一类三五阶Duffing振子的周期解

Periodic Solution of a Cubic-Quintic Duffing Oscillator

三五阶Duffing振子(Cubic-Quintic Duffing Oscillator)在物理学和工程中有着重要的应用.提出了对大振幅振子研究的简化方法,找到了一个渐近解,并利用该解给出了三五阶Duffing振子周期的简单有效的表达式.结果显示,当0<A<∞时,基本谐波里的能量超过80%.

The cubic-quintic Duffing oscillator covers important applications in physics and engineering.A simplification of recent methods,for large amplitudes,is proposed.An asymptotic solution is found and utilized to find a simple uniformly valid expression for the period of a cubic-quintic Duffing oscillator.It is shown that for 0A∞,energy stored in the fundamental harmonic exceeds 80%.