强非线性迫振系统的频率展开法

Frequency Expansion Method for Strongly Nonlinear Forced Oscillation Systems

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 strongly nonlinear differential equation which is modelled on the forced oscillation systems,is described as an integration equation in terms of the independent variable with the phase angle and the unknown function with frequency.The nonlinear restoring force is expressed into both parts of the linear mainbody and the nonlinear auxiliary.The frequency and excitation force is indicated as power series of the parameter.The approximation relationship between phase angle and time is determined.The periodic solution and the response curve are obtained by equating the coefficient of the corresponding terms of parameter.