2016
2
2
0
74
Linear dynamic response of nanobeams accounting for higher gradient effects
2
2
Linear dynamic response of simply supported nanobeams subjected to a variable axial force is assessed by Galerkin numerical approach. Constitutive behavior is described by three functional forms of elastic energy densities enclosing nonlocal and strain gradient effects and their combination. Linear stationary dynamics of nanobeams is modulated by an axial force which controls the global stiffness of nanostrucure and hence its angular frequencies. Influence of the considered elastic energy densities on dynamical response is investigated and thoroughly commented.
1

54
64


Dario
Abbondanza
Dipartimento di ingegneria meccanica e aeronautica, “La Sapienza”, Rome, Italy
Dipartimento di ingegneria meccanica e aeronautica
Iran


Daniele
Battista
Dipartimento di ingegneria meccanica e aeronautica, “La Sapienza”, Rome, Italy
Dipartimento di ingegneria meccanica e aeronautica
Iran


Francescogiuseppe
Morabito
Dipartimento di ingegneria meccanica e aeronautica, “La Sapienza”, Rome, Italy
Dipartimento di ingegneria meccanica e aeronautica
Iran


Chiara
Pallante
Dipartimento di ingegneria meccanica e aeronautica, “La Sapienza”, Rome, Italy
Dipartimento di ingegneria meccanica e aeronautica
Iran


Raffaele
Barretta
Dipartimento di strutture per l’ingegneria e l’architettura, Università degli Studi di Napoli “Federico II”, Naples, Italy
Dipartimento di strutture per l’ingegneria
Iran
rabarret@unina.it


Raimondo
Luciano
Dipartimento di ingegneria civile e meccanica, Università degli Studi di Cassino e del Lazio Meridionale, Cassino (FR), Italy
Dipartimento di ingegneria civile e meccanica,
Iran


Francesco
Marotti de Sciarra
Dipartimento di strutture per l’ingegneria e l’architettura, Università degli Studi di Napoli “Federico II”, Naples, Italy
Dipartimento di strutture per l’ingegneria
Iran


Giuseppe
Ruta
Dipartimento di ingegneria strutturale e geotecnica, “La Sapienza”, Rome, Italy
Dipartimento di ingegneria strutturale e
Iran
Nanobeams
Higher gradient effects
Dynamic response
[[1] J. Pei, F. Tian, T. Thundat, Glucose biosensor based on the microcantilever, Analytical Chemistry 76:292–297 (2004) ##[2] C. Ke, H.D. Espinosa, Numerical analysis of nanotubebased NEMS devices. Part I: Electrostatic charge distribution on multiwalled nanotubes, Journal of Applied Mechanics 72:721–725 (2005) ##[3] M. Li, H.X. Tang, M.L. Roukes, Ultrasensitive NEMSbased cantilevers for sensing, scanned probe and very highfrequency applications, Nature Nanotechnology 2:114–120 (2007) ##[4] Y.Q. Fu, H.J. Du, W.M. Huang, S. Zhang, M. Hu, TiNibased thin films in MEMS applications: a review, Journal of Sensors and Actuators A 112:395–408 (2004) ##[5] Z. Lee, C. Ophus, L.M. Fischer et al., Metallic NEMS components fabricated from nanocomposite Al–Mo films, Nanotechnology 17:3063–3070 (2006) ##[6] H.M. Sedighi, The influence of small scale on the Pullin behavior of nonlocal nanoBridges considering surface effect, Casimir and van der Waals attractions, International Journal of Applied Mechanics 6(3):1450030 (2014) ##[7] N.A. Ali, A.K. Mohammadi, Effect of thermoelastic damping in nonlinear beam model of MEMS resonators by differential quadrature method, Journal of Applied and Computational Mechanics 1(3):112121 (2015) ##[8] H.M. Sedighi, F. Daneshmand, M. Abadyan, Dynamic instability analysis of electrostatic functionally graded doublyclamped nanoactuators, Composite Structures 124:5564 (2015) ##[9] H.M. Sedighi, M. Keivani, M. Abadyan, Modified continuum model for stability analysis of asymmetric FGM doublesided NEMS: Corrections due to finite conductivity, surface energy and nonlocal effect, Composites Part B 83:117133 (2015) ##[10] H.M. Sedighi, F. Daneshmand, M. Abadyan, Modified model for instability analysis of symmetric FGM doublesided nanobridge: Corrections due to surface layer, finite conductivity and size effect, Composite Struct 132:545557 ##[11] H.M. Sedighi, Modeling of surface stress effects on the dynamic behavior of actuated nonclassical nanobridges, Transactions of the Canadian Society for Mechanical Engineering 39(2):137151 (2015) ##[12] A.C. Eringen, D.G.B. Edelen, On nonlocal elasticity, International