Browse > Article
http://dx.doi.org/10.12989/cac.2022.30.6.433

On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations  

Hao-Xuan, Ding (College of Mechanical and Vehicle Engineering, Chongqing University)
Yi-Wen, Zhang (College of Mechanical and Vehicle Engineering, Chongqing University)
Gui-Lin, She (College of Mechanical and Vehicle Engineering, Chongqing University)
Publication Information
Computers and Concrete / v.30, no.6, 2022 , pp. 433-443 More about this Journal
Abstract
In the current paper, the nonlinear resonance response of functionally graded graphene platelet reinforced (FG-GPLRC) beams by considering different boundary conditions is investigated using the Euler-Bernoulli beam theory. Four different graphene platelets (GPLs) distributions including UD and FG-O, FG-X, and FG-A are considered and the effective material parameters are calculated by Halpin-Tsai model. The nonlinear vibration equations are derived by Euler-Lagrange principle. Then the perturbation method is used to discretize the motion equations, and the loadings and displacement are all expanded, so as to obtain the first to third order perturbation equations, and then the asymptotic solution of the equations can be obtained. Then the nonlinear amplitude-frequency response is obtained with the help of the modified Lindstedt-Poincare method (Chen and Cheung 1996). Finally, the influences of the distribution types of GPLs, total GPLs layers, GPLs weight fraction, elastic foundations and boundary conditions on the resonance problems are comprehensively studied. Results show that the distribution types of GPLs, total GPLs layers, GPLs weight fraction, elastic foundations and boundary conditions have a significant effect on the nonlinear resonance response of FG-GPLRC beams.
Keywords
boundary conditions; elastic foundations; graphene platelet reinforced beams; Modified Lindstedt-Poincare method; non-linear vibration;
Citations & Related Records
Times Cited By KSCI : 13  (Citation Analysis)
연도 인용수 순위
1 Alnujaie, A., Akba, E.D., Eltaher, M. and Assie, A. (2021), "Forced vibration of a functionally graded porous beam resting on viscoelastic foundation", Geomech. Eng., 24(1), 91-103. http://doi.org/10.12989/gae.2021.24.1.091.   DOI
2 Anvari, M., Mohammadimehr, M. and Amiri, A. (2020), "Vibration behavior of a micro cylindrical sandwich panel reinforced by graphene platelet", J. Vib. Control, 26(13-14), 1311-1343. http://doi.org/10.1177/1077546319892730.   DOI
3 Arefi, M., Firouzeh, S., Bidgoli, E.M.R. and Civalek, O. (2020), "Analysis of porous micro-plates reinforced with FG-GNPs based on Reddy plate theory", Compos. Struct., 247, 112391. https://doi.org/10.1016/j.compstruct.2020.112391.   DOI
4 Baghbadorani, A.A. and Kiani, Y. (2021), "Free vibration analysis of functionally graded cylindrical shells reinforced with graphene platelets", Compos. Struct., 276, 114546. http://doi.org/10.1016/j.compstruct.2021.114546.   DOI
5 Barati, M.R. and Shahverdi, H. (2020), "Finite element forced vibration analysis of refined shear deformable nanocomposite graphene platelet-reinforced beams", J. Brazil. Soc. Mech. Sci. Eng., 42(1), 1-14. http://doi.org/10.1007/s40430-019-2118-8.   DOI
6 Barati, M.R. and Zenkour, A.M. (2018), "Vibration analysis of functionally graded graphene platelet reinforced cylindrical shells with different porosity distributions", Mech. Adv. Mater. Struct., 26(18), 1580-1588. http://doi.org/10.1080/15376494.2018.1444235.   DOI
7 Chen, S.H. and Cheung, Y.K. (1996), "A modified lindstedt-poincare method for a strongly nonlinear system with quadratic and cubic nonlinearities", Shock Vib., 3(4), 279-285. https://doi.org/10.1155/1996/231241.   DOI
8 Civalek, O. and Avcar, M. (2022). "Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method", Eng. Comput., 38(Suppl1), 489-521. https://doi.org/10.1007/s00366-020-01168-8.   DOI
9 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
10 Daikh, A.A., Houari, M.S.A., Karami, B., Eltaher, M.A., Dimitri, R. and Tornabene, F. (2021), "Buckling analysis of CNTRC curved sandwich nanobeams in thermal environment", Appl. Sci., 11, 3250. https://doi.org/10.3390/app11073250.   DOI
11 Ding, H.X. and She, G.L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80(1), 63-72. http://doi.org/10.12989/sem.2021.80.1.063.   DOI
