一类单自由度非自治系统的非线性振动

本文用奇异摄动理论多尺度法的导数展开法[1],求解了在微粘性阻尼作用下,连结在一个非线性弹簧上的一个质点的受迫振动方程.研究的是四次非线性问题,讨论了四种情况:非共振的软激发;非共振的硬激发;共振的软激发;共振的硬激发.

A Kind of Nonlinear Oscillations of Single Degree of Non-Autonomy System

In this paper we use the method of derivative expansion of multiple scales of singular perturbations, and we have solve the forced vibration equation of a particle attached to a nonlinear spring under the influence of slight viscous damping. The problem is of the fourth order nonlinearity. The four cases discussed are the soft excitation of non-resonance, the hard excitation of non-resonance, the soft excitation of resonance, the hard excitation of resonance.