Journal of Engineering Science 10:233–248 (1972) ##[13] A.C. Eringen, On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves Journal of Applied Physics 54:47034710 (1983) ##[14] A.C. Eringen, Nonlocal Continuum Field Theories, Springer, New York, 2002 ##[15] J. Peddieson, G.R. Buchanan, R.P. McNitt, Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science 41:305–312 (2003) ##[16] Q. Wang, Wave propagation in carbon nanotubes via nonlocal continuum mechanics, Journal of Applied Physics 98:124301 (2005) ##[17] J.N. Reddy, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science 45:288–307 (2007) ##[18] H.M. Ma, X.L. Gao, J.N. Reddy, A microstructuredependent Timoshenko beam model based on a modified couple stress theory, Journal of the Mechanics and Physics of Solids 56:3379–3391 (2008) ##[19] H.M. Sedighi, Sizedependent dynamic pullin instability of vibrating electrically actuated microbeams based on the strain gradient elasticity theory, Acta Astronautica 95:111123 (2014) ##[20] M. Karimi, M.H. Shokrani, A.R. Shahidi, 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):122–133 (2015) ##[21] R. Barretta, L. Feo, R. Luciano, F. Marotti de Sciarra, An Eringenlike model for Timoshenko nanobeams, Composite Structures 139(1):104110 (2016) ##[22] R. Barretta, M. Čanadija, F. Marotti de Sciarra, A higherorder Eringen model for BernoulliEuler nanobeams, Archive of Applied Mechanics 86:483–495 (2016) ##[23] R. Barretta, L. Feo, R. Luciano, F. Marotti de Sciarra, Application of an enhanced version of the Eringen differential model to nanotechnology, Composites B 96:274–280 (2016) ##[24] R. Barretta, L. Feo, R. Luciano, F. Marotti de Sciarra, R. Penna, Functionally graded Timoshenko nanobeams: A novel nonlocal gradient formulation, Composites B 100:208–219 (2016) ##[25] M.A. Eltaher, M.E. Khater, S.A. Emam, A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams, Applied Mathematical Modelling 40:4109–4128 (2016) ##[26] R. Barretta, L. Feo, R. Luciano, F. Marotti de Sciarra, Variational formulations for functionally graded nonlocal BernoulliEuler nanobeams, Composite Structures 129:80–89 (2015) ##[27] S. WoinowskyKrieger, The effect of an axial force on the vibration of hinged bars, Journal of Applied Mechanics 17:35–36 (1950) ##[28] R.E.D. Bishop, W.G. Price, The vibration characteristics of a beam with an axial force, Journal of Sound and Vibration 59:237–244 (1974) ##[29] A. Bokaian, Natural frequencies of beams under compressive axial loads, Journal of Sound and Vibration 126:49–65 (1988) ##[30] A. Bokaian, Natural frequencies of beams under tensile axial loads, Journal of Sound and Vibration 142:481–498 (1990) ##[31] N.G. Stephen, Beam compression under compressive axial loadupper and lower bound approximation, Journal of Sound and Vibration 131:345–350 (1989) ##[32] Z.P. Bazant, L. Cedolin, Stability of structures, Oxford University Press, New York, 1991 ##[33] S.P. Timoshenko, J.M. Gere, Theory of elastic stability, McGrawHill, New York, 1961 ##[34] M. Pignataro, N. Rizzi, A. Luongo, Stability, Bifurcation and Postcritical Behaviour of Elastic Structures, Elsevier, Amsterdam, 1991 ##[35] D. Abbondanza, D. Battista, F. Morabito, C. Pallante, R. Barretta, R. Luciano, F. Marotti de Sciarra, G. Ruta, Modulated linear dynamics of nanobeams accounting for higher gradient effects, submitted for publication.##]
Deflection of a hyperbolic shear deformable microbeam under a concentrated load
2
2
Deflection analysis of a simply supported microbeam subjected to a concentrated load at the middle is investigated on the basis of a shear deformable beam theory and nonclassical theory. Effects of shear deformation and small size are taken into consideration by hyperbolic shear deformable beam theory and modified strain gradient theory, respectively. The governing differential equations and corresponding boundary conditions are obtained by implementing minimum total potential energy principle. Naviertype solution is employed to achieve an analytical solution for deflections of simply supported homogeneous microbeams. The effects of shear deformation, material length scale parameter and slenderness ratio on the bending response of microbeams are investigated in detail.
1

