Browse > Article
http://dx.doi.org/10.12989/scs.2021.39.6.811

Dynamic analysis of axially functionally graded porous beams under a moving load  

Akbas, S.D. (Department of Civil Engineering, Bursa Technical University)
Publication Information
Steel and Composite Structures / v.39, no.6, 2021 , pp. 811-821 More about this Journal
Abstract
In presented paper, moving load problem of functionally graded beams is investigated with porosity effects based on the first shear beam theory. The material properties of beam vary along the axial direction. The porosity is depicted by two different distributions along axial direction. The governing equations of problem are derived by using the Lagrange procedure. In the solution of the problem the Ritz method is used and algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of the moving load problem, the Newmark average acceleration method is used in the time history. In the numerical examples, the effects of material graduation, porosity distribution, porosity coefficients and velocity of moving load on the dynamic responses of axially functionally graded beam are presented and discussed. The dynamic responses are obtained for different boundary conditions.
Keywords
functionally graded beams; moving load problems; porosity; Ritz method;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457.   DOI
2 Wang, Y., Xie, K., Fu, T. and Shi, C. (2019), "Vibration response of a functionally graded graphene nanoplatelet reinforced composite beam under two successive moving masses", Compos. Struct., 209, 928-939. https://doi.org/10.1016/j.compstruct.2018.11.014   DOI
3 Wang, Y., Zhou, A., Fu, T. and Zhang, W. (2020a), "Transient response of a sandwich beam with functionally graded porous core traversed by a non-uniformly distributed moving mass", Int. J. Mech. Mater. Design, 16(3), 519-540. https://doi.org/10.1007/s10999-019-09483-9   DOI
4 Akgoz, B. and Civalek, O. (2016), "Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory", Acta Astronautica, 119, 1-12. https://doi.org/10.1016/j.actaastro.2015.10.021.   DOI
5 Taati, E. and Fallah, F. (2019), "Exact solution for frequency response of sandwich microbeams with functionally graded cores", J. Vib. Control, 25(19-20), 2641-2655. https://doi.org/10.1177/1077546319864645.   DOI
6 Wang, Y., Xie, K. and Fu, T. (2020b), "Size-dependent dynamic stability of a FG polymer microbeam reinforced by graphene oxides", Struct. Eng. Mech., 73(6), 685-698. https://doi.org/10.12989/sem.2020.73.6.685.   DOI
7 Sheng, G.G. and Wang, X. (2019), "Nonlinear forced vibration of functionally graded Timoshenko microbeams with thermal effect and parametric excitation", Int. J. Mech. Sci., 155, 405-416. https://doi.org/10.1016/j.ijmecsci.2019.03.015.   DOI
8 Wang, Y., Xie, K. and Fu, T. (2020d), "Vibration analysis of functionally graded graphene oxide-reinforced composite beams using a new Ritz-solution shape function", J. Braz. Soc. Mech. Sci. Eng., 42(4), 1-14. https://doi.org/10.1007/s40430-020-2258-x   DOI
9 Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002.   DOI
10 Wu, D., Liu, A., Huang, Y., Huang, Y., Pi, Y. and Gao, W. (2018), "Dynamic analysis of functionally graded porous structures through finite element analysis", Eng. Struct., 165, 287-301. https://doi.org/10.1016/j.engstruct.2018.03.023.   DOI
11 Tao, C., Fu, Y.M. and Dai, H.L. (2016), "Nonlinear dynamic analysis of fiber metal laminated beams subjected to moving loads in thermal environment", Compos. Struct., 140, 410-416. https://doi.org/10.1016/j.compstruct.2015.12.011.   DOI
12 Wang, Y. and Wu, D. (2016), "Thermal effect on the dynamic response of axially functionally graded beam subjected to a moving harmonic load", Acta Astronautica, 127, 171-181. https://doi.org/10.1016/j.actaastro.2016.05.030.   DOI
