Details
Title
Dynamic behaviour of axially functionally graded beam resting on variable elastic foundationJournal title
Archive of Mechanical EngineeringYearbook
2020Volume
vol. 67Issue
No 4Affiliation
Kumar, Saurabh : Department of Mechanical Engineering, School of Engineering, University of Petroleum andEnergy Studies (UPES), Dehradun, 248007, India.Authors
Keywords
free vibration ; variable elastic foundation ; axially functionally graded beam ; Euler-Bernoulli beam ; Timoshenko beamDivisions of PAS
Nauki TechniczneCoverage
451-470Publisher
Polish Academy of Sciences, Committee on Machine BuildingBibliography
[1] J. Neuringer and I. Elishakoff. Natural frequency of an inhomogeneous rod may be independent of nodal parameters. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 456(2003):2731–2740, 2000. doi: 10.1098/rspa.2000.0636.
[2] I. Elishakoff and S. Candan. Apparently first closed-form solution for vibrating: inhomogeneous beams. International Journal of Solids and Structures, 38(19):3411–3441, 2001. doi: 10.1016/S0020-7683(00)00266-3.
[3] Y. Huang and X.F. Li. A new approach for free vibration of axially functionally graded beams with non-uniform cross-section. Journal of Sound and Vibration, 329(11):2291–2303, 2010. doi: 10.1016/j.jsv.2009.12.029.
[4] M. Şimşek, T. Kocatürk, and Ş.D. Akbaş.. Dynamic behavior of an axially functionally graded beam under action of a moving harmonic load. Composite Structures, 94(8):2358–2364, 2012. doi: 10.1016/j.compstruct.2012.03.020.
[5] B. Akgöz and Ö. Civalek. Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory. Composite Structures, 98:314-322, 2013. doi: 10.1016/j.compstruct.2012.11.020.
[6] K. Sarkar and R. Ganguli. Closed-form solutions for axially functionally graded Timoshenko beams having uniform cross-section and fixed–fixed boundary condition. Composites Part B: Engineering, 58:361–370, 2014. doi: 10.1016/j.compositesb.2013.10.077.
[7] M. Rezaiee-Pajand and S.M. Hozhabrossadati. Analytical and numerical method for free vibration of double-axially functionally graded beams. Composite Structures, 152:488–498, 2016. doi: 10.1016/j.compstruct.2016.05.003.
[8] M. Javid and M. Hemmatnezhad. Finite element formulation for the large-amplitude vibrations of FG beams. Archive of Mechanical Engineering, 61(3):469–482, 2014. doi: 10.2478/meceng-2014-0027.
[9] W.R. Chen, C.S. Chen and H. Chang. Thermal buckling of temperature-dependent functionally graded Timoshenko beams. Archive of Mechanical Engineering, 66(4): 393–415, 2019. doi: 10.24425/ame.2019.131354.
[10] W.Q. Chen, C.F. Lü, and Z.G. Bian. A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation. Applied Mathematical Modelling, 28(10):877–890, 2004. doi: 10.1016/j.apm.2004.04.001.
[11] J. Ying, C.F. Lü, and W.Q. Chen. Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations. Composite Structures, 84(3):209–219, 2008. doi: 10.1016/j.compstruct.2007.07.004.
[12] T. Yan, S. Kitipornchai, J. Yang, and X.Q. He. Dynamic behaviour of edge-cracked shear deformable functionally graded beams on an elastic foundation under a moving load. Composite Structures, 93(11):2992–3001, 2011. doi: 10.1016/j.compstruct.2011.05.003.
[13] A. Fallah and M.M. Aghdam. Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation. European Journal of Mechanics – A/Solids, 30(4):571–583, 2011. doi: 10.1016/j.euromechsol.2011.01.005.
[14] A. Fallah and M.M. Aghdam. Thermo-mechanical buckling and nonlinear free vibration analysis of functionally graded beams on nonlinear elastic foundation. Composites Part B: Engineering, 43(3):1523–1530, 2012. doi: 10.1016/j.compositesb.2011.08.041.
[15] H. Yaghoobi and M. Torabi. An analytical approach to large amplitude vibration and post-buckling of functionally graded beams rest on non-linear elastic foundation. Journal of Theoretical and Applied Mechanics, 51(1):39–52, 2013.