65
73


Bekir
Akgöz
Akdeniz University Civil Eng. Dept.
Akdeniz University Civil Eng. Dept.
Iran
bekirakgoz@akdeniz.edu.tr


Ömer
Civalek
Civil Engineering Dept.
Civil Engineering Dept.
Iran
civalek@yahoo.com
Bending
hyperbolic shear deformation theory
modified strain gradient theory
size dependency
[References ##[1] Younis, M.I., AbdelRahman, E.M., Nayfeh, A.H., “A reducedorder model for electrically actuated microbeambased MEMS”, Journal of Microelectromechanical Systems, Vol. 12, pp. 672–680, 2003. ##[2] Li, P., Fang, Y., “A molecular dynamics simulation approach for the squeezefilm damping of MEMS devices in the free molecular regime”, Journal of Micromechanics and Microengineering, Vol. 20, 035005, 2010. ##[3] Wu, Z.Y., Yang, H., Li, X.X., Wang, Y.L., “Selfassembly and transfer of photoresist suspended over trenches for microbeam fabrication in MEMS”, Journal of Micromechanics and Microengineering, Vol. 20, 115014, 2010. ##[4] Zook, J.D., Burns, D.W., Guckel, H., Sniegowski, J.J., Engelstad, R.L., Feng, Z., “Characteristics of polysilicon resonant microbeams”, Sensors and Actuators A: Physics, Vol. 35, pp. 51–59, 1992. ##[5] Torii, A., Sasaki, M., Hane, K., Okuma, S., “Adhesive force distribution on microstructures investigated by an atomic force microscope”, Sensors and Actuators A: Physics, Vol. 44, pp. 153–158, 1994. ##[6] Hung, E.S., Senturia, S.D., “Extending the travel range of analogtuned electrostatic actuators”, Journal of Microelectromechanical Systems, Vol. 8, pp. 497–505, 1999. ##[7] Acquaviva, D., Arun, A., Smajda, R., Grogg, D., Magrez, A., Skotnicki, T., Ionescu, A.M., “MicroElectroMechanical Switch Based on Suspended Horizontal Dense Mat of CNTs by FIB Nanomanipulation”, Procedia Chemistry, Vol. 1, pp. 1411–1414, 2009. ##[8] Poole, W.J., Ashby, M.F., Fleck, N.A., “Microhardness of annealed and work hardened copper polycrystals”, Scripta Materialia, Vol. 34, pp. 559–564, 1996. ##[9] Stölken, J.S., Evans, A.G., “A microbend test method for measuring the plasticity length scale”, Acta Materialia, Vol. 46, pp. 5109–5115, 1998. ##[10] Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P., “Experiments and theory in strain gradient elasticity”, Journal of the Mechanics and Physisc of Solids, Vol. 51, pp. 1477–1508, 2003. ##[11] McFarland, A.W., Colton, J.S., “Role of material microstructure in plate stiffness with relevance to microcantilever sensors”, Journal of Micromechanics and Microengineering, Vol. 15, pp. 1060–1067, 2005. ##[12] Mindlin, R.D., Tiersten, H.F., “Effects of couplestresses in linear elasticity”, Archive for Rational Mechanics and Analysis, Vol. 11, pp. 415–448, 1962. ##[13] Koiter, W.T., “Couple stresses in the theory of elasticity: I and II”, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen (B), Vol. 67, pp. 17–44, 1964. ##[14] Toupin, R.A., “Theory of elasticity with couple stresses”, Archive for Rational Mechanics and Analysis, Vol. 17, pp. 85–112, 1964. ##[15] Eringen, A.C., “Theory of micropolar plates”. Zeitschrift für angewandte Mathematik und Physik, Vol. 18, pp. 12–30, 1967. ##[16] Eringen, A.C., “Nonlocal polar elastic continua”, International Journal of Engineering Science, Vol. 10, pp. 1–16, 1972. ##[17] Eringen, A.C., “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves”, Journal of Applied Physics, Vol. 54, pp. 4703–4710, 1983. ##[18] Fleck, N.A., Hutchinson, J.W., “A phenomenological theory for strain gradient effects in plasticity”, Journal of the Mechanics and Physics of Solids, Vol. 41, pp. 1825–1857, 1993. ##[19] Vardoulakis, I., Sulem, J., “Bifurcation Analysis in Geomechanics”. Blackie/Chapman and Hall, London, 1995. ##[20] Aifantis, E.C., “Gradient deformation models at nano, micro, and macro scales”, Journal of Engineering Materials and Technology, Vol. 121, pp. 189–202, 1999. ##[21] Fleck, N.A., Hutchinson, J.W., “A reformulation of strain gradient plasticity”, Journal of the Mechanics and Physics of Solids, Vol. 49, pp. 2245–2271, 2001. ##[22] Akgöz, B., Civalek, Ö., “Longitudinal vibration analysis for microbars based on strain gradient elasticity theory”, Journal of Vibration and Control, Vol. 20, pp. 606–616, 2001. ##[23] Akgöz, B., Civalek, Ö., “Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM)”, Composites Part B, Vol. 55, pp. 263–268, 2013. ##[24] Kahrobaiyan, M.H., Asghari, M., Ahmadian, M.T., “Longitudinal behavior of strain gradient bars”, International Journal of Engineering Science, Vol. 66–67, pp. 44–59, 2013. ##[25] Kahrobaiyan, M.H., Tajalli, S.A., Movahhedy, M.R., Akbari, J., Ahmadian, M.T., “Torsion of strain gradient bars”, International Journal of Engineering Science, Vol. 49, pp. 856–866, 2011. ##[26] Kong, S., Zhou, S., Nie, Z., Wang, K., “Static and dynamic analysis of micro beams based on strain gradient elasticity theory”, International Journal of Engineering Science, Vol. 47, pp. 487–498, 2009. ##[27] Wang, B., Zhao, J., Zhou, S., “A micro scale Timoshenko beam model based on strain gradient elasticity theory”, European Journal of Mechanics A/Solids, Vol. 29, pp. 591–599, 2010. ##[28] Akgöz, B., Civalek, Ö., “Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded microscaled beams”, International Journal of Engineering Science, Vol. 49, pp. 1268–1280, 2011. ##[29] Akgöz, B., Civalek, Ö., “Analysis of microsized beams for various boundary conditions based on the strain gradient elasticity theory”, Archive of Applied Mechanics, Vol. 82, pp. 423–443, 2012. ##[30] Akgöz, B., Civalek, Ö., “Buckling analysis of linearly tapered microcolumns based on strain gradient elasticity”, Structural Engineering and Mechanics, Vol. 48, pp. 195–205, 2013. ##[31] Asghari, M., Kahrobaiyan, M.H., Nikfar, M., Ahmadian, M.T., “A sizedependent nonlinear