13 Wang, Y. and Wu, D. (2017), "Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory", Aerosp. Sci. Technol., 66, 83-91. https://doi.org/10.1016/j.ast.2017.03.003.   DOI
14 Wang, Y., Xie, K. and Fu, T. (2018), "Vibration analysis of functionally graded porous shear deformable tubes excited by moving distributed loads", Acta Astronautica, 151, 603-613. https://doi.org/10.1016/j.actaastro.2018.06.003.   DOI
15 Akbas, S.D. (2018b), "Forced vibration analysis of cracked nanobeams", J. Braz. Soc. Mech. Sci. Eng., 40(8), 1-11. https://doi.org/10.1007/s40430-018-1315-1.   DOI
16 Yang, J., Chen, D. and Kitipornchai, S. (2018), "Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method", Compos. Struct., 193, 281-294. https://doi.org/10.1016/j.compstruct.2018.03.090.   DOI
17 Zhao, J., Xie, F., Wang, A., Shuai, C., Tang, J. and Wang, Q. (2019), "Vibration behavior of the functionally graded porous (FGP) doubly-curved panels and shells of revolution by using a semi-analytical method", Compos. Part B: Eng., 157, 219-238. https://doi.org/10.1016/j.compositesb.2018.08.087.   DOI
18 Akbas, S.D. (2015b), "Free Vibration Analysis of Edge Cracked Functionally Graded Beams Resting on Winkler-Pasternak Foundation", Int. J. Eng. Appl. Sci., 7(3), 1-15. https://doi.org/10.24107/ijeas.251252.   DOI
19 Akbas, S.D. (2017), "Stability of a non-homogenous porous plate by using generalized differantial quadrature method", Int. J. Eng. Appl. Sci., 9(2), 147-155. https://doi.org/10.24107/ijeas.322375.   DOI
20 Akbas, S.D. (2018a), "Forced vibration analysis of functionally graded porous deep beams", Compos. Struct., 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013.   DOI
21 Akbas, S.D. (2018c), "Geometrically nonlinear analysis of functionally graded porous beams", Wind Struct., 27(1), 59-70. https://doi.org/10.12989/was.2018.27.1.059.   DOI
22 Akbas, S.D. (2018d), "Investigation on free and forced vibration of a bi-material composite beam", J. Polytechnic-Politeknik Dergisi, 21(1), 65-73. https://doi.org/10.2339/politeknik.386841.   DOI
23 Akbas, S.D. (2019b), "Hygro-thermal nonlinear analysis of a functionally graded beam", J. Appl. Comput. Mech., 5(2), 477-485. http://dx.doi.org/10.22055/JACM.2018.26819.1360.   DOI
24 Akbas, S.D. (2019c), "Hygro-thermal post-buckling analysis of a functionally graded beam", Coupled Syst. Mech., 8(5), 459-471. http://dx.doi.org/10.12989/csm.2019.8.5.459.   DOI
25 Akgoz, B. and Civalek, O. (2013), "Buckling analysis of functionally graded microbeams based on the strain gradient theory", Acta Mechanica, 224(9), 2185-2201. https://doi.org/10.1007/s00707-013-0883-5.   DOI
26 Wang, Y., Ren, H., Fu, T. and Shi, C. (2020c), "Hygrothermal mechanical behaviors of axially functionally graded microbeams using a refined first order shear deformation theory", Acta Astronautica, 166, 306-316. https://doi.org/10.1016/j.actaastro.2019.10.036.   DOI
27 Akbas, S.D., (2020a), "Dynamic responses of laminated beams under a moving load in thermal environment", Steel Compos. Struct., 35(6), 729-737. https://doi.org/10.12989/scs.2020.35.6.729.   DOI
28 Akbas, S.D. (2020b), "Geometrically nonlinear analysis of axially functionally graded beams by using finite element method", J. Comput. Appl. Mech., 51(2), 411-416. http://dx.doi.org/10.22059/JCAMECH.2020.309019.548.   DOI
29 Akbas, S.D. (2021a), "Forced Vibration Responses of Axially Functionally Graded Beams by using Ritz Method", J. Appl. Comput. Mech., 7(1), 109-115. http://dx.doi.org/10.22055/JACM.2020.34865.2491.   DOI
30 Akbas, S.D. (2021b), "Forced vibration analysis of a fiber reinforced composite beam", Adv. Mater. Res., 10(1), 57. http://dx.doi.org/10.12989/amr.2021.10.1.057.   DOI
