In He's frequency-amplitude formulation, the relationship between frequency and amplitude of a nonlinear oscillator can be obtained through residuals of two trial solutions. Although a high accurate solution can be obtained, this method has some space to be further improved. Here, we show that the calculation of the residuals can be further simplified without loss of accuracy. Duffing oscillator with high nonlinearity is used as an example to show the solution process and accuracy.

Orig i nal sci en tific pa per

A complete numerical comparison is given between the He's frequency-amplitude formulation and its modification with average residuals for both weak and strong nonlinear oscillators, showing both methods have good accuracy. This paper concludes that both methods provide a simple but effective tool to various nonlinear oscillators.

A fast insight into the frequency-amplitude relationship of a rehabilitation training device and other nonlinear vibrations as well is of great importance. This paper applies Ren's frequency-amplitude formulation to obtain approximate frequencies of nonlinear oscillators with little calculation while keeping high relative accuracy. The golden mean location is used in the example procedures.