Application of the modified frequency formulation to a nonlinear oscillator

He's frequency formulation is used to obtain the relationship between the frequency and amplitude of a nonlinear oscillator. The general approach is to choose two linear oscillators; in this paper, however, one linear oscillator and the Duffing oscillator are chosen as trial equations. The solution procedure is of utter simplicity, while the result is of high accuracy.

[1]  Ji-Huan He,et al.  An Improved Amplitude-frequency Formulation for Nonlinear Oscillators , 2008 .

[2]  M. O. Kaya,et al.  Application of He's Max-Min Approach to a Generalized Nonlinear Discontinuity Equation , 2010 .

[3]  Ling Zhao,et al.  He's frequency-amplitude formulation for nonlinear oscillators with an irrational force , 2009, Comput. Math. Appl..

[4]  D. Ganji,et al.  He's Energy Balance Method for Nonlinear Oscillators with Discontinuities , 2009 .

[5]  Davood Domiri Ganji,et al.  Applications of He's Homotopy Perturbation Method to Obtain Second-order Approximations of the Coupled Two-Degree-of-Freedom Systems , 2009 .

[6]  Ji-Huan He AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING , 2008 .

[7]  J. R. Chang,et al.  Application of He's Energy Balance Method to a Nonlinear Oscillator with Discontinuity , 2009 .

[8]  Fei Xu,et al.  Exact solution for nonlinear Schrödinger equation by He's frequency formulation , 2009, Comput. Math. Appl..

[9]  Augusto Beléndez,et al.  Homotopy perturbation method for a conservative x1/3 force nonlinear oscillator , 2009, Comput. Math. Appl..

[10]  Ji-Huan He,et al.  Max-Min Approach to Nonlinear Oscillators , 2008 .

[11]  Xu-Chu Cai,et al.  He's frequency formulation for nonlinear oscillators , 2007 .

[13]  Hui-Li Zhang Application of He's amplitude-frequency formulation to a nonlinear oscillator with discontinuity , 2009, Comput. Math. Appl..

[14]  F. Austin,et al.  THE VARIATIONAL ITERATION METHOD WHICH SHOULD BE FOLLOWED , 2010 .

[15]  Jie Fan,et al.  He's frequency-amplitude formulation for the Duffing harmonic oscillator , 2009, Comput. Math. Appl..

[16]  Xu-Chu Cai,et al.  He's frequency formulation for the relativistic harmonic oscillator , 2009, Comput. Math. Appl..

[17]  Ji-Huan He SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS , 2006 .

[18]  S. Mohyud-Din,et al.  Parameter-expansion Techniques for Strongly Nonlinear Oscillators , 2009 .

[19]  Yiu-Yin Lee,et al.  Analysis of Strongly Nonlinear Oscillator using the Max-Min Approach , 2009 .

[20]  Zhong-Fu Ren,et al.  Application of He's amplitude–frequency formulation to nonlinear oscillators with discontinuities , 2009 .

[21]  G. H. Erjaee,et al.  The modified homotopy perturbation method for solving strongly nonlinear oscillators , 2009, Comput. Math. Appl..

[22]  Hui-Li Zhang,et al.  Periodic solutions for some strongly nonlinear oscillations by He's energy balance method , 2009, Comput. Math. Appl..