31 Akgoz, B. and Civalek, O. (2015), "A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory", Acta Mechanica, 226(7), 2015, 2277-2294. https://doi.org/10.1007/s00707-015-1308-4   DOI
32 Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006.   DOI
33 Aydogdu, M., Arda, M. and Filiz, S. (2018), "Vibration of axially functionally graded nano rods and beams with a variable nonlocal parameter", Adv. Nano Res., 6(3), 257-278. https://doi.org/10.12989/anr.2018.6.3.257.   DOI
34 Jouneghani, F.Z., Dimitri, R. and Tornabene, F. (2018), "Structural response of porous FG nanobeams under hygro-thermomechanical loadings", Compos. Part B: Eng., 152, 71-78. https://doi.org/10.1016/j.compositesb.2018.06.023.   DOI
35 Akbas, S.D. (2019a), "Forced vibration analysis of functionally graded sandwich deep beams", Coupled Syst. Mech., 8(3), 259-271. http://dx.doi.org/10.12989/csm.2019.8.3.259.   DOI
36 Chen, X.L. and Liew, K.M. (2004), "Buckling of rectangular functionally graded material plates subjected to nonlinearly distributed in-plane edge loads", Smart Mater. Struct., 13(6), 1430. https://doi.org/10.1088/0964-1726/13/6/014.   DOI
37 Civalek, O. (2019), "Vibration of functionally graded carbon nanotube reinforced quadrilateral plates using geometric transformation discrete singular convolution method", Int. J. Numer. Method. Eng., 11, 205-216,2019. https://doi.org/10.1002/nme.6254.   DOI
38 Civalek, O. and Demir, C. (2011), "Bending analysis of microtubules using nonlocal Euler-Bernoulli beam theory", Appl. Math. Model., 35(5), 2053-2067. https://doi.org/10.1016/j.apm.2010.11.004.   DOI
39 Fazzolari, F.A. (2018), "Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations", Compos. Part B: Eng., 136, 254-271. https://doi.org/10.1016/j.compositesb.2017.10.022.   DOI
40 Gurses, M., Akgoz, B. and Civalek, O. (2012), "Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation", Appl. Math. Comput., 219, 3226-3240. https://doi.org/10.1016/j.amc.2012.09.062.   DOI
41 Ebrahimi, F., Barati, M.R. and Civalek, O. (2020), "Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures", Eng. with Comput., 36, 2020, 953-964. https://doi.org/10.1007/s00366-019-00742-z.   DOI
42 Akbas, S.D. (2014), "Free vibration of axially functionally graded beams in thermal environment", Int. J. Eng. Appl. Sci., 6(3), 37-51. https://doi.org/10.24107/ijeas.251224.   DOI
43 Kirlangic, O. and Akbas, S.D. (2020), "Comparison study between layered and functionally graded composite beams for static deflection and stress analyses", J. Comput. Appl. Mech., 51(2), 294-301. http://dx.doi.org/10.22059/JCAMECH.2020.296319.473.   DOI
44 Pegios, I.P. and Hatzigeorgiou, G.D. (2018), "Finite element free and forced vibration analysis of gradient elastic beam structures", Acta Mechanica, 229(12), 4817-4830. https://doi.org/10.1007/s00707-018-2261-9   DOI
45 Akbas, S.D. (2015a), "Post-buckling analysis of axially functionally graded three-dimensional beams", Int. J. Appl. Mech., 7(03), 1550047. https://doi.org/10.1142/S1758825115500477.   DOI
46 Civalek, O. and Demir, C. (2016), "A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method", Appl. Math. Comput., 289, 335-352. https://doi.org/10.1016/j.amc.2016.05.034.   DOI
47 Civalek, O., Uzun, B., Yayli, M.O. and Akgoz, B. (2020), "Size-dependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes by nonlocal finite element method", Eur. Phys. J. Plus, 135: 381 https://doi.org/10.1140/epjp/s13360-020-00385-w.   DOI
48 Ebrahimi, F. and Jafari, A. (2016), "A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities", J. Eng., 2016. http://dx.doi.org/10.1155/2016/9561504.   DOI