Investigating of free vibration behavior of bidirectional FG beams resting on variable elastic foundation |
Benaberrahmane, Ismail
(Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology)
Benyoucef, Samir (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) Sekkal, Mohamed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) Mekerbi, Mohamed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) Bouiadjra, Rabbab Bachir (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) Selim, Mahmoud M. (Department of Mathematics, Al-Aflaj College of Science and Humanities, Prince Sattam bin Abdulaziz University) Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) Hussain, Muzamal (Department of Mathematics, Government College University Faisalabad) |
1 | Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175. DOI |
2 | Al-Osta, M.A. (2019), "Shear behaviour of RC beams retrofitted using UHPFRC panels epoxied to the sides", Comput. Concrete, 24(1), 37-49. http://doi.org/10.12989/cac.2019.24.1.037 DOI |
3 | Panjehpour, M., Loh, E.W.K. and Deepak, T.J. (2018), "Structural insulated panels: State-of-the-Art", Trends Civ. Eng. Arch., 3(1), 336-340. https://doi.org/10.32474/TCEIA.2018.03.000151. DOI |
4 | Pradhan, S.C. and Murmu, T. (2009), "Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method", J. Sound Vib., 321, 342-362. https://doi.org/10.1016/j.jsv.2008.09.018. DOI |
5 | Pydah, A. and Sabale, A. (2017), "Static analysis of bi-directional functionally graded curved beams", Compos. Struct., 160, 867-876. https://doi.org/10.1016/j.compstruct.2016.10.120. DOI |
6 | Faroughi, S., Rahmani, A. and Friswell, M.I. (2020), "On wave propagation in two-dimensional functionally graded porous rotating nano-beams using a general nonlocal higher-order beam model", Appl. Math. Model., 80, 169-190. https://doi.org/10.1016/j.apm.2019.11.040. DOI |
7 | Nemati, A.R. and Mahmoodabadi, M.J. (2019), "Effect of micromechanical models on stability of functionally graded conical panels resting on Winkler-Pasternak foundation in various thermal environments", Arch. Appl. Mech., 1-33. https://doi.org/10.1007/s00419-019-01646-6. DOI |
8 | Nguyen, D.K., Nguyen, Q.H., Tran, T.T. and Bui, V.T. (2017), "Vibration of bi-dimensional functionally graded Timoshenko beams excited by a moving load", Acta Mech., 228(1), 141-155. http://doi.org/10.1007/s00707-016-1705-3. DOI |
9 | Ouldlarbi, L., Kaci, A., Houari, M.S.A. and Tounsi, A., (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Based Des. Struct. Mach., 41(4), 421-433. https://doi.org/10.1080/15397734.2013.763713. DOI |
10 | Fariborz, J. and Batra, R.C. (2019), "Free vibration of bidirectional functionally graded material circular beams using shear deformation theory employing logarithmic function of radius", Compos. Struct., 210, 217-230. https://doi.org/10.1016/j.compstruct.2018.11.036. DOI |
11 | Hadji, L. (2020), "Influence of the distribution shape of porosity on the bending of FGM beam using a new higher order shear deformation model", Smart Struct. Syst., 26(2), 253-262. http://doi.org/10.12989/sss.2020.26.2.25. DOI |
12 | Hadji, L. and Avcar, M. (2021), "Free vibration analysis of FG porous sandwich plates under various boundary conditions", J. Appl. Comput. Mech., 7(2), 505-519. http://doi.org/10.22055/JACM.2020.35328.2628. DOI |
13 | Hao, D. and Wei, C. (2016), "Dynamic characteristics analysis of bi-directional functionally graded Timoshenko beams", Compos. Struct., 141, 253-263. https://doi.org/10.1016/j.compstruct.2016.01.051. DOI |
14 | Jalaei, M.H. and Civalek, O. (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 |
15 | Ramteke, P.M., Panda, S.K. and Sharma, N. (2019), "Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure", Steel Compos. Struct., 33(6), 865-875. http://doi.org/10.12989/scs.2019.33.6.865. DOI |