Timoshenko microbeam model based on the strain gradient theory”, Acta Mechanica, Vol. 223, 1233–1249, 2012. ##[32] Ghayesh, M.H., Amabili, M., Farokhi, H., “Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory”, International Journal of Engineering Science, Vol. 63, pp. 52–60, 2013. ##[33] Kahrobaiyan, M.H., Asghari, M., Ahmadian, M.T., “Strain gradient beam element”, Finite Element Analysis in Design, Vol. 68, pp. 63–75, 2013. ##[34] Zhang, B., He, Y., Liu, D., Gan, Z., Shen, L., “Nonclassical Timoshenko beam element based on the strain gradient elasticity theory”, Finite Element Analysis in Design, Vol. 79, pp. 22–39, 2014. ##[35] Mercan, K., Civalek, Ö., “DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix”, Composite Structures, Vol. 143, pp. 300–309, 2016. ##[36] Demir, Ç., Civalek, Ö., “Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models”, Applied Mathematical Modelling, Vol. 37, pp. 9355–9367, 2013. ##[37] Levinson, M., “A new rectangular beam theory”, Journal of Sound and Vibration, Vol. 74, pp. 81–87, 1981. ##[38] Reddy, J.N., “A simple higherorder theory for laminated composite plates”, Journal of Applied Mechanics, Vol. 51, pp. 745–752, 1984. ##[39] Touratier, M., “An efficient standard plate theory”, International Journal of Engineering Science, Vol. 29, pp. 901–916, 1991. ##[40] Soldatos, K.P., “A transverse shear deformation theory for homogeneous monoclinic plates”, Acta Mechanica, Vol. 94, pp. 195–220, 1992. ##[41] Karama, M., Afaq, K.S., Mistou, S., “Mechanical behaviour of laminated composite beam by the new multilayered laminated composite structures model with transverse shear stress continuity”, International Journal of Solids and Structures, Vol. 40, pp. 1525–1546, 2003. ##[42] Aydogdu, M., “A new shear deformation theory for laminated composite plates”, Composite Structures, Vol. 89, pp. 94–101, 2009. ##[43] Nateghi, A., Salamattalab, M., Rezapour, J., Daneshian, B., “Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory”, Applied Mathematical Modelling, Vol. 36, pp. 4971–4987, 2012. ##[44] Salamattalab, M., Nateghi, A., Torabi, J., “Static and dynamic analysis of thirdorder shear deformation FG micro beam based on modified couple stress theory”, International Journal of Mechanical Sciences, Vol. 57, pp. 63–73, 2012. ##[45] Akgöz, B., Civalek, Ö., “A sizedependent shear deformation beam model based on the strain gradient elasticity theory”, International Journal of Engineering Science, Vol. 70, pp. 1–14, 2013. ##[46] Lei, J., He, Y., Zhang, B., Gan, Z., Zeng, P., “Bending and vibration of functionally graded sinusoidal microbeams based on the strain gradient elasticity theory”, International Journal of Engineering Science, Vol. 72, pp. 36–52, 2013. ##[47] Şimşek, M., Reddy, J.N., “Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory”, International Journal of Engineering Science, Vol. 64, pp. 37–53, 2013. ##[48] Şimşek, M., Reddy, J.N., “A unified higher order beam theory for buckling of a functionally graded microbeam embedded in elastic medium using modified couple stress theory”, Composite Structures, 101, pp. 47–58, 2013. ##[49] Akgöz, B., Civalek, Ö., “A new trigonometric beam model for buckling of strain gradient microbeams”, International Journal of Mechanical Sciences, Vol. 57, pp. 88–94, 2014. ##[50] Akgöz, B., Civalek, Ö., “Shear deformation beam models for functionally graded microbeams with new shear correction factors”, Composite Structures, Vol. 112, pp. 214–225, 2014. ##[51] Akgöz, B., Civalek, Ö., “Thermomechanical buckling behavior of functionally graded microbeams embedded in elastic medium”. International Journal of Engineering Science, Vol. 85, pp. 90–104, 2014. ##[52] Darijani, H., Mohammadabadi, H., “A new deformation beam theory for static and dynamic analysis of microbeams”, International Journal of Mechanical Sciences, Vol. 89, pp. 31–39, 2014. ##[53] Akgöz, B., Civalek, Ö., “A microstructuredependent sinusoidal plate model based on the strain gradient elasticity theory”, Acta Mechanica, Vol. 226, pp. 2277–2294, 2015. ##[54] Akgöz, B., Civalek, Ö., “A novel microstructuredependent shear deformable beam model”, International Journal of Mechanical Sciences, Vol. 99, pp. 10–20, 2015. ##[55] Akgöz, B., Civalek, Ö., “Bending analysis of FG microbeams resting on Winkler elastic foundation via strain gradient elasticity”, Composite Structures, Vol. 134, pp. 294–301, 2015. ##[56] Zhang, B., He, Y., Liu, D., Gan, Z., Shen, L., “Sizedependent functionally graded beam model based on an improved thirdorder shear deformation theory”, European Journal of MechanicsA/Solids, Vol. 47, pp. 211–230, 2014.##]
Time integration of rectangular membrane free vibration using splinebased differential quadrature
2
2
In this paper, numerical splinebased differential quadrature is presented for solving the boundary and initial value problems, and its application is used to solve the fixed rectangular membrane vibration equation. For the time integration of the problem, the Runge–Kutta and splinebased differential quadrature methods have been applied. The Runge–Kutta method was unstable for solving the problem, with large errors in its results, but the splinebased differential quadrature method obtained results that agree with the exact solution. The relative errors were calculated and investigated for different values of time and spatial nodes of discretisation. It seems that the splinebased differential quadrature method is proper for the full simulation of membrane vibration in both spatial and temporal solutions. For the time solving of the membrane vibration, conventional methods, such as the Runge–Kutta method, are not useful even if the time steps are considered too small.
1

