1 |
Xu, L. and He, J.H. (2010), "Determination of limit cycle by Hamiltonian Approach for strongly nonlinear oscillators", Int. J. Nonlinear Sci., 11(12), 1097-1101.
|
2 |
Zarutsky, V.A. (1993), "Oscillations of ribbed shells", Int. Appl. J. Mech., 29(10), 837-841.
DOI
|
3 |
Raouf, R.A. and Palazotto, A.N. (1992), "Non-linear free vibrations of symmetrically laminated, slightly compressible cylindrical shell panels", Compos. Struct., 20(4), 249-257.
DOI
ScienceOn
|
4 |
Reddy, J.N. and Chandrashekhara, K. (1985), "Geometrically non-linear transient analysis of laminated, doubly curved shells", Int. J. Non-linear Mech., 20(2), 79-90.
DOI
ScienceOn
|
5 |
Sinharay, G.C. and Bane, B. (1985), "Large amplitude free vibrations of shallow spherical shell and cylindrical shell - A new approach", Int. J. Non-linear Mech., 20(2), 69-78.
DOI
ScienceOn
|
6 |
Shahidi, M., Bayat, M., Pakar, I. and Abdollahzadeh, G.R. (2011), "On the solution of free non-linear vibration of beams", Int. J. Phys. Sci., 6(7), 1628-1634.
|
7 |
Shen, Y.Y. and Mo, L.F. (2009), "The max-min approach to a relativistic equation", Comput. Math. Appl., 58(11-12), 2131-2133.
DOI
ScienceOn
|
8 |
Wang, S.Q. (2009), "A variational approach to nonlinear two-point boundary value problems", Comput. Math. Appl., 58(11-12), 2452-2245.
DOI
ScienceOn
|
9 |
He, J.H. (1999), "Variational iteration method: A kind of nonlinear analytical technique: some examples", Int. J. Non-Linear Mech., 34(4), 699-708.
DOI
ScienceOn
|
10 |
He, J.H. (2010), "Hamiltonian approach to nonlinear oscillators", Phys. Letters A, 374(23), 2312-2314.
DOI
ScienceOn
|
11 |
He, J.H. (2007), "Variational approach for nonlinear oscillators", Chaos. Soliton. Fractals., 34(5), 1430-1439.
DOI
ScienceOn
|
12 |
He, J.H. (2002), "Preliminary report on the energy balance for nonlinear oscillations", Mech. Res. Comm., 29(2-3), 107-111.
DOI
ScienceOn
|
13 |
Bayat, M. and Pakar, I. (2013a), "On the approximate analytical solution to non-linear oscillation systems", Shock Vib., 20(1), 43-52.
DOI
|
14 |
Andrianov, I.V., Awrejcewicz, J. and Manevitch, L.I. (2004), Asymptotical Mech. Thin-Walled Struct., Springer - Verlag Berlin Heidelberg, Germany.
|
15 |
Bayat, M., Pakar, I. and Domaiirry, G. (2012a), "Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: A review", Latin Am. J. Solids Struct., 9(2), 145-234.
|
16 |
Bayat, M. and Pakar, I. (2011a), "Application of He's Energy Balance Method for Nonlinear vibration of thin circular sector cylinder", Int. J. Phys. Sci., 6(23), 5564-5570.
|
17 |
Bayat, M., Pakar, I. and Bayat, M. (2011b), "Analytical study on the vibration frequencies of tapered beams", Latin Am. J. Solids Struct., 8(2), 149-162.
DOI
|
18 |
Bayat, M., Pakar, I. and Shahidi, M. (2011c), "Analysis of nonlinear vibration of coupled systems with cubic nonlinearity", Mechanika, 17(6), 620-629.
|
19 |
Bayat, M. and Pakar, I. (2012), "Accurate analytical solution for nonlinear free vibration of beams", Struct. Eng. Mech., Int. J., 43(3), 337-347.
DOI
ScienceOn
|
20 |
Bayat, M., Pakar, I, and Bayat, M. (2013b), "On the large amplitude free vibrations of axially loaded Euler-Bernoulli beams", Steel Compos. Struct., Int. J., 14(1), 73-83.
DOI
ScienceOn
|
21 |
Bayat, M. and Pakar, I. (2011c), "Nonlinear free vibration analysis of tapered beams by Hamiltonian approach", J. Vibroeng., 13(4), 654-661.
|
22 |
Pakar, I. and Bayat, M. (2011a), "Analytical solution for strongly nonlinear oscillation systems using Energy balance method", Int. J. Phy. Sci., 6(22), 5166-5170.
|
23 |
Pakar, I. and Bayat, M. (2012a), "Analytical study on the non-linear vibration of Euler-Bernoulli beams", J. Vibroeng., 14(1), 216-224.
|
24 |
Pakar, I. and Bayat, M. (2013b), "An analytical study of nonlinear vibrations of buckled Euler-Bernoulli Beams", Acta Phys. Polonica A, 123(1), 48-52.
