I. Analytical Foundation, Journal of Applied Mechanics, 36(3), 1969, 431439. ##[11] Shah, H., Ramkrishana, C.V., Datta, S.K., Three Dimensional and Shell Theory Analysis of Elastic Waves in a Hollow SpherePart II. Numerical Results, Journal of Applied Mechanics, 36(3), 1969, 440444. ##[12] Cohen, H., Shah, A.H., Free Vibrations of a Spherically Isotropic Hollow Sphere, Acustica, 26, 1972, 329–333. ##[13] Grigorenko, Y.M., Kilina, T.N., Analysis of the Frequencies and Modes of Natural Vibration of Laminated Hollow Spheres in ThreeDimensional and TwoDimensional Formulations, Soviet Applied Mechanics, 25, 1989, 11651171. ##[14] Jiang, H., Young, P.G., Dickinson, S.M., Natural Frequencies of Vibration of Layered Hollow Spheres Using ThreeDimensional Elasticity Equations, Journal of Sound and Vibration, 195(1), 1996, 155162. ##[15] Chen, W.Q., Ding, H.J., Xu, R.Q., ThreeDimensional Free Vibration Analysis of a FluidFilled Piezoceramic Hollow Sphere, Computers and Structures, 79(6), 2001, 653663. ##[16] Chen, W.Q., Cai, J.B., Ye, G.R., Ding, H.J., On Eigen Frequencies of an Anisotropic Sphere, Journal of Applied Mechanics, 67(2), 2000, 422424. ##[17] Chen, W. Q., Ding, H.J., Free Vibration of MultiLayered Spherically Isotropic Hollow Spheres, International Journal of Mechanical Sciences, 43(3), 2001, 667680. ##[18] Chen, W.Q., Ding, H.J., Natural Frequencies of a FluidFilled Anisotropic Spherical Shell, Journal of the Acoustical Society of America, 105, 1999, 174182. ##[19] Hoppmann II, W.H., Baker, W.E., Extensional Vibrations of Elastic orthotropic Spherical Shells, Journal of Applied Mechanics, 28, 1961, 229237. ##[20] Shul'ga, N.A., Grigorenko, A.Y., E’mova, T.L., Free NonAxisymmetric oscillations of a ThickWalled, Nonhomogeneous, Transversely Isotropic, Hollow Sphere, Soviet Applied Mechanics, 24, 1988, 439444. ##[21] Heyliger, P.R., Jilani, A., The Free Vibrations of Inhomogeneous Elastic Cylinders and Spheres, International Journal of Solids and Structures, 29(22), 1992, 26892708. ##[22] Ding, H.J., Chen, W.Q., Nonaxisymmetric Free Vibrations of a Spherically Isotropic Spherical Shell Embedded in an Elastic Medium, International Journal of Solids and Structures, 33, 1996, 25752590. ##[23] Ding, H.J., Chen, W.Q., Natural Frequencies of an Elastic Spherically Isotropic Hollow Sphere Submerged in a Compressible Fluid Medium, Journal of Sound and Vibration, 192(1), 1996, 173198. ##[24] Heyliger, P.R., Wu, Y.C., Electrostatic Fields in Layered Piezoelectric Spheres, International Journal of Engineering Science, 37, 1999, 143–161. ##[25] Stavsky, Y., Greenberg, J.B., Radial Vibrations of orthotropic Laminated Hollow Spheres, Journal of the Acoustical Society of America, 113, 2003, 847–851. ##[26] Ding, H.J., Wang, H.M., Discussions on “Radial vibrations of orthotropic laminated hollow spheres, [J. Acoust. Soc.Am. 113, 847–851 (2003)]”, Journal of the Acoustical Society of America, 115, 2004, 1414. ##[27] Chiroiu, V., Munteanu, L., On the Free Vibrations of a Piezoceramic Hollow Sphere, Mechanics Research Communications, 34, 2007, 123–129. ##[28] Keles, İ., Novel Approach to Forced Vibration Behavior of Anisotropic ThickWalled Spheres, AIAA Journal, 54(4), 2016, 14381442. ##[29] Sharma, J.N., Sharma, N., Vibration Analysis of Homogeneous Transradially Isotropic Generalized Thermoelastic Spheres, Journal of Vibration and Acoustics, 133(4), 2011, 041001. ##[30] Sharma, N., Modeling and Analysis of Free Vibrations in Thermoelastic Hollow Spheres, Multidiscipline Modeling in Materials and Structures, 11(2), 