Browse > Article
http://dx.doi.org/10.12989/scs.2020.34.4.615

Free vibration analysis of functionally graded cylindrical nanoshells resting on Pasternak foundation based on two-dimensional analysis  

Arefi, Mohammad (Department of Solid Mechanics, University of Kashan)
Zur, Krzysztof Kamil (Faculty of Mechanical Engineering, Bialystok University of Technology)
Publication Information
Steel and Composite Structures / v.34, no.4, 2020 , pp. 615-623 More about this Journal
Abstract
In this paper, free vibration analysis of a functionally graded cylindrical nanoshell resting on Pasternak foundation is presented based on the nonlocal elasticity theory. A two-dimensional formulation along the axial and radial directions is presented based on the first-order shear deformation shell theory. Hamilton's principle is employed for derivation of the governing equations of motion. The solution to formulated boundary value problem is obtained based on a harmonic solution and trigonometric functions for various boundary conditions. The numerical results show influence of significant parameters such as small scale parameter, stiffness of Pasternak foundation, mode number, various boundary conditions, and selected dimensionless geometric parameters on natural frequencies of nanoshell.
Keywords
size-dependent natural vibration; functionally graded materials; cylindrical nanoshell; nonlocal parameters; various boundary conditions;
Citations & Related Records
Times Cited By KSCI : 5  (Citation Analysis)
연도 인용수 순위
1 Santos, H., Soares, C.M.M., Soares, C.A.M. and Reddy, J.N. (2009), "A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials", Compos. Struct., 91(4), 427-432. https://doi.org/10.1016/j.compstruct.2008.03.004.   DOI
2 Shakeri, M., Akhlaghi, M. and Hoseini, S.M. (2006), "Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder", Compos. Struct., 76, 174-181. https://doi.org/10.1016/j.compstruct.2006.06.022.   DOI
3 Shao, Z.S. and Wang, T.J., (2006), "Three-dimensional solutions for the stress fields in functionally graded cylindrical panel with finite length and subjected to thermal/mechanical loads", Int. J. Solids. Struct., 43, 3856-3874. https://doi.org/10.1016/j.ijsolstr.2005.04.043   DOI
4 Sheng, G.G. and Wang, X. (2010), "Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells", Appl. Math. Model., 34, 2630-2643. https://doi.org/10.1016/j.apm.2009.11.024.   DOI
5 Shokrollahi, H. (2018), "Deformation and stress analysis of a sandwich cylindrical shell using HDQ Method", Steel. Compos. Struct., 27(1), 35-48. https://doi.org/10.12989/scs.2018.27.1.035.   DOI
6 Sun, S. Cao, D. and Han, Q. (2013), "Vibration studies of rotating cylindrical shells with arbitrary edges using characteristic orthogonal polynomials in the Rayleigh-Ritz method", Int. J. Mech. Sci., 68, 180-189. https://doi.org/10.1016/j.ijmecsci.2013.01.013   DOI
7 Tornabene, F. (2009), "Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Method. Appl. M., 198, 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011.   DOI
8 Tutuncu, N. and Ozturk, M. (2001), "Exact solution for stresses in functionally graded pressure vessels", Compos. Part B. Eng., 32:683-686. https://doi.org/10.1016/S1359-8368(01)00041-5.   DOI
9 Arefi, M., Abbasi, A.R. and Vaziri Sereshk, M.R. (2016), "Two-dimensional thermoelastic analysis of FG cylindrical shell resting on the Pasternak foundation subjected to mechanical and thermal loads based on FSDT formulation", J. Therm. Stresses, 39, 554-570. http://dx.doi.org/10.1080/01495739.2016.1158607   DOI
10 Arefi, M., Kiani, M. and Zenkour, A.M. (2017), "Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak's foundation via MCST", J. Sandw. Struct. Mater., Doi: 1099636217734279.