DOI
|
25 |
Pakar, I. and Bayat, M. (2013a) "Vibration analysis of high nonlinear oscillators using accurate approximate methods", Struct. Eng. Mech., Int. J., 46(1), 137-151.
DOI
ScienceOn
|
26 |
Raouf, R.A. and Palazotto, A.N. (1991), "Non-linear dynamic response of anisotropic, arbitrarily laminated shell panels: An asymptotic analysis", Compos. Struct., 18(2), 63-192.
|
27 |
Liu, J.F. (2009), "He's variational approach for nonlinear oscillators with high nonlinearity", Comp. Math. Appl., 58(11-12), 2423-2426.
DOI
ScienceOn
|
28 |
Hui, D. (1984), "Influence of geometric imperfections and in-plane constraints on nonlinear vibrations of simply supported cylindrical panels", J. Appl. Mech., 51(2), 383-390.
DOI
|
29 |
Kapania, R.K. and Byum, C. (1992), "Vibrations of imperfect laminated panels under complex preloads", Int. J. Non-linear Mech., 27(1), 51-62,
DOI
ScienceOn
|
30 |
Koiter, W.T. (1966), "On the nonlinear theory of thin elastic shells", Proceedings of Kon. Ned. Ak. Wet., Series B, 69(1), 1-54.
|
31 |
Leissa, A.W. and Kadi, A.S. (1971), "Curvature effects on shallow shell vibrations", J. Sound Vib., 16(2), 173-187.
DOI
ScienceOn
|
32 |
Manevitch, A.I. (1972), "Stability and optimal design of reinforced shells", Visha Shkola, Kiev-Donetzk. (In Russian)
|
33 |
Pakar, I., Bayat, M. and Bayat, M. (2012b), "On the approximate analytical solution for parametrically excited nonlinear oscillators", J. Vibroeng., 14(1), 423-429.
|
34 |
Pakar, I., Bayat, M. and Bayat, M. (2011b), "Analytical evaluation of the nonlinear vibration of a solid circular sector object", Int. J. Phys. Sci., 6(30), 6861-6866.
|
35 |
Bayat, M., Shahidi, M. and Bayat, M. (2011d), "Application of iteration perturbation method for nonlinear oscillators with discontinuities", Int. J. Phys. Sci., 6(15), 3608-3612.
|
36 |
Cummings, B.E. (1964), "Large-amplitude vibration and response of curved panels", AIAA J., 2(4), 709-16.
DOI
|
37 |
Chia, C.Y. (1987), "Nonlinear vibration and postbuckling of unsymmetrically laminated imperfect shallow cylindrical panels with mixed boundary conditions resting on elastic foundation", Int. J. Eng. Sci., 25(4), 427-441.
DOI
ScienceOn
|
38 |
Fu, Y.M. and Chia, C.Y. (1993), "Non-linear vibration and postbuckling of generally laminated circular cylindrical thick shells with non-uniform boundary conditions", Int. J. Non-linear Mech., 28(3), 313-327.
DOI
ScienceOn
|
39 |
Evakin A. Yu. and Kalamkarov, A. (2001), "Analysis of large deflection equilibrium state of composite shells of revolution - Part 1. General model and singular perturbation analysis", Int. J. Solids Struct., 38(50-51), 8961-8974.
DOI
ScienceOn
|
40 |
Fu, Y.M. and Chia, C.Y. (1989), "Multi-mode non-linear vibration and postbuckling of anti-symmetric imperfect angle-ply cylindrical thick panels", Int. J. Non-linear Mech., 24(5), 365-381.
DOI
ScienceOn
|
41 |
Filippov, S.B. (1999), "Theory of conjugated and reinforced shells", St. Petersburg State University, St. Petersburg, Russia. (In Russian)
|
42 |
Ganji, DD. (2006), "The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer," Physics Letters A, 355(4-5), 337-341.
DOI
ScienceOn
|
43 |
Ganji, D.D., Rafei, M., Sadighi, A. and Ganji, Z.Z. (2009), "A comparative comparison of He's Method with perturbation and numerical methods for nonlinear vibrations equations", Int. J. Nonlinear Dyn. in Eng. Sci., 1(1), 1-20.
|
44 |
Grigolyuk, E.I. and Kabanov, V.V. (1987), "Stability of shells", Nauka, Moscow. (In Russian)
|
45 |
Han, S. (1965), "On the free vibration of a beams on a nonlinear elastic foundation", Trans. ASME J. Appl. Mech., 32(2), 445-447.
DOI
|
46 |
Abdollahzade, G.R., Bayat, M., Shahidi, M., Domairry, G. and Rostamian, M. (2010), "Analysis of dynamic model of a structure with nonlinear damped behavior", Int. J. Eng. Tech., 2(2), 160-168.
|
47 |
Amiro, I.Y., Zarutsky, V.A. (1981), "Studies of the dynamics of ribbed shells", Soviet. Appl. Mech., 17(11), 949-962.
DOI
|