【摘要】 用一种新方法研究达芬-谐波振子的解析逼近解.将牛顿线性化方法与谐波平衡法组合起来应用于变形后的控制方程,建立了达芬-谐波振子频率及周期解的改进解析逼近.改进的解析逼近在振幅的全部取值范围内,包括振幅趋于零及无穷的情况,都有令人满意的精度.更多还原

【Abstract】 This paper deals with analytical approximate solutions to the Duffing-Harmonic oscillator by a new method.By combining the Newton method and the method of harmonic balance into the rewritten governing(equation),we have established improved analytical approximations to the frequency and the corresponding(periodic) solution of the oscillator.The improved analytical approximations show excellent agreement with the accurate solution,and are valid for the total range of oscillation amplitudes,including the two(extreme) cases of the oscillation amplitudes respectively approaching zero and infinity.更多还原