References
- N.N. Krylov, N.N. Bogoliubov, Introduction to Nonlinear Mechanics, Princeton University Press, New Jersey, 1947.
- M. S. Alam, M. A. Akbar, M. Z. Islam, A General Form of Krylov-Bogoliubov-mitropolskii Method for Solving Nonlinear Partial Differential Equations, Journal of Sound and Vibration, Vol. 285, pp. 173-185, 2005. doi: 10.1016/j.jsv.2004.08.001
- M. S. Rahman, Y. Y. Lee, New modified multi-level residue harmonic balance method for solving nonlinearly vibrating double-beam problem, Journal of Sound and Vibration, Vol. 406, pp. 295-327, 2017. doi: 10.1016/j.jsv.2017.06.017
- T. Pirbodaghi, S.H. Hoseini, M.T. Ahmadian, G.H. Farrahi, Duffing equations with cubic and quintic nonlinearities, Computers & Mathematics with Applications, Vol. 57(3), pp. 500-506, 2009. doi: 10.1016/j.camwa.2008.10.082
- D. Younesian, Z. Saadatnia, H. Askari, Analytical solutions for free oscillations of beams on nonlinear elastic foundations using the variational iteration method, Journal of Theoretical and Applied Mechanics, Vol. 50, pp. 639-652, 2012.
- I. S. N. Murty, A unified Krylov-Bogoliubov method for solving second-order nonlinear systems, Int. J. Nonlinear Mech., Vol. 6, pp. 45-53, 1971. doi: 10.1016/0020-7462(71)90033-3
- M. S. Alam, A unified Krylov-Bogoliubov-Mitropolskii method for solving n-order nonlinear systems, J. Franklin Inst., Vol. 339, pp. 239–248, 2002. doi: 10.1016/S0016-0032(02)00020-0
- M. S. Alam, A modified and compact form of Krylov-Bogoliubov-Mitropolskii unified method for solving an n-th order nonlinear differential equation, Int. J. Nonlinear Mech., Vol. 39, pp. 1343-1357, 2004. doi: 10.1016/j.ijnonlinmec.2003.08.008
- M. S. Alam, M. A. K. Azad and M. A. Haque, A general Struble’s technique for solving an n-th order weakly nonlinear differential system with damping, Int. J. Nonlinear Mech., Vol. 41, pp. 905-918, 2006. doi: 10.1016/j.ijnonlinmec.2006.08.001
- M. S. Alam, M. A. K. Azad, K. C. Roy, M. M. Rahman, An extension of the general Struble’s method for solving an n-th order non-linear differential equation when the corresponding unperturbed equation has some repeated eigen-values, J. Franklin Inst., Vol. 346(2), pp.112–125, 2009. doi: 10.1016/j.jfranklin.2008.06.010
- M. A. Akbar, M. S. Alam, M. A. Sattar, KBM unified method for solving an nth order nonlinear differential equation under some special conditions including the case of internal resonance, Int. J. Nonlinear Mech., Vol. 41, pp. 26-42, 2006. doi: 10.1016/j.ijnonlinmec.2005.02.006