74
79


Sara
Javidpoor
Bachelor’s degree student of department of marine engineering, Khorramshahr university of marine science and technology
Bachelor’s degree student of department
Iran
sara.javidpour73@gmail.com


Nassim
Ale Ali
Department of Marine Engineering, Khorramshahr University of Marine Science &amp; Technology
Department of Marine Engineering, Khorramshahr
Iran
aleali@kmsu.ac.ir


Amer
Kabi
3Assistant professor of department of marine engineering, Khorramshahr university of marine science and technology
3Assistant professor of department of marine
Iran
kaabi_amer@kmsu.ac.ir
Runge–Kutta method
splinebased differential quadrature method
membrane vibration
Time integration
[[1] R.E. Bellman, J. Casti, “Differential quadrature and long term integration”, Journal of Mathematical Analysis and Applications 34 (1971) 235–238. ##[2] M. Mehri, H. Asadi, Q. Wang, “Buckling and vibration analysis of a pressurized CNT reinforced functionally graded truncated conical shell under an axial compression using HDQ method”, Comput. Methods Appl. Mech. Engrg. 303 (2016) 75–100. ##[3] Mohammad Zamani Nejad, Amin Hadi, “Nonlocal analysis of free vibration of bidirectional functionally graded Euler–Bernoulli nanobeams”, International Journal of Engineering Science 105 (2016) 1–11. ##[4] Hadi Arvin, YouQi Tang, Afshin Ahmadi Nadooshan, “Dynamic stability in principal parametric resonance of rotating beams: Method of multiple scales versus differential quadrature method”, International Journal of NonLinear Mechanics 85 (2016) 118–125. ##[5] Michele Bacciocchi, Moshe Eisenberger, Nicholas Fantuzzi, Francesco Tornabene, Erasmo Viola, “Vibration analysis of variable thickness plates and shells by the Generalized Differential Quadrature method”, Composite Structures xxx (2015) xxx–xxx. ##[6] Francesco Tornabene, Nicholas Fantuzzi, Michele Bacciocchi, Erasmo Viola, “Effect of agglomeration on the natural frequencies of functionally graded carbon nanotubereinforced laminated composite doubly curved shells”, Composites Part B 89 (2016) 187218. ##[7] Francesco Tornabene, Nicholas Fantuzzi, Michele Bacciocchi, “The local GDQ method for the natural frequencies of doublycurved shells with variable thickness: A general formulation”, Composites Part B 92 (2016) 265289. ##[8] Laxmi Behera, S. Chakraverty, “Application of Differential Quadrature method in free vibration analysis of nanobeams based on various nonlocal theories”, Computers and Mathematics with Applications 69 (2015) 1444–1462. ##[9] R. Ansari, M. Faghih Shojaei, A. Shahabodini, M. BazdidVahdati, “Threedimensional bending and vibration analysis of functionally graded nanoplates by a novel differential quadraturebased approach”, Composite Structures 131 (2015) 753–764. ##[10] R.C. Mittal, Sumita Dahiya, “Numerical simulation on hyperbolic diffusion equations using modified cubic Bspline differential quadrature methods”, Computers and Mathematics with Applications 70 (2015) 737–749. ##[11] Zhi Zong and Yingyan Zhang, Advanced Differential Quadrature Methods, Chapman & Hall/CRC. ##[12] Nassim Ale Ali, Ardeshir Karami Mohamadi, “Effect of thermoelastic damping in nonlinear beam model of MEMS resonators by differential quadrature method”, Journal of Applied and Computational Mechanics, Vol. 1, No. 3, (2015), 112121. ##[13] M. Tanaka, W. Chen, “Coupling dual reciprocity BEM and di€erential quadrature method for timedependent diffusion problems”, Applied Mathematical Modelling, vol. 25 (2001) pp. 257268. ##[14] Shahriar Dastjerdi, Mehrdad Jabbarzadeh, Sharifeh Aliabadi, “Nonlinear static analysis of single layer annular/circular graphene sheets embedded in Winkler–Pasternak elastic matrix based on nonlocal theory of Eringen”, Ain Shams Engineering Journal (2016) 7, pp. 873–884.##]
Bending Analysis of Thick Isotropic Plates by Using 5th Order Shear Deformation Theory
2
2
A 5th order shear deformation theory considering transverse shear deformation effect as well as transverse normal strain deformation effect is presented for static flexure analysis of simply supported isotropic plate. The assumed displacement field accounts for nonlinear variation of inplane displacements as well as transverse displacement through the plate thickness. The condition of zero transverse shear stresses on the upper and lower surface of plate is satisfied. Hence the present formulation does not require the shear correction factor generally associated with the first order shear deformable theory. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Closedform analytical solutions for simply supported square isotropic thick plates subjected to single sinusoidal distributed loads are obtained. Numerical results for static flexure analysis include the effects of side to thickness ratio and plate aspect ratio for simply supported isotropic plates. Numerical results are obtained using MATLAB programming. The results of present theory are in close agreement with those of higher order shear deformation theories and exact 3D elasticity solutions.
1

