Frequency–Amplitude Relationship of Coupled Anharmonic Oscillators
The frequency–amplitude relationship of coupled anharmonic oscillators is an important problem. Many powerful methods for solving this problem have been proposed. He’s parameter-expanding method is an important one. It holds the advantages of modified Lindstedt–Poincare parameter method and bookkeeping parameter method. The first iteration is enough. It is very effective and convenient and quite accurate to both linear and nonlinear problems. In this paper, He’s parameter-expanding method is applied to coupled anharmonic oscillators. The frequency-amplitude relationship and the first-order approximate solution of the oscillators are obtained respectively. The solution procedure shows that the method is very powerful and convenient to nonlinear oscillator. This method has great potential and can be applied to other types of nonlinear oscillator problems.
Paul P. Lin and Chunliang Zhang
Z. B. Li and W. H. Zhu, "Frequency–Amplitude Relationship of Coupled Anharmonic Oscillators", Applied Mechanics and Materials, Vols. 105-107, pp. 271-274, 2012