双质量扭振系统的1/2次亚谐共振

1/2 Subharmonic resonance of double mass torsional vibration system

建立了双质量扭振系统的数学模型,此模型具有平方非线性项和立方非线性项并受双频简谐激励作用。应用多尺度法,求得了固有频率ω_0及与外激励频率存在ω_0≈ω_1/2时的一次近似解和对应的定常解,对定常解进行了理论分析和数值计算,结果表明外激励幅值F_1、F_2的变化会影响系统1/2次亚谐幅频响应曲线发生改变。

A mathematical model of double mass torsional vibration system was built with quadratic nonlinearities, cubic nonlinearities and two harmoric excitation. By using the method of multiple scale under the conditions ω_0≈ ω_1/2, the first approximation solution and its corresponding steady-state solution are obtained. The theoretical a- nalysis and numerical analysis are made and steady-state curves are obtained. It is pointed out that amplitude- frequency response curves of system will be changed with the change of forced excitations amplitude F_1 or F_2.