16 | Ozutok, A. and Madenci, E. (2017), "Static analysis of laminated composite beams based on higher-order shear deformation theory by using mixed-type finite element method", Int. J. Mech. Sci., 130, 234-243. https://doi.org/10.1016/j.ijmecsci.2017.06.013. DOI |
17 | Kar, V.R. and Panda, S.K. (2020), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693. DOI |
18 | Rahmani, M., Mohammadi, Y. and Kakavand, F. (2019), "Vibration analysis of sandwich truncated conical shells with porous FG face sheets in various thermal surroundings", Steel Compos. Struct., 32(2), 239-252. http://doi.org/10.12989/scs.2019.32.2.239. DOI |
19 | Rajasekaran, S. and Khaniki, H.B. (2018), "Free vibration analysis of bi-directional functionally graded single/multi-cracked beams", Int. J. Mech. Sci., 144, 341-356. https://doi.org/10.1016/j.ijmecsci.2018.06.004. DOI |
20 | Al-Basyouni, K. S., Ghandourah, E., Mostafa, H.M. and Algarni, A. (2020), "Effect of the rotation on the thermal stress wave propagation in non-homogeneous viscoelastic body", Geomech. Eng., 21(1), 1-9. https://doi.org/10.12989/gae.2020.21.1.001. DOI |
21 | Shahmohammadi, M.A., Azhari, M. and Saadatpou, M.M. (2020), "Free vibration analysis of sandwich FGM shells using isogeometric B-spline finite strip method", Steel Compos. Struct., 34(3), 361-376. http://doi.org/10.12989/scs.2020.34.3.361. DOI |
22 | Simsek, M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher order beam theories", Nucl. Eng. Des., 240(4), 697-705. https://doi.org/10.1016/j.nucengdes.2009.12.013. DOI |
23 | Kiani, Y. (2019), "NURBS-based thermal buckling analysis of graphene platelet reinforced composite laminated skew plates", J. Therm. Stresses, 1-19. https://doi.org/10.1080/01495739.2019.1673687. DOI |
24 | simsek, M. (2016), "Buckling of Timoshenko beams composed of two-dimensional functionally graded material (2D-FGM) having different boundary conditions", Compos. Struct., 149, 304-314. https://doi.org/10.1016/j.compstruct.2016.04.034. DOI |
25 | Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. https://doi.org/10.12989/SCS.2015.19.6.1421. DOI |
26 | Attia, M.A. (2017), "On the mechanics of functionally graded nanobeams with the account of surface elasticity", Int. J. Eng. Sci., 115, 73-101. https://doi.org/10.1016/j.ijengsci.2017.03.011. DOI |
27 | Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603. DOI |
28 | Madenci, E. (2019), "A refined functional and mixed formulation to static analyses of fgm beams", Struct. Eng. Mech., 69(4), 427-437. https://doi.org/10.12989/sem.2019.69.4.427. DOI |
29 | Timesli, A. (2020), "Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation", Comput. Concrete, 26(1), 53-62. https://doi.org/10.12989/cac.2020.26.1.053. DOI |
30 | simsek, M. (2015), "Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions", Compos. Struct., 133, 968-978. http://doi.org/10.1016/j.compstruct.2015.08.021. DOI |
31 | Bachir Bouiadjra, R., Bachiri, A., Benyoucef, S., Fahsi, B. and Bernard, F. (2020), "An investigation of the thermodynamic effect of FG beam on elastic foundation", Struct. Eng. Mech., 76(1), 115-127. https://doi.org/10.12989/sem.2020.76.1.115. DOI |
32 | Tang, Y. and Ding, Q. (2019), "Nonlinear vibration analysis of a bi-directional functionally graded beam under hygro-thermal loads", Compos. Struct., 225,111076. https://doi.org/10.1016/j.compstruct.2019.111076. DOI |
33 | Li, J., Guan, Y., Wang, G., Zhao, G., Lin, J., Naceur, H. and Coutellier, D. (2018), "Meshless modeling of bending behavior of bi-directional functionally graded beam structures", Compos. Part B Eng., 155, 104-111. https://doi.org/10.1016/j.compositesb.2018.08.029. DOI |
34 | Lu, Y. and Chen, X. (2020), "Nonlinear parametric dynamics of bidirectional functionally graded beams", Shock Vib., 8840833, https://doi.org/10.1155/2020/8840833. DOI |
