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

作者：Chen, Y M; Liu, J K^*

来源：Physics Letters, Section A: General, Atomic and Solid State Physics , 2007, 368(5): 371-378.

DOI：10.1016/j.physleta.2007.04.025

• nonlinear oscillator
• harmonic balance method
• duffing equation
• duffing-harmonic equation
• arbitrary initial conditions
• uniformly valid

The harmonic balance (HB) method as an analytical approach is widely used for nonlinear oscillators, in which the initial conditions are generally simplified by setting velocity or displacement to be zero. Based on HB, we establish a new theory to address nonlinear conservative systems with arbitrary initial conditions, and deduce a set of over-determined algebraic equations. Since these deduced algebraic equations are not solved directly, a minimization problem is constructed instead and an iterative algorithm is employed to seek the minimization point. Taking Duffing and Duffing-harmonic equations as numerical examples, we find that these attained solutions are not only with high degree of accuracy, but also uniformly valid in the whole solution domain.

• 出版日期2007-8-27
• 单位中山大学