80
95


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


Param D.
Gajbhiye
MTECH STUDENT
MTECH STUDENT
Iran
gparam786@gmail.com
Thick isotropic plate
5th order shear deformation theory
static flexure
transverse shear stress
transverse normal stress
Navier solution
[[1] Ghugal, Y. M., and Shimpi, R. P., “A Review of Refined Shear Deformation Theories of Isotropic and Anisotropic Laminated Plates”, Journal of Reinforced Plastics and Composites, Vol. 21, No. 9, pp. 775813, 2002. ##[2] Sayyad, A. S., and 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, Vol. 129, pp. 177201, 2015. ##[3] Timoshenko, S. P., and Krieger, W. S., Theory of Plates and Shells, McGrawHill Publication, Second edition, 1959. ##[4] Jemielita, G., “On the Winding Paths of the Theory of Plates”, Journal of Theoretical and Applied Mechanics (Mechanika Teoretyczna I Stosowana), Vol. 2, No. 31, pp. 317327, 1993. ##[5] Levy, M., “Memoire sur la Theorie des Plaques Elastiques Planes”, Journal des Mathematiques Pures et Appliqees, Vol. 30, pp. 219306, 1877. ##[6] Reissner, E., “The Effect of Transverse Shear Deformation on The Bending of Elastic Plates”, ASME Journal of Applied Mechanics, Vol. 12, pp. A69A77, 1945. ##[7] Hencky, H., “Uber die Berucksichtigung der Schubverzerrung in Ebenen Platten”, Ingenieur Archiv, Vol. 16, pp. 7276, 1947. ##[8] Mindlin, R. D., “Influence of Rotary Inertia and Shear on Flexure Motions of Isotropic, Elastic Plates”, ASME Journal of Applied Mechanics, Vol. 18, pp. 3138, 1951. ##[9] Kromm, A., “Verallgemeinerete Theorie der Plattenstatik”, Ingenieur Archiv, Vol. 21, pp. 266286, 1953. ##[10] Lo, K. H., Christensen, R. M. and Wu E. M., “A Higher Order Theory of Plate Deformation, Part 1: Homogeneous Plates”, ASME Journal of Applied Mechanics, Vol. 44, pp. 663668, 1977. ##[11] Lo, K. H., Christensen, R. M. and Wu, E. M., “A Higher Order Theory of Plate Deformation, Part 2: Laminated Plates”, ASME Journal of Applied Mechanics, Vol. 44, pp. 669676, 1977. ##[12] Kant, T., “Numerical Analysis of Thick Plate”, Computer Methods in Applied Mechanics and Engineering, Vol. 31, pp. 118, 1982. ##[13] Kant, T., and Swaminathan K., “Estimation of transverse/interlaminar stresses in laminated composites A selective review and survey of current developments”, Composite Structures, Vol. 49, No. 1, pp. 6575, 2000. ##[14] Jemielita, G., “On Kinematical Assumptions of Refined Theories of Plates: A Survey”, ASME Journal of Applied Mechanics, Vo. 57, pp. 10881091, 1990. ##[15] Vlasov, B. F., “On the Equation of Bending of Plates” (in Russian), Doklady AN Azerbaidzhanskoi SSR, Vol. 13, No. 9, pp. 955959, 1957. ##[16] Vlasov, B. F., “On the Equation of Theory of Bending of Plates” (in Russian), Izv. AN SSR, OMN, No. 12, pp. 5760, 1957. ##[17] Reddy, J. N., “A Simple Higher Order Theory for Laminated Composite Plates”, ASME Journal of Applied Mechanics, Vol. 51, No. 4, pp. 745752, 1984. ##[18] Reddy, J. N., Mechanics of Laminated and Composite Plates and Shell Theory and Analysis, 2nd edition, CRC Press, Boca Raton, FL, 2004. ##[19] Todhunter, I. and Pearson, K. (1893). A History of the Theory of Elasticity, VolII, PartI, pp. 273, and VolII, PartII, pp. 206207, 273276. Dover Publications, Inc. New York. ##[20] Touratier, M., “An Efficient Standard Plate Theory”, International Journal of Engineering Science, Vol. 29, No. 8, pp. 901916, 1991. ##[21] Ghugal, Y. M., Sayyad A. S., “A Static Flexure of Thick Isotropic Plate Using Trigonometric Shear Deformation Theory”, Journal of Solid Mechanics, Vol. 2, No. 1, pp. 7990, 2010. ##[22] Ghugal, Y. M. and Sayyad, A. S., “Static Flexure of Thick Orthotropic Plates Using Trigonometric Shear Deformation Theory”, Journal of Structural Engineering, Vol. 39, No. 5, pp. 512521, 2013. ##[23] Ghugal, Y. M. and Sayyad A. S., “Stress Analysis of Thick Laminated Plates Using Trigonometric Shear Deformation Theory”, International Journal of Applied Mechanics, Vol. 5, No. 1, pp. 123, 2013. ##[24] Sayyad, A. S., Ghugal, Y. M., “Effect of Stress Concentration on Laminated Plates”, Cambridge Journal of Mechanics, Vol. 29, pp. 241252, 2013. ##[25] Sayyad, A. S. and Ghugal, Y. M., “A New Shear and Normal Deformation Theory for Isotropic, Transversely Isotropic, Laminated Composite and Sandwich Plates”,International Journal of Mechanics and Materials in Design., Vol. 10, No. 3, pp. 247267, 2014. ##[26] Sayyad, A. S. and Ghugal, Y. M., “Flexure of CrossPly Laminated Plates Using Equivalent Single Layer Trigonometric Shear Deformation Theory”, Structural Engineering and Mechanics: An International Journal, Vol. 51, No. 5, pp. 867891, 2014. ##[27] Sayyad, A. S., Shinde, B. M. and Ghugal, Y. M., “Thermoelastic Bending Analysis of Laminated Composite Plates According to Various Shear Deformation Theories”, Open Engineering (formerly Central European Journal of Engineering),Vol. 5, No.1, pp. 1830, 2015 ##[28] Sayyad, A. S. and Ghugal, Y. M., “Cylindrical Bending of Multilayered Composite Laminates and Sandwiches”, Advances in Aircraft and Spacecraft Science: An International Journal. Vol. 3, No. 2. pp. 113148, 2016. ##[29] Carrera, E., “Temperature Profile Influence on Layered Plates Response Considering Classical and Advaced Theories”, AIAA Journal, Vol. 40, No. 9, pp. 18851896, 2002. ##[30] Rohwer, K., Rolfes, R., and Sparr, H., “Higherorder Theories for Thermal Stresses in Layered Plates”, International Journal of Solids and Structures, Vol. 38, pp. 36733687, 2001. ##[31] Sayyad A. S., Ghugal Y. M., “Bending and free vibration analysis of thick isotropic plates by using exponential shear deformation theory”, Applied and Computational Mechanics, Vol. 6, 2012, pp. 6582. ##[32] Ghugal, Y. M. and Pawar, M. D., “Flexural Analysis of Thick Plates by Hyperbolic Shear Deformation Theory”, Journal of Experimental & Applied Mechanics, Vol. 2, No. 1, pp. 121, 2011. ##[33] Pagano N. J., “Exact Solutions for Bidirectional Composite and Sandwich Plates”, Journal of Composite Material, Vol. 4, pp. 2034, 1970.##]
Concerning the Effect of a Viscoelastic Foundation on the Dynamic Stability of a Pipeline System Conveying an Incompressible Fluid
2
2
In this paper, we present an analytical method for solving a wellposed boundary value problem of mathematical physics governing the vibration characteristics of an internal flow propelled fluidstructure interaction where the pipeline segment is idealized as an elastic hollow beam conveying an incompressible fluid on a viscoelastic foundation. The effect of Coriolis and damping forces on the overall dynamic response of the system is investigated. In actuality, for a pipe segment supported at both ends and subject to a free motion, these two forces generate conjugate complex frequencies for all flow velocities. On employing integral transforms and complex variable functions, a closed form analytical expression is derived for the overall dynamic response. It is demonstrated that a concise mathematical expression for the natural frequency associated with any mode of vibration can be deduced from the algebraic product of the complex frequency pairs. By a way of comparative analysis for damping decrement physics reminiscent with laminated structures, mathematical expressions are derived to illustrate viscoelastic damping effects on dynamic stability for any flow velocity. The integrity of the analytical solution is verified and validated by confirming theresults in literature in appropriate asymptotic limits.
1

