A new method based on the harmonic balance method for nonlinear oscillators

2007 ◽  
Vol 368 (5) ◽  
pp. 371-378 ◽  
Author(s):  
Y.M. Chen ◽  
J.K. Liu
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Nonlinear Oscillators ◽  
Balance Method ◽  
New Method

RATIONAL ENERGY BALANCE METHOD TO NONLINEAR OSCILLATORS WITH CUBIC TERM

2013 ◽  
Vol 06 (02) ◽  
pp. 1350019 ◽  
Author(s):  
M. Daeichin ◽  
M. A. Ahmadpoor ◽  
H. Askari ◽  
A. Yildirim
Keyword(s):  
Energy Balance ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Nonlinear Problems ◽  
Nonlinear Oscillators ◽  
Initial Guess ◽  
Second Order ◽  
Balance Method ◽  
Strong Nonlinearity ◽  
Novel Approach

In this paper, a novel approach is proposed for solving the nonlinear problems based on the collocation and energy balance methods (EBMs). Rational approximation is employed as an initial guess and then it is combined with EBM and collocation method for solving nonlinear oscillators with cubic term. Obtained frequency amplitude relationship is compared with exact numerical solution and subsequently, a very excellent accuracy will be revealed. According to the numerical comparisons, this method provides high accuracy with 0.03% relative error for Duffing equation with strong nonlinearity in the second-order of approximation. Furthermore, achieved results are compared with other types of modified EBMs and the second-order of harmonic balance method. It is demonstrated that the new proposed method has the highest accuracy in comparison with different approaches such as modified EBMs and the second-order of harmonic balance method.

scholarly journals Application of a modified rational harmonic balance method for a class of strongly nonlinear oscillators

2008 ◽  
Vol 372 (39) ◽  
pp. 6047-6052 ◽  
Author(s):  
A. Beléndez ◽  
E. Gimeno ◽  
M.L. Álvarez ◽  
D.I. Méndez ◽  
A. Hernández
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Nonlinear Oscillators ◽  
Balance Method ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear Oscillators

scholarly journals The modified Lindstedt–Poincare method for solving quadratic nonlinear oscillators

2020 ◽  
pp. 146134842097975
Author(s):  
Ismot A Yeasmin ◽  
MS Rahman ◽  
MS Alam
Keyword(s):  
Analytical Solution ◽  
Small Parameter ◽  
Harmonic Balance ◽  
Nonlinear Oscillator ◽  
Harmonic Balance Method ◽  
Nonlinear Oscillators ◽  
Balance Method ◽  
Algebraic Equations ◽  
Related Parameter ◽  
Nonlinear Algebraic Equations

Recently, an analytical solution of a quadratic nonlinear oscillator has been presented based on the harmonic balance method. By introducing a small parameter, a set of nonlinear algebraic equations have been solved which usually appear among unknown coefficients of several harmonic terms. But the method is not suitable for all quadratic oscillators. Earlier, introducing a small parameter to the frequency series, Cheung et al. modified the Lindstedt–Poincare method and used it to solve strong nonlinear oscillators including a quadratic oscillator. But due to some limitations of both parameters, a changed form of frequency-related parameter (introduced by Cheung et al.) has been presented for solving various quadratic oscillators.

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