References
1. Krylov, N.N. and Bogoliubov, N.N., Introduction to
Nonlinear Mechanics, Princeton University Press, New
Jersey (1947).
2. Bogoliubov, N.N. and Mitropolskii, Yu.A., Asymptotic
Methods in the Theory of Nonlinear Oscillations, Gordan
and Breach, New York (1961).
3. Nayfeh, A.H. and Mook, D.T., Nonlinear Oscillations,
John Wiley & Sons, New York (1979).
4. Nayfeh, A.H., Introduction to Perturbation Techniques,
John Wiley & Sons, New York (1981).
5. He, J.H., Wu, G.C., and Austin, F. \The variational
iterative method which should be followed", Nonlinear
Science Letter A, 1(1), pp. 1-30 (2010).
6. Herisanu, N. and Marinca, V. \A modied variational
iterative method for strongly nonlinear oscillators",
Nonlinear Science Letter A, 1(2), pp. 183-192 (2010).
7. He, J.H. \The homotopy perturbation method for nonlinear
oscillators with discontinuous", Applied Mathematics
and Computation, 151, pp. 287-292 (2004).
8. Ganji, D.D. \The application of He's homotopy perturbation
method to nonlinear equations arising in heat
transfer", Physics Letter A, 355, pp. 337-341 (2006).
9. Rafei, M., Ganji, D.D., and Daniali, H. \Solution of the
epidemic model by homotopy perturbation method",
Applied Mathematics and Computation, 187, pp. 1056-
1062 (2007).
10. Mickens, R.E. \A general procedure for calculating
approximation to periodic solutions of truly nonlinear
oscillators", Journal of Sound and Vibration, 287, pp.
1045-1051 (2005).
11. Lim, C.W., Wu, B.S., and Sun, W.P. \Higher accuracy
analytical approximations to the Dung-harmonic
oscillator", Journal of Sound and Vibration, 296, pp.
1039-1045 (2006).
12. Hu, H. \Solutions of Dung-harmonic oscillator by an
iteration procedure", Journal of Sound and Vibration,
298, pp. 446-452 (2006).
13. Mickens, R.E., Truly Nonlinear Oscillations, World
Scientic, Singapore (2010).
14. Haque, B.M. I., Alam, M.S., and Rahmam, M.M.
\Modied solutions of some oscillators by iteration
procedure", Journal of the Egyptian Mathematical
Society, 21, pp. 68-73 (2013).
15. Wu, B.S., Sun, W.P., and Lim, C.W. \An analytical
approximate technique for a class of strongly nonlinear
oscillators", International Journal of Non-Linear
Mechanics, 41, pp. 766-774 (2006).
16. Alam, M.S., Haque, M.E., and Hossian, M.B. \A
new analytical technique to nd periodic solutions
of nonlinear systems", International Journal of Non-
Linear Mechanics, 42, pp. 1035-1045 (2007).
17. Hosen, M.A., Rahman, M.S., Alam, M.S., and Amin,
M.R. \A new analytical technique for solving a class
of strongly nonlinear conservative systems", Applied
Mathematics and Computation, 218, pp. 5474-5486
(2012).
998 Md. Abdur Razzak/Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 991{998
18. He, J.H. \Variational approach for nonlinear oscillators",
Chaos, Solitions & Fractals, 34(5), pp. 1430-
1439 (2007).
19. Khan, Y., Faraz, N., and Yildirim, A. \New soliton
solutions of the generalized Zakharov equations using
He's variational approach", Applied Mathematics Letters,
24(6), pp. 965-968 (2011).
20. Khan, Y., Akbarzade, M., and Kargar, A. \Coupling of
homotopy and the variational approach for a conservative
oscillator with strong odd-nonlinearity", Scientia
Iranica A, 19(3), pp. 417-422 (2012).
21. He, J.H. \Preliminary report on the energy balance for
nonlinear oscillators", Mechanics Research Communications,
29, pp. 107-111 ( 2002).
22. Zhang, H.L. \Periodic solutions for some strongly
nonlinear oscillators by He's energy balance method",
Computers & Mathematics with Applications, 58, pp.
2480-2485 (2009).
23. Durmaz, S., Demirbag, S.A., and Kaya, M.O. \Highorder
energy balance method based on collocation
method", International Journal of Nonlinear Sciences
and Numerical Simulation, 11, pp. 1-5 (2010).
24. Durmaz, S. and Kaya, M.O. \High-order energy
balance method to nonlinear oscillators", Journal of
Applied Mathematics, pp. 1-7 (2012).
25. Xie, F. and Gao, X. \Exact travelling wave solutions
for a class of nonlinear partial dierential equations",
Chaos, Solitions & Fractals, 19, pp. 1113-1117 (2004).
26. Lai, S.K., Lim, C.W., Wu, B.S., Wang, C., Zeng,
Q.C., and He, X.F. \Newton-harmonic balancing approach
for accurate solutions to nonlinear cubic-quintic
Dung oscillators", Applied Mathematical Modelling,
33(2), pp. 852-866 (2009).
27. Guo, Z., Leung, A.Y.T., and Yang, H.X. \Iterative
homotopy harmonic balancing approach for conservative
oscillator with strong odd-nonlinearity", Applied
Mathematical Modelling, 35, pp. 1717-1728 (2011).
28. Razzak, M.A. and Rahman, M.M. \Application of new
novel energy balance method to strongly nonlinear
oscillator systems", Results in Physics, 5, pp. 304-308
(2015).
29. Khan, Y. and Mirzabeigy, A. \Improved accuracy of
He's energy balance method for analysis of conservative
nonlinear oscillator", Neural Computing and
Applications, 25, pp. 889-895 (2014).
30. Razzak, M.A. \An analytical approximate technique
for solving cubic-quintic Dung oscillator", Alexander
Engineering Journal, 55, pp. 2959-2965 (2015).