96
117


Vincent
Olunloyo
Department of Systems Engineering, Faculty of Engineering, University of Lagos
Department of Systems Engineering, Faculty
Iran
vosoolunloyo@hotmail.com


Charles
Osheku
Centre for Space Transport and Propulsion, National Space Research and Development Agency
Centre for Space Transport and Propulsion,
Iran
charlesosheku2002@yahoo.com


Patrick
Olayiwola
Department of Mechanical & Biomedical Engineering, College of Engineering, Bells University of Technology
Department of Mechanical & Biomedical
Iran
olayiwola_patrickshola@yahoo.com
Analytical method
viscoelastic foundation
Coriolis and damping forces
conjugate complex frequency pairs and damping decrement physics
[[1] Paidoussis, M.P. (2013) Fluidstructure interactions: slender structures and axial flows, Vol. 1, Academic Press, Revised Edition. ##[2] Mostafa N.H. (2014) “Effect of a Viscoelastic foundation on the Dynamic Stability of a Fluid Conveying Pipe”. International Journal of Applied Science and Engineering 12, 1:5974. ##[3] Paidoussis, M.P. &Issid, N.T. (1974) Dynamic stability of pipes conveying fluid. Journal of Sound and Vibration 33, 267294. ##[4] Murai, M. and Yamamoto, M. (2010) An Experimental Analysis of the Internal Flow Effects on Marine Risers. Proceedings of MARTEC 2010, P.159165. ##[5] Marakala N, Appukutttan K.K, and Kadoli R. (2014) Experimental and Theoretical Investigation of Combined Effects of Fluid and Thermal Induced Vibration on Vertical Thin Slender Tube. IOSR JMCE, ISSN: 22781684, pp: 6368. ##[6] Ziegler, H. (1968) Principles of Structural Stability. Waltham, MA: Blaisdell. ##[7] Lottati, I. and Kornecki, A. (1986) The effect of an elastic foundation and of dissipative forces on the stability of fluid conveying pipes. Journal of Sound and Vibration, 109(2): 327338. ##[8] Stein, R.A., Tobriner, M.W. (1970) Vibration of pipes containing flowing fluids. Trans ASME J Appl. Mechanics; 906916. ##[9] DermendjianIvanova, D.S. (1992) Critical flow velocities of a simply supported pipeline on an elastic foundation. J Sound Vibration; 157: 370374. ##[10] Chary, S.R., Rao, C.K., Iyengar, R.N. (1993) Vibration of Fluid Conveying Pipe on Winkler Foundation, Proceedings of the 8th National Convention of Aerospace Engineers on Aeroelasticity, Hydroelasticity and other FluidStructure Interaction Problems, IIT Kharagpur, India; pp. 266287. ##[11] Doaré, O., de Langre, O. (2002) Local and global instability of fluid conveying pipes on elastic foundation. J Fluids &Structures; 16: 114. ##[12] Chellapilla, K.R. and Simha, H.S. (2008) Vibrations of FluidConveying Pipes Resting on TwoParameter Foundation. The Open Acoustics Journal, 1, 2433. ##[13] Mahrenholtz, O. H. (2010) Beam on viscoelastic foundation: an extension of Winkler’s model. Archive of Applied Mechanics, 80(1): 93102. ##[14] Saxena, A. and Patel, R.K. (2013) Vibration Control of Cantilever Beam Using Eddy Current Damper. International Journal of Engineering and Innovative Technology (IJESIT) Volume 2, Issue 3. ##[15] Jaeung, B., Moon, K.K. and Daniel, J.I. (2005) Vibration Suppression of a Cantilever Beam Using Eddy Current Damper. Journal of Sound and Vibration 284, 805824. ##[16] Tonoli, A. (2007) Dynamic characteristics of Eddy current dampers and couplers. Journal of Sound and Vibration 301: 576591. ##[17] Olayiwola, P.S. (2016) Mechanics of a FluidConveying Pipeline System Resting on a Viscoelastic Foundation. Journal of Multidisciplinary Engineering Science Studies (JMESS), ISSN: 2458925X Vol. 2. Issue 3. ##[18] Szmidt T and Przybylowicz P. (2013) Critical Flow Velocity with Electromagnetic Actuators. Journal of Theoretical and Applied Mechanics 51, 2, pp. 487496. ##[19] Kuye, S.I. (2013) Analysis of the Dynamics of Offshore FluidConveying Viscoelastic Pipes Resting on a Deformable Sea Bed. Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 4(5): 742751. ##[20] Jeffrey A. (2002) Advanced Engineering Mathematics, Harcourt Academic Press. U.S.A, p.596. ##[21] Wrede, R. C. and Spiegel, M. (2002) Thoery and Problems of Advanced Calculus 2nd Ed. Schaum’s Outline Serises, McGrawHill, p. 364. ##[22] Nash, W. A. (1977) Thoery and Problems of Strength of Materials, 2nd Ed. Schaum’s Outline Series, McGrawHill, p. 83, 159161. ##[23] Cole E.B. (1960) Theory of Vibrations. The University of Liverpool. ##[24] Darkov, A. (1983) Structural Mechanics. Mir Publishers, Moscow.##]
Thermoelastic Analysis of Functionally Graded Hollow Cylinder Subjected to Uniform Temperature Field
2
2
This paper deals with the determination of displacement function and thermal stresses of a finite length isotropic functionally graded hollow cylinder subjected to uniform temperature field. The solution of the governing thermoelastic equation is obtained, as suggested by Spencer et al. for anisotropic laminates. Numerical calculations are also carried out for FGM (Functionally graded material) system consisting of ceramic Alumina (Al2O3), along with Nickel (Ni) as the metallic component varying with distance in one direction and illustrated graphically.
1

