时间-频率联合非平稳激励下非线性随机动力系统响应一直是随机振动理论关注的重点。基于在时间-频率子域上对非线性系统实施统计线性化，得到了非线性系统在一般随机动力激励下响应的演变功率谱密度。利用周期广义谐和小波及其联系系数，建立线性系统响应与输入功率谱之间的关系。通过对运动方程中非线性项在时间-频率子域上的统计线性化，得到了等价线性参数与响应功率谱之间的联系。二者构成一类相互依赖的迭代关系，并由此可得非线性系统随机动力响应的近似功率谱密度。算例以多项式非线性振子为例，与Monte Carlo模拟估计的响应功率谱对比，说明了所建议方法的有效性。

Stochastic response of non-linear systems to joint time-frequency non-stationary excitation has been always the focus of random vibration theory. A procedure on determination of response evolutionary power spectrum (EPS) density of nonlinear systems is presented, via the concept of statistical linearization on the time-frequency domain. Based on the newly proposed periodic generalized harmonic wavelet and its connection coefficients, the EPS relationship between the excitation and the response of linear system is obtained, by the wavelet-Galerkin solution of the linear stochastic differential equation of the motion. The response EPS dependent equivalent linear parameters of non-linear system are obtained, by employing the statistical linearization on distinct time-frequency domains. The mutually dependency between the response EPS and the equivalent linear parameters constitutes a procedure to obtain the response EPS approximately in an iterative manner. Pertinent Monte Carlo simulations demonstrate the reliability and the efficiency of the proposed approach.