2015, 134159. ##[31] Abbas, I., Natural Frequencies of a Poroelastic Hollow Cylinder, Acta Mechanica, 186(1–4), 2006, 229–237. ##[32] Abbas, I., Analytical Solution for a Free Vibration of a Thermoelastic Hollow Sphere, Mechanics Based Design of Structures and Machines, 43(3), 2015, 265276. ##[33] Nelson, R.B., Natural Vibrations of Laminated orthotropic Spheres, International Journal of Solids and Structures, 9(3), 1973, 305311. ##[34] Chen, W.Q., Wang, X., Ding, H.J., Free Vibration of a FluidFilled Hollow Sphere of a Functionally Graded Material with Spherical Isotropy, Journal of the Acoustical Society of America, 106, 1999, 25882594. ##[35] Chen, W.Q., Wang, L.Z., Lu, Y., Free Vibrations of Functionally Graded Piezoceramic Hollow Spheres with Radial Polarization, Journal of Sound and Vibration, 251(1), 2002, 103114. ##[36] Ding, H.J., Wang, H.M., Chen, W.Q., Dynamic Responses of a Functionally Graded Pyroelectric Hollow Sphere for Spherically Symmetric Problems, International Journal of Mechanical Sciences, 45, 2003, 1029–1051. ##[37] Kanoria, M., Ghosh, M.K., Study of Dynamic Response in a Functionally Graded Spherically Isotropic Hollow Sphere with Temperature Dependent Elastic Parameters, Journal of Thermal Stresses, 33, 2010, 459–484. ##[38] Keleş, İ., Tütüncü, N., Exact Analysis of Axisymmetric Dynamic Response of Functionally Graded Cylinders (or Disks) and Spheres, Journal of Applied Mechanics, 78(6), 2011, 0610141. ##[39] Sharma, P.K., Mishra, K.C., Analysis of Thermoelastic Response in Functionally Graded Hollow Sphere without Load, Journal of Thermal Stresses, 40(2), 2017, 185197. ##[40] Yıldırım, V., HeatInduced, PressureInduced and CentrifugalForceInduced Exact Axisymmetric ThermoMechanical Analyses in a ThickWalled Spherical Vessel, an Infinite Cylindrical Vessel, and a Uniform Disk Made of an Isotropic and Homogeneous Material, International Journal of Engineering Applied Sciences, 9(3), 2017, 6687. ##[41] Kamdi, D., Lamba, N.K., Thermoelastic Analysis of Functionally Graded Hollow Cylinder Subjected to Uniform Temperature Field, Journal of Applied and Computational Mechanics, 2(2), 2016, 118127. ##[42] Talebi, S., Uosofvand, H., Ariaei, A., Vibration Analysis of a Rotating Closed Section Composite Timoshenko Beam by Using Differential Transform Method, Journal of Applied and Computational Mechanics, 1(4), 2015, 181186. ##[43] Mercan, K., Ersoy, H., Civalek, O., Free Vibration of Annular Plates by Discrete Singular Convolution and Differential Quadrature Methods, Journal of Applied and Computational Mechanics, 2(3), 2016, 28133. ##[44] Joubari, M.M., Ganji, D.D., Jouybari, H.J., Determination of Periodic Solution for Tapered Beams with Modified Iteration Perturbation Method, Journal of Applied and Computational Mechanics, 1(1), 2015, 4451. ##[45] Sedighi H.M., Daneshmand F., Nonlinear Transversely Vibrating Beams by the Homotopy Perturbation Method with an Auxiliary Term, Journal of Applied and Computational Mechanics, 1(1), 2015, 19. ##[46] Karimi, M., Shokrani, M.H., Shahidi, A.R., SizeDependent Free Vibration Analysis of Rectangular Nanoplates with the Consideration of Surface Effects Using Finite Difference Method, Journal of Applied and Computational Mechanics, 1(3), 2015, 122133. ##[47] Watson, J.N., A Treatise on the Theory of Bessel Functions, Cambridge University Press, London, 1922. ##[48] Kim, J.O., Lee, J.G., Chun, H.Y., Radial Vibration Characteristics of Spherical Piezoelectric Transducers, Ultrasonics, 43, 2005, 531–537.##]