[16] A.S. Kanani, H. Niknam, A.R. Ohadi, and M.M. Aghdam. Effect of nonlinear elastic foundation on large amplitude free and forced vibration of functionally graded beam. Composite Structures, 115:60–68, 2014. doi: 10.1016/j.compstruct.2014.04.003.
[17] N. Wattanasakulpong and Q. Mao. Dynamic response of Timoshenko functionally graded beams with classical and non-classical boundary conditions using Chebyshev collocation method. Composite Structures, 119:346–354, 2015. doi: 10.1016/j.compstruct.2014.09.004.
[18] F.F. Calim. Free and forced vibration analysis of axially functionally graded Timoshenko beams on two-parameter viscoelastic foundation. Composites Part B: Engineering, 103:98–112, 2016. doi: 10.1016/j.compositesb.2016.08.008.
[19] H. Deng, K. Chen, W. Cheng, and S. Zhao. Vibration and buckling analysis of double-functionally graded Timoshenko beam system on Winkler-Pasternak elastic foundation. Composite Structures, 160:152–168, 2017. doi: 10.1016/j.compstruct.2016.10.027.
[20] H. Lohar, A. Mitra, and S. Sahoo. Nonlinear response of axially functionally graded Timoshenko beams on elastic foundation under harmonic excitation. Curved and Layered Structures, 6(1):90–104, 2019. doi: 10.1515/cls-2019-0008.
[21] B. Karami and M. Janghorban. A new size-dependent shear deformation theory for free vibration analysis of functionally graded/anisotropic nanobeams. Thin-Walled Structures, 143:106227, 2019. doi: 10.1016/j.tws.2019.106227.
[22] I. Esen. Dynamic response of a functionally graded Timoshenko beam on two-parameter elastic foundations due to a variable velocity moving mass. International Journal of Mechanical Sciences, 153–154:21–35, 2019. doi: 10.1016/j.ijmecsci.2019.01.033.
[23] L.A. Chaabane, F. Bourada, M. Sekkal, S. Zerouati, F.Z. Zaoui, A. Tounsi, A. Derras, A.A. Bousahla, and A. Tounsi. Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation. Structural Engineering and Mechanics, 71(2):185–196, 2019. doi: 10.12989/sem.2019.71.2.185.
[24] M. Eisenberger and J. Clastornik. Vibrations and buckling of a beam on a variable Winkler elastic foundation. Journal of Sound and Vibration, 115(2):233–241, 1987. doi: 10.1016/0022-460X(87)90469-X.
[25] A. Kacar, H.T. Tan, and M.O. Kaya. Free vibration analysis of beams on variable Winkler elastic foundation by using the differential transform method. Mathematical and Computational Applications, 16(3):773–783, 2011. doi: 10.3390/mca16030773.
[26] A. Mirzabeigy and R. Madoliat. Large amplitude free vibration of axially loaded beams resting on variable elastic foundation. Alexandria Engineering Journal, 55(2):1107–1114, 2016. doi: 10.1016/j.aej.2016.03.021.
[27] H. Zhang, C.M. Wang, E. Ruocco, and N. Challamel. Hencky bar-chain model for buckling and vibration analyses of non-uniform beams on variable elastic foundation. Engineering Structures, 126:252–263, 2016. doi: 10.1016/j.engstruct.2016.07.062.
[28] M.H. Yas, S. Kamarian, and A. Pourasghar. Free vibration analysis of functionally graded beams resting on variable elastic foundations using a generalized power-law distribution and GDQ method. Annals of Solid and Structural Mechanics, 9(1-2):1–11, 2017. doi: 10.1007/s12356-017-0046-9.
[29] S.K. Jena, S. Chakraverty, and F. Tornabene. Vibration characteristics of nanobeam with exponentially varying flexural rigidity resting on linearly varying elastic foundation using differential quadrature method. Materials Research Express, 6(8):085051, 2019. doi: 10.1088/2053-1591/ab1f47.
[30] S. Kumar, A. Mitra, and H. Roy. Geometrically nonlinear free vibration analysis of axially functionally graded taper beams. Engineering Science and Technology, an International Journal, 18(4):579–593, 2015. doi: 10.1016/j.jestch.2015.04.003.