118
127


Dilip
Kamdi
Head Department of Mathematics, R.M. G. College, Saoli, Chandrapur, India
Head Department of Mathematics, R.M. G. College,
Iran
navvanna@rediffmail.com


Navneet
Lamba
Head Deptt. of Mathematics
Shri Lemdeo Patil Mahavidyalaya, Nagpur, INDIA
Head Deptt. of Mathematics
Shri Lemdeo Patil
Iran
navneetkumarlamba@gmail.com
Uniformly heated
Hollow cylinder
Thermoelastic stresses
Functionally graded material
Inverse problem
[[1] Noda, N., “Thermal stresses in functionally graded materials”, Journal of Thermal Stresses, Vol. 22, pp. 477512, 1999. ##[2] Horgan, C. O. and Chan, A. M., “The pressurized Hollow cylinder or Disk problem for functionally graded isotropic linearly Elastic material”, Journal of Elasticity, Vol. 55, pp. 4359, 1999. ##[3] Lutz, M. P. and Zimmerman, R. W., “Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder”, Journal of Thermal Stresses, Vol. 22, pp. 177188, 1999. ##[4] Chen, W., Ye, G. and Cai, J., “Thermoelastic Stresses in a uniformly heated functionally graded isotropic hollow cylinder”, Journal of Zhejiang University Science, Vol. 3, No. 1, pp. 15, 2002. ##[5] Eraslan, A.N., and Akis, T., “Elastoplastic Response of a Long Functionally Graded Tube Subjected to Internal Pressure”, Turkish J. Eng. Env. Sci., Vol. 29, pp. 361368, 2005. ##[6] Lekhnitskii, S. G., “Theory of Elasticity of an Anisotropic Body”, Mir, Moscow, 1981. ##[7] Spencer, A. J. M., Watson, P. and Rogers, T. G., “Thermoelastic Distortions in laminated anisotropic tubes and channel section”, Journal of Thermal Stresses, Vol. 15, pp. 129141, 1992. ##[8] Noda, N., Hetnarski, R.B., and Tanigawa, Y., “Thermal stresses”, First Edition, Lastran, Rochester, 2000. ##[9] Shariyat, M., “Dynamic thermal buckling of suddenly heated temperaturedependent FGM cylindrical shells, under combined axial compression and external pressure”, International Journal of Solids and Structures, Volume 45 , pp. 2598–2612 , 2008. ##[10] Na, S., Kim, K.W., Lee, B. H. and Marzocca, P., “Dynamic Response Analysis Of Rotating Functionally Graded ThinWalled Blades Exposed To Steady Temperature And External Excitation”, Journal of Thermal Stresses, vol. 32, pp. 209–225, 2009. ##[11] Ootao, Y., “Transient Thermoelastic and Piezothermoelastic Problems of Functionally Graded Materials”, Journal of Thermal Stresses, vol. 32, pp. 656–697, 2009. ##[12] Houari, M. S. A., Benyoucef, S., Mechab, I., Tounsi, A. and Bedia, El A. A., “TwoVariable Refined Plate Theory For Thermoelastic Bending Analysis Of Functionally Graded Sandwich Plates”, Journal of Thermal Stresses, vol. 34, pp. 315–334, 2011. ##[13] Marzocca, P., Fazelzadeh, S. A. and Hosseini, M., “A Review of Nonlinear AeroThermoElasticity of Functionally Graded Panels”, Journal of Thermal Stresses, vol. 34, pp. 536–568, 2011. ##[14] Chang, W.J., Lee, H.L. and Yang, Y. C., “Estimation of Heat Flux and Thermal Stresses in Functionally Graded Hollow Circular Cylinders”, Journal of Thermal Stresses, vol. 34, pp. 740–755, 2011. ##[15] Fazelzadeh, S. A., Hosseini, M. and Madani, H., “Thermal Divergence of Supersonic Functionally Graded Plates, Journal of Thermal Stresses”, vol. 34, pp. 759–777, 2011. ##[16] Sheng, G. G. and Wang, X., “NonLinear Response of Functionally Graded Cylindrical Shells under Mechanical and Thermal Loads”, Journal of Thermal Stresses, vol. 34, pp.1105–1118, 2011. ##[17] Sumi, N., Tanigawa, Y., Eslami, M. R., Hetnarski, R., Noda, N. and Ignaczak, J., Theory of Elasticity and Thermal Stresses, Springer, 2013. ##[18] Bayat, M., Rahimi, M., Saleem, M., Mohazzab, A.H., Wudtke, I., and Talebi, H., “Onedimensional analysis for magnetothermomechanical response in a functionally graded annular variablethickness rotating disk”, Applied Mathematical Modeling, vol. 38 , pp. 4625–4639 , 2014. ##[19] Ashida, F., Morimoto, T., and Ohtsuka, T., “Dynamic Behavior of Thermal Stress in a Functionally Graded Material Thin Film Subjected to Thermal Shock”, Journal of Thermal Stresses, volume 37, pp. 1037–1051, 2014.##]