Bending of Shear Deformable Plates Resting on Winkler Foundations According to Trigonometric Plate Theory
2
2
A trigonometric plate theory is assessed for the static bending analysis of plates resting on Winkler elastic foundation. The theory considers the effects of transverse shear and normal strains. The theory accounts for realistic variation of the transverse shear stress through the thickness and satisfies the traction free conditions at the top and bottom surfaces of the plate without using shear correction factors. The governing equations of equilibrium and the associated boundary conditions of the theory are obtained using the principle of virtual work. A closedform solution is obtained using double trigonometric series. The numerical results are obtained for flexure of simply supported plates subjected to various static loadings. The displacements and stresses are obtained for three different values of foundation modulus. The numerical results are also generated using higher order shear deformation theory of Reddy, first order shear deformation theory of Mindlin, and classical plate theory for the comparison of the present results.
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187
201


Atteshamuddin
Sayyad
SRES College of Engineering, Kopargaon, Maharashtra, India.
SRES College of Engineering, Kopargaon, Maharashtr
Iran
attu_sayyad@yahoo.co.in


Yuwaraj M.
Ghugal
Head of Department of Applied Mechanics, Govt. College of EngineeringKarad, Shivaji University, Maharashtra415124, India
Head of Department of Applied Mechanics,
Iran
ghugal@rediffmail.com
Shear deformation
normal strain
Shear stress
shear correction factor
Winkler elastic foundation
[[1] Kirchhoff, G.R., Uber das gleichgewicht und die bewegung einer elastischen Scheibe, Journal for Pure and Applied Mathematics, 40, 1850, 5188. ##[2] Mindlin, R.D., Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, Journal of Applied Mechanics, 18, 1951, 3138. ##[3] Reddy, J.N., A simple higher order theory for laminated composite plates, Journal of Applied Mechanics, 51, 1984, 745752. ##[4] Matsunaga, H., Vibration and stability of thick plates on elastic foundations, Journal of Engineering Mechanics, 126(1), 2000, 27–34. ##[5] Huang, M.H., Thambiratnam, D.P., Analysis of plate resting on elastic supports and elastic foundation by finite strip method, Computers and Structures,79(2930), 2001, 25472557. ##[6] Chen, W.Q., Bian, Z.G., A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation, Applied Mathematical Modelling,28(10), 2004, 877–890. ##[7] Atmane, H.A., Tounsi, A., Mechab, I., Bedia, E.A.A., Free vibration analysis of functionally graded plates resting on Winkler–Pasternak elastic foundations using a new shear deformation theory, International Journal of Mechanics and Materials in Design, 6(2), 2010, 113121. ##[8] Thai, H.T., Park, M., Choi, D.H., A simple refined theory for bending, buckling, and vibration of thick plates resting on elastic foundation, International Journal of Mechanical Science, 73, 2013, 40–52. ##[9] Zenkour, A.M., Bending of orthotropic plates resting on Pasternak's foundations by mixed shear deformation theory, Acta Mechanica Sinica,27(6), 2011, 956–962. ##[10] Zenkour, A.M., Allam, M.N.M., Shaker, M.O., Radwan, A.H., On the simple and mixed firstorder theories for plates resting on elastic foundations, Acta Mechanica,220(14), 2011, 33–46. ##[11] Sayyad, A.S., Flexure of thick orthotropic plates by exponential shear deformation theory, Latin American Journal of Solids and Structures,10, 2013, 473490. ##[12] Akbas, S.D., Vibration and static