12 Do, V. and Lee, C.H. (2020), "Static bending and free vibration analysis of multilayered composite cylindrical and spherical panels reinforced with graphene platelets by using isogeometric analysis method", Eng. Struct., 215, 110682. http://doi.org/10.1016/j.engstruct.2020.110682.   DOI
13 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. Comput., 36, 953-964. https://doi.org/10.1007/s00366-019-00742-z.   DOI
14 Eltaher, M.A., Abdelrahman, A.A. and Esen, I. (2021), "Dynamic analysis of nanoscale Timoshenko CNTs based on doublet mechanics under moving load", Eur. Phys. J. Plus, 136, 705. https://doi.org/10.1140/epjp/s13360-021-01682-8.   DOI
15 Hachemi, H., Bousahla, A.A., Kaci, A., Bourada, F., Tounsi, A., Benrahou, K., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S. R. (2021), "Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position", Steel Compos. Struct., 39(1), 51-64. https://doi.org/10.12989/scs.2021.39.1.051.   DOI
16 Esen, I., Daikh, A.A. and Eltaher, M.A. (2021), "Dynamic response of nonlocal strain gradient FG nanobeam reinforced by carbon nanotubes under moving point load", Eur. Phys. J. Plus, 136, 458. https://doi.org/10.1140/epjp/s13360-021-01419-7.   DOI
17 Esmaeili, H.R., Kiani, Y. and Beni, Y.T. (2022), "Vibration characteristics of composite doubly curved shells reinforced with graphene platelets with arbitrary edge supports", Acta Mechanica, 233(2), 665-683. http://doi.org/10.1007/s00707-021-03140-z.   DOI
18 Ghandourah, E.E., Daikh, A.A., Alhawsawi, A.M., Fallatah, O.A., Eltaher, M.A. (2022), "Bending and buckling of FG-GRNC laminated plates via Quasi-3D nonlocal strain Gradient theory", Math., 10, 1321 https://doi.org/10.3390/math10081321.   DOI
19 Jafari, P. and Kiani, Y. (2021), "Free vibration of functionally graded graphene platelet reinforced plates: A quasi 3D shear and normal deformable plate model-ScienceDirect", Compos. Struct., 275, 114409. http://doi.org/10.1016/j.compstruct.2021.114409.   DOI
20 Jalaei, M.H. and Civalek, Ӧ. (2019), "On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam", Int. J. Eng. Sci., 143, 14-32. https://doi.org/10.1016/j.ijengsci.2019.06.013.   DOI
21 Jalaei, M.H., Thai, H.T. and Civalek, Ӧ. (2022), "On viscoelastic transient response of magnetically imperfect functionally graded nanobeams", Int. J. Eng. Sci., 172, 103629. https://doi.org/10.1016/j.ijengsci.2022.103629.   DOI
22 Liu, D. (2020), "free vibration of functionally graded graphene platelets reinforced magnetic nanocomposite beams resting on elastic foundation", Nanomater., 10(11), 2193. http://doi.org/10.3390/nano10112193.   DOI
23 Jia, H., Kong, Q.Q., Liu, Z., Wei, X.X., Li, X., M., Chen, J.P., Li, F., Yang, X., Sun, G.H. and Chen, C.M. (2019), "3D graphene/ carbon nanotubes/Polydimethylsiloxane composites as high-performance electromagnetic shielding material in X-band", Compos. Part A: Appl. Sci. Manuf., 129, 105712. http://doi.org/10.1016/j.compositesa.2019.105712.   DOI
24 Khadir, A.I., Daikh, A.A. and Eltaher, M.A. (2021), "Novel four-unknowns quasi 3D theory for bending, buckling and free vibration of functionally graded carbon nanotubes reinforced composite laminated nanoplates", Adv. Nano Res., 11(6), 621-640. https://doi.org/10.12989/anr.2021.11.6.621.   DOI
25 Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Des., 116, 656-665. http://doi.org/10.1016/j.matdes.2016.12.061.   DOI
26 Liu, H., Wu, H. and Lyu, Z. (2020), "Nonlinear resonance of FG multilayer beam-type nanocomposites: Effects of graphene nanoplatelet-reinforcement and geometric imperfection", Aerosp. Sci. Technol., 98, 105702. http://doi.org/10.1016/j.ast.2020.105702.   DOI
27 Lu, L., She, G.L. and Guo, X. (2021b), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199, 106428. https://doi.org/10.1016/j.ijmecsci.2021.106428.   DOI
28 Lu, L., Wang, S., Li, M. and Guo, X.M. (2021a), "Free vibration and dynamic stability of functionally graded composite microtubes reinforced with graphene platelets", Compos. Struct., 272, 114231. http://doi.org/10.1016/j.compstruct.2021.114231.   DOI
29 Malikan, M., Wiczenbach, T. and Eremeyev, V.A. (2021), "Thermal buckling of functionally graded piezomagnetic micro-and nanobeams presenting the flexomagnetic effect", Continuum. Mech. Therm., 34(4), 1051-1066. https://doi.org/10.1007/s00161-021-01038-8.   DOI