11 Asgari, M. and Akhlaghi, M. (2011), "Natural frequency analysis of 2D-FGM thick hollow cylinder based on three-dimensional elasticity equations", Eur. J. Mech. A/Solids, 30, 72-81. DOI: 10.1016/j.euromechsol.2010.10.002.   DOI
12 Ferreira, A.J.M. Roque, C.M.C. and Jorge, R.M.N. (2007), "Natural frequencies of FSDT cross-ply composite shells by multiquadrics", Compos. Struct., 77, 296-305. https://doi.org/10.1016/j.compstruct.2005.07.009.   DOI
13 Guo, H., Zhuang, X. and Rabczuk, T. (2019), "A deep collocation method for the bending analysis of Kirchhoff plate", Comput. Mater. Contin. 59, 433-456. doi:10.32604/cmc.2019.06660.   DOI
14 Ahmadi, I. and Najafi, M. (2016), "Three-dimensional stresses analysis in rotating thin laminated composite cylindrical shells", Steel. Compos. Struct., 22(5), 1193-1214. https://doi.org/10.12989/scs.2016.22.5.1193.   DOI
15 Jabbari, M., Bahtui, A. and Eslami, M.R. (2009), "Axisymmetric mechanical and thermal stresses in thick short length FGM cylinders", Int. J. Pres. Ves. Pip., 86(5), 296-306. https://doi.org/10.1016/S0308-0161(02)00043-1.   DOI
16 Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2014a), "The size-dependent vibration of embedded magneto-electro-elastic cylindrical nanoshells", Smart. Mater. Struct., 23, 125036. https://doi.org/10.1088/0964-1726/23/12/125036.   DOI
17 Ke, L.L. Wang, Y.S. and Reddy, J.N. (2014b), "Thermo-electro-mechanical vibration of size-dependent piezoelectric cylindrical nanoshells under various boundary conditions", Compos. Struct., 116, 626-636. https://doi.org/10.1016/j.compstruct.2014.05.048.   DOI
18 Vu-Bac, N. Lahmer, T. Zhuang, X. Nguyen-Thoi, T. Rabczuk, T. (2016), "A software framework for probabilistic sensitivity analysis for computationally expensive models", Adv. Eng. Softw., 100, 19-31. doi:10.1016/j.advengsoft.2016.06.005.   DOI
19 Wang, Q. and Varadan, V.K. (2007), "Application of nonlocal elastic shell theory in wave propagation analysis of carbon nanotubes", Smart. Mater. Struct., 16, 178. https://doi.org/10.1088/0964-1726/16/1/022.   DOI
20 Zhang, B., He, Y., Liu, D., Shen, L. and Lei, J. (2015), "Free vibration analysis of four-unknown shear deformable functionally graded cylindrical microshells based on the strain gradient elasticity theory", Compos. Struct., 119, 578-597. https://doi.org/10.1016/j.compstruct.2014.09.032.   DOI
21 Loy, C.T. Lam, K.Y. and Reddy, J.N. (1999), "Vibration of functionally graded cylindrical shells", Int. J. Mech. Sci., 41(3), 309-324. https://doi.org/10.1016/S0020-7403(98)00054-X.   DOI
22 Malekzadeh, P. and Heydarpour, Y. (2012), "Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment", Compos. Struct., 94, 2971-2981. DOI, 10.1016/j.compstruct.2012.04.011.   DOI
23 Mehralian, F., Tadi Beni, Y. and Ansari, R. (2016), "Size dependent buckling analysis of functionally graded piezoelectric cylindrical nanoshell", Compos. Struct., 152, 45-61. DOI, 10.1016/j.compstruct.2016.05.024.   DOI
24 Niu, B. and Huang, Y. (2019), "An Improved Method for Web Text Affective Cognition Computing Based on Knowledge Graph", Comput. Mater. Contin., 59, 31-55. doi:10.32604/cmc.2019.06032.   DOI
25 Ootao, Y. and Tanigawa, Y. (2006), "Transient Thermoelastic Analysis for a Functionally Graded Hollow Cylinder, J. Therm. Stresses, 29(11), 1031-1046. https://doi.org/10.1080/01495730600710356.   DOI
26 Ansari, R., Pourashraf, T., Gholami, R. and Rouhi, H. (2016), "Analytical solution approach for nonlinear buckling and postbuckling analysis of cylindrical nanoshells based on surface elasticity theory", Appl. Math. Mech.-Engl. Ed., 37(7), 903-918. https://doi.org/10.1007/s10483-016-2100-9.   DOI
27 Pradhan, S.C., Loy, C.T., Lam, K.Y. and Reddy, J.N. (2000), "Vibration characteristics of functionally graded cylindrical shells under various boundary conditions", Appl. Acoust., 61(1), 111-129. https://doi.org/10.1016/S0003-682X(99)00063-8   DOI
28 Shen, H.S. and Xiang, Y. (2012), "Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments", Comput. Method. Appl. M., 213-216, 196-205. https://doi.org/10.1016/j.cma.2011.11.025.   DOI
29 Ahmadi, H. and Foroutan, K. (2019), "Combination resonance analysis of FG porous cylindrical shell under two-term excitation", Steel. Compos. Struct., 32(2), 253-264. https://doi.org/10.12989/scs.2019.32.2.253.   DOI
30 Alibeigloo, A. and Jafarian, H. (2016), "Three-dimensional static and free vibration analysis of carbon nano tube reinforced composite cylindrical shell using differential quadrature method, Int. J. Appl. Mech., 8(3), 1650033. https://doi.org/10.1142/S1758825116500332.   DOI
31 Anitescu, C., Atroshchenko, E., Alajlan, N. and Rabczuk, T. (2019), "Artificial neural network methods for the solution of second order boundary value problems", Comput. Mater. Contin., 59, 345359. doi:10.32604/cmc.2019.06641.