analysis of functionally graded porous plates,Journal of Applied and Computational Mechanics, 3(3), 2017, 199207. ##[13] Akbas, S.D., Stability of a nonhomogenous porous plate by using generalized differantial quadrature method, International Journal of Engineering & Applied Sciences, 9(2), 2017, 147155. ##[14] Akbas, S.D., Static analysis of a nano plate by using generalized differential quadrature method,International Journal of Engineering & Applied Sciences, 8(2), 2016, 3039. ##[15] Civalek, O., Analysis of thick rectangular plates with symmetric crossply laminates based on firstorder shear deformation theory, Journal of Composite Materials, 42(26), 2008, 28532867. ##[16] Gurses, M., Civalek, O., Korkmaz, A.K., Ersoy, H., Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on firstorder shear deformation theory, International Journal for Numerical Methods in Engineering, 79, 2009, 290–313. ##[17] Sayyad, A.S., Ghugal, Y.M., On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results, Composite Structures, 129, 2015, 177–201. ##[18] Sayyad, A.S., Ghugal, Y.M., Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature, Composite Structures, 171, 2017, 486–504. ##[19] Ghugal, Y.M., Sayyad, A.S., A static flexure of thick isotropic plates using trigonometric shear deformation theory, Journal of Solid Mechanics, 2(1), pp. 7990, 2010. ##[20] Ghugal, Y.M., Sayyad, A.S., Free vibration of thick isotropic plates using trigonometric shear deformation theory, Journal of Solid Mechanics, 3(2), 2011, 172182. ##[21] Ghugal, Y.M., Sayyad, A.S., Static flexure of thick orthotropic plates using trigonometric shear deformation theory, Journal of Structural Engineering, 39(5), 2013, 512521. ##[22] Ghugal, Y.M., Sayyad, A.S., Free vibration of thick orthotropic plates using trigonometric shear deformation theory, Latin American Journal of Solids and Structures, 8, 2011, 229243. ##[23] Timoshenko, S.P., Goodier, J.M., Theory of Elasticity, McGrawHill, Singapore, 1970.##]
SemiAnalytical Solution for Vibration of Nonlocal Piezoelectric Kirchhoff Plates Resting on Viscoelastic Foundation
2
2
Semianalytical solutions for vibration analysis of nonlocal piezoelectric Kirchhoff plates resting on viscoelastic foundation with arbitrary boundary conditions are derived by developing Galerkin strip distributed transfer function method. Based on the nonlocal elasticity theory for piezoelectric materials and Hamilton's principle, the governing equations of motion and boundary conditions are first obtained, where external electric voltage, viscoelastic foundation, piezoelectric effect, and nonlocal effect are considered simultaneously. Subsequently, Galerkin strip distributed transfer function method is developed to solve the governing equations for the semianalytical solutions of natural frequencies. Numerical results from the model are also presented to show the effects of nonlocal parameter, external electric voltages, boundary conditions, viscoelastic foundation, and geometric dimensions on vibration responses of the plate. The results demonstrate the efficiency of the proposed methods for vibration analysis of nonlocal piezoelectric Kirchhoff plates resting on viscoelastic foundation.
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202
215


D.P.
Zhang
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
College of Aerospace Science and Engineering,
Iran
d.p.zhang@hotmail.com


Yongjun
Lei
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
College of Aerospace Science and Engineering,
Iran
leiyj108@nudt.edu.cn


Z.B.
