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将描述迫振系统的强非线性微分方程,化为以相角为自变量、振动瞬时频率为未知函数的积分方程;将系统的非线性恢复力表示为线性主部和非线性辅部;将频率和干扰力展开为参数的幂级数;确定时间与相角的近似关系,比较参数的同次幂级数,得到系统的周期解及振幅频率响应曲线.
The strong nonlinear differential equation of forced vibration system will be described as integral equation with phase angle as independent variable and instantaneous frequency of vibration as unknown function. The nonlinear restoring force of system is expressed as linear principal part and nonlinear auxiliary part. The frequency and the disturbance force are expanded into the power series of the parameters. The approximate relationship between time and phase angle is determined. The power series of the parameters are compared to obtain the periodic solution and the amplitude-frequency response curve of the system.