[1]
|
I. Kovacic and M. J. Brennan, “The Duffing Equation: Nonlinear Oscillators and Their Behaviour,” John Wiley & Sons, Hoboken, 2011. doi:10.1002/9780470977859
|
[2]
|
P. Amore and A. Aranda, “Improved Lindstedt-Poincaré Method for the Solution of Nonlinear Problems,” Journal of Sound and Vibration, Vol. 283, No. 3-5, 2005, pp. 1115-1136. doi:10.1016/j.jsv.2004.06.009
|
[3]
|
R. R. Pu?enjak, “Extended Lindstedt-Poincare Method for Non-Stationary Resonances of Dynamical Systems with Cubic Nonlinearities,” Journal of Sound and Vibration, Vol. 314, No. 1-2, 2008, pp. 194-216.
doi:10.1016/j.jsv.2008.01.002
|
[4]
|
B. S. Wu and P. S. Li, “A method for Obtaining Approximate Analytic Periods for a Class of Nonlinear Oscillators,” Meccanica, Vol. 36, No. 2, 2001, pp. 167-176.
doi:10.1023/A:1013067311749
|
[5]
|
H. L. Zhang, “Periodic Solutions for Some Strongly Nonlinear Oscillations by He’s Energy Balance Method,” Computers and Mathematics with Applications, Vol. 58, No. 11-12, 2009, pp. 2480-2485.
doi:10.1016/j.camwa.2009.03.068
|
[6]
|
I. Mehdipour, D. D. Ganji and M. Mozaffari, “Application of the Energy Balance Method to Nonlinear Vibrating Equations,” Current Applied Physics, Vol. 10, No. 1, 2010, pp. 104-112. doi:10.1016/j.cap.2009.05.016
|
[7]
|
L. Geng and X. C. Cai, “He’s Frequency Formulation for Nonlinear Oscillators,” European Journal of Physics, Vol. 28, 2007, pp. 923-931. doi:10.1088/0143-0807/28/5/016
|
[8]
|
J. Fan, “He’s Frequency-Amplitude Formulation for the Duffing Harmonic Oscillator,” Computers and Mathematics with Applications, Vol. 58, No. 11-12, 2009, pp. 2473-2476. doi:10.1016/j.camwa.2009.03.049
|
[9]
|
S. J. Liao, “Beyond Perturbation: Introduction to the Homotopy Analysis Method,” Chapman & Hall, Boca Raton, 2003. doi:10.1201/9780203491164
|
[10]
|
S. H. Hoseini, T. Pirbodaghi, M. T. Ahmadian and G. H. Farrahi, “On the Large Amplitude Free Vibrations of Tapered Beams: An Analytical Approach,” Mechanics Research Communications, Vol. 36, No. 8, 2009, pp. 892-897. doi:10.1016/j.mechrescom.2009.08.003
|
[11]
|
Y. H. Qian, S. K. Lai, W. Zhang and Y. Xiang, “Study on Asymptotic Analytical Solutions Using HAM for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam with an Intermediate Lumped Mass,” Numerical Algorithms, Vol. 58, No. 3, 2011, pp. 293-314.
doi:10.1007/s11075-011-9456-7
|
[12]
|
Y. H. Qian, D. X. Ren, S. K. Lai and S. M. Chen, “Analytical Approximations to Nonlinear Vibration of an Electrostatically Actuated Microbeam,” Communications in Nonlinear Science and Numerical Simulation, Vol. 17, No. 4, 2012, pp. 1947-1955.
doi:10.1016/j.cnsns.2011.09.018
|
[13]
|
R. A. Van Gorder and K. Vajravelu, “On the Selection of Auxiliary Functions, Operators, and Convergence Control Parameters in the Application of the Homotopy Analysis Method to Nonlinear Differential Equations: A General Approach,” Communication in Nonlinear Sciences and Numerical Simulation, Vol. 14, No. 12, 2009, pp. 4078-4089. doi:10.1016/j.cnsns.2009.03.008
|
[14]
|
S. J. Liao, “An Optimal Homotopy-Analysis Approach for Strongly Nonlinear Differential Equations,” Communication in Nonlinear Sciences and Numerical Simulation, Vol. 15, No. 8, 2010, pp. 2003-2016.
doi:10.1016/j.cnsns.2009.09.002
|
[15]
|
Y. Davood, A. Hassan, S. Zia and K. Mohammad, “Frequency Analysis of Strongly Nonlinear Generalized Duffing Oscillators Using He’s Frequency-Amplitude Formulation and He's Energy Balance Method,” Computers and Mathematics with Applications, Vol. 59, No. 9, 2010, pp. 3222-3228. doi:10.1016/j.camwa.2010.03.013
|