Shen
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan 410073, China
College of Aerospace Science and Engineering,
Iran
z.b.shen@hotmail.com
Nonlocal piezoelectric plates
Vibration characteristics
viscoelastic foundation
Galerkin strip distributed transfer function method
[[1] Liu, C., Ke, L.L., Wang, Y.S., Yang, J., Kitipornchai, S., Thermoelectromechanical vibration of piezoelectric nanoplates based on the nonlocal theory, Composite Structures, 106, 2013, 167170. ##[2] Ke, L.L., Wang, Y.S., Thermoelectricmechanical vibration of piezoelectric nanobeams based on the nonlocal theory, Smart Materials and Structures, 21, 2012, 025018. ##[3] Eringen, A.C., Theory of nonlocal plasticity, International Journal of Engineering Science, 21, 1983, 741751. ##[4] Eringen, A.C., Nonlocal continuum field theories, New York: SpringerVerlag; 2002. ##[5] Zhang, D.P., Lei, Y., Wang, C.Y., Shen, Z.B., Vibration analysis of viscoelastic singlewalled carbon nanotubes resting on a viscoelastic foundation, Journal of Mechanical Science and Technology, 31(1), 2017, 8798. ##[6] Wu, C.P., Lai, W.W., Free vibration of an embedded singlewalled carbon nanotube with various boundary conditions using the RMVTbased nonlocal Timoshenko beam theory and DQ method, Physica E, 68, 2015, 821. ##[7] Blasé, X., Rubio, A., Louie, S.G., Cohen, M.L., Stability and band gap constancy of boron nitride nanotubes, Europhysics Letters, 28, 1994, 335341. ##[8] Zenkour, A.M., Nonlocal transient thermal analysis of a singlelayered graphene sheet embedded in viscoelastic medium, Physica E, 78, 2016, 8797. ##[9] Hache, F., Challamel, N., Elishakoff, I., Wang, C.M., Comparison of nonlocal continualization schemes for lattice beams and plates, Archive of Applied Mechanics, 87(7), 2017, 11051138. ##[10] Lei, Y., Friswell, M.I., Adhikari, S., A Galerkin method for distributed systems with nonlocal damping, International Journal of Solids and Structures, 43, 2006, 33813400. ##[11] Lei, Y., Finite element analysis of beams with nonlocal foundations, 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conferrence, Newport, Rhode Island, 2006, 111. ##[12] Zhao, X.C., Lei, Y., Zhou, J.P., Strain analysis of nonlocal viscoelastic Kelvin bar in tension, Applied Mathematics and Mechanics, 29(1), 2008, 6774. ##[13] Friswell, M.I., Adhikari, S., Lei, Y., Nonlocal finite element analysis of damped beams, International Journal of Solids and Structures, 44, 2007, 75647576. ##[14] Asemi, S.R., Farajpour, A., Thermoelectromechanical vibration of coupled piezoelectricnanoplate systems under nonuniform voltage distribution embedded in Pasternak elastic medium, Current Applied Physics, 14, 2014, 814832. ##[15] Asemi, S.R., Farajpour, A., Asemi, H.R., Mohammadi, M., Influence of initial stress on the vibration of doublepiezoelectricnanoplate systems with various boundary conditions using DQM, Physica E, 63, 2014, 169179. ##[16] Kolahchi, R., Hosseini, H., Esmailpour, M., Differential cubature and quadratureBolotin methods for dynamic stability of embedded piezoelectric nanoplates based on viscononlocalpiezoelasticity theories, Composite Structures, 157, 2016, 174186. ##[17] Kolahchi, R., Zarei, M.S., Hajmohammad, M.H., Oskouei, A.N., Viscononlocalrefined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubatureBolotin methods, ThinWalled Structures, 113, 2017, 162169. ##[18] Arefi, M., Zenkour, A.M., Sizedependent free vibration and dynamic analyses of piezoelectromagnetic sandwich nanoplates resting on viscoelastic foundation, Physica B, 521, 2017, 188197. ##[19] Bouafia, K., Kaci, A., Houari, M., Benzair, A., Tounsi, A., A nonlocal quasi3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams, Smart Structures and Systems, 19(2), 2017, 115126. ##[20] Bounouara, F., Benrahou, K.H., Belkorissat, I., Tounsi, A., A nonlocal zerothorder shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation, Steel and Composite Structures, 20(2), 2016, 227249. ##[21] Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A., Mahmoud, S.R., A nonlocal zerothorder shear deformation theory for nonlinear postbuckling of nanobeams, Structural Engineering and Mechanics, 62(6), 2017, 695702. ##[22] Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A., Beg, O.A., Mahmoud, S.R., Bending and buckling analyses of functionally graded material (FGM) sizedependent nanoscale beams including the thickness stretching effect, Steel and Composite Structures, 18(2), 2015, 