35 | Si Tayeb, T., Zidour, M., Bensattalah, T., Heireche, H., Benahmed, A. and Adda Bedia, E.A. (2020), "Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle", Adv. Nano Res., 8(2), 135-148. https://doi.org/10.12989/anr.2020.8.2.135. DOI |
36 | Sobhy, M. (2015), "Thermoelastic response of FGM plates with temperature-dependent properties resting on variable elastic foundations", J. Appl. Mech., 7(6), 1550082. https://doi.org/10.1142/S1758825115500829. DOI |
37 | Demir., C. and Civalek, O. (2017), "On the analysis of microbeams", Int. J. Eng. Sci., 121, 14-33. https://doi.org/10.1016/j.ijengsci.2017.08.016. DOI |
38 | Karamanli, A. (2017a), "Elastostatic analysis of two-directional functionally graded beams using various beam theories and symmetric smoothed particle hydrodynamics method", Compos. Struct., 160, 653-669. http://doi.org/10.1016/j.compstruct.2016.10.065. DOI |
39 | Madenci, E., Ozkilic, Y.O. and Gemi, L. (2020), "Experimental and theoretical investigation on flexure performance of pultruded GFRP composite beams with damage analyses", Compos. Struct., 242, 112162. https://doi.org/10.1016/j.compstruct.2020.112162. DOI |
40 | Shafiei, N., Mirjavadi, S.S., Mohasel Afshari, B., Rabby, S. and Kazemi, M. (2017), "Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams", Comput. Meth. Appl. Mech. Eng., 322, 615-632. https://doi.org/10.1016/j.cma.2017.05.007. DOI |
41 | Chami., K., Massafer, T. and Hadji, L. (2020), "Analytical modeling of bending and free vibration of thick advanced composite beams resting on Winkler-Pasternak elastic foundation", Earthq. Struct., 19(2), 91-101. http://doi.org/10.12989/eas.2020.19.2.091. DOI |
42 | Bhattacharya, S. and Das, D. (2019), "Free vibration analysis of bidirectional-functionally graded and double-tapered rotating micro-beam in thermal environment using modified couple stress theory", Compos. Struct., 215, 471-492. https://doi.org/10.1016/j.compstruct.2019.01.080. DOI |
43 | Bachiri, A., Bourada, M., Mahmoudi, A., Benyoucef, S. and Tounsi, A. (2018), "Thermodynamic effect on the bending response of elastic foundation FG plate by using a novel four variable refined plate theory", J. Therm. Stresses, 41(8), 1042-1062. https://doi.org/10.1080/01495739.2018.1452169. DOI |
44 | Benferhat, R., Daouadji, T.H. and Adim, B. (2016), "A novel higher order shear deformation theory based on the neutral surface concept of FGM plate under transverse load", Adv. Mater. Res., 5(2), 107-120. https://doi.org/10.12989/amr.2016.5.2.107. DOI |
45 | Boulal, A., Bensattalah, T., Karas, A., Zidour, M., Heireche, H. and Adda Bedia, E.A. (2020), "Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle", Struct. Eng. Mech., 73(2), 209-223. https://doi.org/10.12989/sem.2020.73.2.209. DOI |
46 | Karamanli, A. (2017b), "Bending behaviour of two directional functionally gradedsandwich beams by using a quasi-3d shear deformation theory", Compos. Struct., 174, 70-86. https://doi.org/10.1016/j.compstruct.2017.04.046 DOI |
47 | Tran, T.T. and Nguyen D.K. (2018), "Free vibration analysis of 2-DFGM beams in thermal environment based on a newthird-order shear deformation theory", Vietnam J. Mech., 40(2), 121-140. https://doi.org/10.15625/0866-7136/10503. DOI |
48 | Rahmani, A., Faroughi, S. and Friswell, M.I. (2020), "The vibration of two-dimensional imperfect functionally graded(2D-FG) porous rotating nanobeams based on general nonlocaltheory", Mech. Syst. Signal Process., 144, 106854. https://doi.org/10.1016/j.ymssp.2020.106854. DOI |
49 | Ali Rachedi, M., Benyoucef, S., Bouhadra, A., Bachir Bouiadjra, R., Sekkal, M. and Benachour, A. (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. Eng., 22(1), 65-80. http://doi.org/10.12989/gae.2020.22.1.065. DOI |