30 Malikan, M. and Eremeyev, V.A. (2020), "A new hyperbolic-polynomial higher-order elasticity theory for mechanics of thick FGM beams with imperfection in the material composition", Compos. Struct., 249, 112486. https://doi.org/10.1016/j.compstruct.2020.112486.   DOI
31 Melaibari, A., Daikh, A.A., Basha, M., Abdalla, A.W., Othman, R., Almitani, K.H., Hamed, M.A., Abdelrahman, A. and Eltaher, M.A. (2022), "Free vibration of FG-CNTRCs nano-plates/shells with temperature-dependent properties", Math., 10, 583. https://doi.org/10.3390/math10040583.   DOI
32 Wang, M., Xu, Y.G., Qiao, P. and Li, Z.M. (2021), "Buckling and free vibration analysis of shear deformable graphene-reinforced composite laminated plates", Compos. Struct., 280, 114854. http://doi.org/10.1016/j.compstruct.2021.114854.   DOI
33 Niu, Y. and Yao, M.H. (2021), "Linear and nonlinear vibrations of graphene platelet reinforced composite tapered plates and cylindrical panels", Aerosp. Sci. Technol., 115, 106798. http://doi.org/10.1016/j.ast.2021.106798.   DOI
34 Rahimi, A., Alibeigloo, A. and Safarpour, M. (2020), "Three-dimensional static and free vibration analysis of graphene platelet-reinforced porous composite cylindrical shell", J. Vib. Control, 26(19-20), 1627-1645. http://doi.org/10.1177/1077546320902340.   DOI
35 Rezaiee-Pajand, M., Sobhani, E. and Masoodi, A.R. (2021a), "Semi-analytical vibrational analysis of functionally graded carbon nanotubes coupled conical-conical shells", Thin Wall. Struct., 159, 107272. https://doi.org/10.1016/j.tws.2020.107272.   DOI
36 Song, M., Gong, Y.H., Yang, J., Zhu, W. and Kitipornchai, S. (2020), "Nonlinear free vibration of cracked functionally graded graphene platelet-reinforced nanocomposite beams in thermal environments", J. Sound Vib., 468, 115115. http://doi.org/10.1016/j.jsv.2019.115115.   DOI
37 She, G.L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Therm. Stress., 44(10), 1289-1305. https://doi.org/10.1080/01495739.2021.1974323.   DOI
38 She, G.L., Ding, H.X. and Zhang, Y.W. (2022), "Wave propagation in a FG circular plate via the physical neutral surface concept", Struct. Eng. Mech., 82(2), 225-232. https://doi.org/10.12989/sem.2022.82.2.225.   DOI
39 Shen, H.S., Xiang, Y., Lin, F. (2017), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments", Comput. Meth. Appl. Mech. Eng., 319, 175-193. http://doi.org/10.1016/10.1016/j.cma.2017.02.029.   DOI
40 Wang, Y., Feng, C. and Wang, X. (2019), "Nonlinear free vibration of graphene platelets (GPLs)/polymer dielectric beam", Smart Mater. Struct., 28(5), 055013. http://doi.org/10.1088/1361-665X/ab0b51.   DOI
41 Wang, Y.Q., Ye, C. and Zu, J.W. (2019), "Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets", Aerosp. Sci. Technol., 85, 359-370. https://doi.org/10.1016/j.ast.2018.12.022.   DOI
42 Zhang, Y.W. and She, G.L. (2022), "Wave propagation and vibration of FG pipes conveying hot fluid", Steel Compos. Struct., 42(3), 397-405. http://doi.org/10.12989/scs.2022.42.3.397.   DOI
43 Zhang, Y.W., Ding, H.X. and She, G.L. (2022), "Snap-buckling and resonance of functionally graded graphene reinforced composites curved beams resting on elastic foundations in thermal environment", J. Therm. Stress., 45(12), 1029-1042. http://doi.org/10.1080/01495739.2022.2125137.   DOI
44 Alazwari M.A., Daikh A.A. and Eltaher M.A. (2022), "Novel quasi 3D theory for mechanical responses of FG-CNTs reinforced composite nanoplates", Adv. Nano Res., 12(2), 117-137. https://doi.org/10.12989/anr.2022.12.2.117.   DOI
45 Zhang, Y.Y., Wang, Y.X., Zhang, X., Shen, H.M. and She, G.L. (2021), "On snap-buckling of FG-CNTR curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. http://dx.doi.org/10.12989/scs.2021.38.3.293.   DOI
46 Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., Pu, H.Y. and Luo, J. (2022), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel Compos. Struct., 43(6), 797-808. http://doi.org/10.12989/scs.2022.43.6.797.   DOI
47 Akbas, S.D., Bashiri, A.H., Assie, A.E. and Eltaher, M.A. (2021), "Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support", J. Vib. Control, 27(13-14), 1644-1655. http://doi.org/10.1177/1077546320947302.   DOI