425442. ##[23] Besseghier, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R., Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory, Smart Structures and Systems, 19(6), 2017, 601614. ##[24] Ahouel, M., Houari, M.S.A., Bedia, E.A.A., Tounsi, A., Sizedependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept, Steel and Composite Structures, 20(5), 2016, 963981. ##[25] Bedia, W.A., Benzair, A., Semmah, A., Tounsi, A., Mahmoud, S.R., On the thermal buckling characteristics of armchair singlewalled carbon nanotube embedded in an elastic medium based on nonlocal continuum elasticity, Brazilian Journal of Physics, 45, 2015, 225233. ##[26] Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E.A.A., Mahmoud, S.R., On vibration properties of functionally graded nanoplate using a new nonlocal refined four variable model, Steel and Composite Structures, 18(4), 2015, 10631081. ##[27] Zhou, Z., Wang, B., The scattering of harmonic elastic antiplane shear waves by a Griffith crack in a piezoelectric material plane by using the nonlocal theory, International Journal of Engineering Science, 40, 2002, 303317. ##[28] Zhou, Z., Wu, L., Du, S., Nonlocal theory solution for a Mode I crack in piezoelectric materials, European Journal of Mechanics A/Solids, 25, 2006, 793807. ##[29] Quek, S.T., Wang, Q., On dispersion relations in piezoelectric coupledplate structures, Smart Materials and Structures, 9, 2000, 859867. ##[30] Ke, L.L., Liu, C., Wang, Y.S., Free vibration of nonlocal piezoelectric nanoplates under various boundary conditions, Physica E, 66, 2015, 93106.##]
The Complementary Functions Method (CFM) Solution to the Elastic Analysis of Polar Orthotropic Rotating Discs
2
2
This study primarily deals with introducing an efficient numerical technique called the Complementary Functions Method (CFM) for the solutions of the initial value problem for the linear elastic analysis of anisotropic rotating uniform discs. To bring the performance of the method to light, first, closed form formulas are derived for such discs. The governing equation of the problem at stake is solved analytically with the help of the EulerCauchy technique under three types of boundary conditions namely freefree, fixedfree, and fixedguided constraints. Secondly, the CFM is applied to the same problem. It was found that both numerical and analytical results coincide with each other up to a desired numerical accuracy. Third, after verifying the results with the literature, a parametric study with CFM on the elastic behavior of discs made up of five different materials which physically exist is performed. And finally, by using hypothetically chosen anisotropy degrees from 0.3 through 5, the effects of the anisotropy on the elastic response of such structures are investigated analytically. Useful graphs are provided for readers.
1

216
230


Vebil
Yıldırım
Department of Mechanical Engineering, Çukurova University, Adana, 01330, Turkey
Department of Mechanical Engineering, Çukur
Iran
vebil@cu.edu.tr
Initial value problem (IVP)
Exact elasticity solution
Polar orthotropic
Rotating disc
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Verification and Validation of Common Derivative Terms Approximation in Meshfree Numerical Scheme
2
2
In order to improve the approximation of spatial derivatives without meshes, a set of meshfree numerical schemes for derivative terms is developed, which is compatible with the coordinates of Cartesian, cylindrical, and spherical. Based on the comparisons between numerical and theoretical solutions, errors and convergences are assessed by a posteriori method, which shows that the approximations for functions and derivatives are of the second accuracy order, and the scale of the support domain has some influences on numerical errors but not on accuracy orders. With a discrete scale h=0.01, the relative errors of the numerical simulation for the selected functions and their derivatives are within 0.65%.
1

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Zhibo
Ma
Institute of Applied Physics and Computational Mathematics, China
Institute of Applied Physics and Computational
Iran
mazhibo@iapcm.ac.cn


Yazhou
Zhao
Division of Water Resources and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
Division of Water Resources and Geoengineering,
Iran
asiabuaasa@163.com
Meshfree method
Smoothed particle hydrodynamics
Physics evoked cloud method
Approximation of spatial derivative
Verification and validation
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