1 |
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.
DOI
|
2 |
Aydin, K. (2013), "Free vibration of functionally graded beams with arbitrary number of surface cracks", Eur. J. Mech. A-Solid., 42, 112-124.
DOI
|
3 |
Aydogdu, M. (2008), "Semi-inverse method for vibration and buckling of axially functionally graded beams", J. Reinforced Plast. Compos., 27(7), 683-691.
DOI
|
4 |
Aydogdu, M. and Taskin, V. (2007), "Free vibration analysis of functionally graded beams with simply supported edges", Mater. Des., 28(5), 1651-1656.
DOI
|
5 |
Bambill, D.V., Rossit, C.A. and Felix, D.H. (2015), "Free vibrations of stepped axially functionally graded timoshenko beams", Meccanica, 50(4), 1073-1087.
DOI
|
6 |
Cunedioglu, Y. (2015), "Free vibration analysis of edge cracked symmetric functionally graded sandwich beams", Struct. Eng. Mech., 56(6), 1003-1020.
DOI
|
7 |
Demir, E., Callioglu, H. and Sayer, M. (2013a), "Vibration analysis of sandwich beams with variable cross section on variable Winkler elastic foundation", Sci. Eng. Compos. Mater., 20(4), 359-370.
|
8 |
Demir, E., Callioglu, H. and Sayer, M. (2013b), "Free vibration of symmetric FG sandwich Timoshenko beam with simply supported edges", Indi. J. Eng. Mater. Sci., 20, 515-521.
|
9 |
Gibson, R.F. (1994), Principles of Composite Material Mechanics, McGraw-Hill, Singapore.
|
10 |
Anandrao, K.S., Gupta, R.K., Ramachandran, P and Ra, G.V. (2012), "Free vibration analysis of functionally graded beams", Defence Sci. J., 62(3), 139-146.
DOI
|
11 |
Jing, L.L., Ming, P.J., Zhang, W.P., Fu, L.R. and Cao, Y.P. (2016), "Static and free vibration analysis of functionally graded beams by combination Timoshenko theory and finite volume method", Compos. Struct., 138, 192-213.
DOI
|
12 |
Kapuria, S., Bhattacharyya, M. and Kumar, A.N. (2008), "Bending and free vibration response of layered functionally graded beams: A theoretical model and its experimental validation", Compos. Struct., 82(3), 390-402.
DOI
|
13 |
Ke, L.L., Yang, J., Kitipornchai, S. and Xiang, Y. (2009), "Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials", Mech. Adv. Mater. Struct., 16(6), 488-502.
DOI
|
14 |
Ke, L.L., Yang, J. and Kitipornchai, S. (2010), "An analytical study on the nonlinear vibration of functionally graded beams", Meccanica, 45(6), 743-752.
DOI
|
15 |
Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2012), "Nonlinear free vibration of size-dependent functionally graded microbeams", Int. J. Eng. Sci., 50(1), 256-267.
DOI
|
16 |
Koizumi, M. (1993), "The concept of FGM", Ceramic Trans., Func. Grade Mater., 34, 3-10.
|
17 |
Koizumi, M. (1997), "FGM Activities in Japan", Compos. Part B, 28B(1-2), 1-4,
DOI
|
18 |
Krodkiewski, J.M. (2008), Mechanical Vibration, Design and Print Centre University of Melbourne.
|
19 |
Li, X.F., Kang, Y.A. and Wu, J.X. (2013), "Exact frequency equations of free vibration of exponentially functionally graded beams", Appl. Acoust., 74(3), 413-420.
DOI
|
20 |
Nguyen, T.K., Nguyen, T.T.P., Vo, T.P. and Thai, H.T. (2015), "Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation", Compos. Part B-Eng., 76, 273-285.
DOI
|
21 |
Pradhan, K.K. and Chakraverty, S. (2013), "Free vibration of euler and Timoshenko functionally graded beams by Rayleigh-Ritz method", Compos. Part B-Eng., 51, 175-184.
DOI
|
22 |
Sina, S.A. Navazi, H.M. and Haddadpour, H. (2009), "An analytical method for free vibration analysis of functionally graded beams", Mater. Des., 30(3), 741-747.
DOI
|
23 |
Thai, H.T. and Vo, T.P. (2012), "Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories", Int. J. Mech. Sci., 62(1), 57-66.
DOI
|
24 |
Wang, C.M., Ke, L.L., Roy Chowdhury, A.N., Yang, J., Kitipornchai, S. and Fernando, D. (2017), "Critical examination of midplane and neutral plane formulations for vibration analysis of FGM beams", Eng. Struct., 130, 275-281.
DOI
|
25 |
Wang, Z.H., Wang, X.H., Xu, G.D., Chen, S. and Zeng, T. (2016), "Free vibration of two-directional functionally graded beams", Compos. Struct., 135, 191-198.
DOI
|
26 |
Wattanasakulpong, N., Prusty, B.G., Kelly, D.W. and Hoffman, M. (2012), "Free vibration analysis of layered functionally graded beams with experimental validation", Mater. Des., 36, 182-190.
DOI
|
27 |
Wei, D., Liu, Y.H. and Xiang, Z.H. (2012), "An analytical method for free vibration analysis of functionally graded beams with edge cracks", J. Sound Vib., 331(7), 1686-1700.
DOI
|
28 |
Wu, L., Wang, Q.S. and Elishakoff, I. (2005), "Semi-inverse method for axially functionally graded beams with anti-symmetric vibration mode", J. Sound Vib., 284(3-5), 1190-1202.
DOI
|
29 |
Vo, T.P., Thai, H.T., Nguyen, T.K., Maheri, A. and Lee, J. (2014), "Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory", Eng. Struct., 64, 12-22.
DOI
|