50 | Merzoug, M., Bourada, M., Sekkal, M., Abir, A.C., Chahrazed, B., Benyoucef, S. and Benachour, A. (2020), "2D and quasi 3D computational models for thermoelastic bending of FG beams on variable elastic foundation: Effect of the micromechanical models", Geomech. Eng., 22(4), 361-374. http://doi.org/10.12989/gae.2020.22.4.361. DOI |
51 | Eisenberger, M. and Clastornik, J. (1987), "Vibrations and buckling of a beam on a variable Winkler elastic foundation", J. Sound Vib., 115, 233-241. https://doi.org/10.1016/0022-460X(87)90469-X. DOI |
52 | Civalek, O., Dastjerdi, S., Akbas, S. and Akgoz, B. (2021), "Vibration analysis of carbon nanotube-reinforced composite microbeams", Math. Meth. Appl. Sci. https://doi.org/10.1002/mma.7069. DOI |
53 | Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H. and Abdel-Wahab, M., (2020), "A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA", Compos. Struct., 259, 113216. https://doi.org/10.1016/j.compstruct.2020.113216. DOI |
54 | Cuong-Le, T., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel-Wahab, M. (2020), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. Comput., 1-12. https://doi.org/10.1007/s00366-020-01154-0. DOI |
55 | Zhou, D. (1993), "A general solution to vibrations of beams on variable Winkler elastic foundation", Comput. Struct., 47(1), 83-90. https://doi.org/10.1016/0045-7949(93)90281-H. DOI |
56 | Vinyas, M. (2020), "On frequency response of porous functionally graded magneto-electro-elastic circular and annular plates with different electro-magnetic conditions using HSDT", Compos. Struct., 240, 112044. https://doi.org/10.1016/j.compstruct.2020.112044. DOI |
57 | Wang, Z.H., Wang, X.H., Xu, G.D., Cheng, S. and Zeng, T. (2016), "Free vibration of two-directional functionally graded beams", Compos. Struct., 135, 191-198. http://doi.org/10.1016/j.compstruct.2015.09.013. DOI |
58 | Yaghoobi, H. and Taheri, F. (2020), "Analytical solution and statistical analysis of buckling capacity of sandwich plates with uniform and non-uniform porous core reinforced with graphene nanoplatelets", Compos. Struct.,252, 112700. https://doi.org/10.1016/j.compstruct.2020.112700 DOI |
59 | Madenci, E. and Ozutok, A. (2020), "Variational approximate for high order bending analysis of laminated composite plates", Struct. Eng. Mech., 73(1), 97-108. https://doi.org/10.12989/sem.2020.73.1.097. DOI |
60 | Madenci, E., Ozkilic, T.O. and Gemi, L. (2020), "Buckling and free vibration analyses of pultruded GFRP laminated composites: Experimental, numerical and analytical investigations", Compos. Struct., 254, 112806. https://doi.org/10.1016/j.compstruct.2020.112806. DOI |
61 | Madenci, E. and Ozutok, A. (2017), "Variational approximate and mixed-finite element solution for static analysis of laminated composite plates", Solid State Phenom., 267, 35-39. https://doi.org/10.4028/www.scientific.net/SSP.267.35 DOI |
62 | Madenci, E. and Gulcu, S. (2020), "Optimization of flexure stiffness of FGM beams via artificial neural networks by mixed FEM", Struct. Eng. Mech., 75(5), 633-642. https://doi.org/10.12989/sem.2020.75.5.633. DOI |
63 | Selmi, A. (2020), "Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam", Smart Struct. Syst., 26(3), 361-371. https://doi.org/10.12989/SSS.2020.26.3.361. DOI |
64 | Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A. and Tounsi, A., (2019), "Analytical study of bending and free vibration response of functionally graded beam resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185. DOI |
65 | Madenci, E., Ozkilic, T.O. and Gemi, L. (2020), "Theoretical investigation on static analysis of pultruded GFRP composite beams", Akademik Platform Muhendislik ve Fen Bilimleri Dergisi, 8(3), 483-490. https://doi.org/10.21541/apjes.734770. DOI |