非线性系统响应功率谱密度的小波-Galerkin方法

发展了广义谐和小波在确定非线性系统随机动力响应中的应用。首先,利用周期广义谐和小波展开非线性动力微分方程,并考虑小波的联系系数后,可将动力微分方程转化为一组非线性代数方程。其次,利用Newton迭代法数值解答了非线性代数方程,得到了非线性动力响应的小波变换。最后,根据响应时变功率谱与各阶小波变换之间的关系,计算求得了非线性动力响应的功率谱密度。数值模拟显示了本文建议方法与Monte Carlo模拟之间的吻合程度。

Determination of power spectrum density of nonlinear system response via wavelet-galerkin approach

An application of generalized harmonic wavelet in the response determination of nonlinear stochastic dynamic system is developed in this paper. Specifically, first, based on the wavelet expansion of the nonlinear differential equation and the newly developed wavelet connection coefficients, the dynamic differential equation is converted into a set of nonlinear algebra equations. Next, the Newton’s method is utilized to solve algebra equations. Finally, according to the relationship between the time-varying Power Spectrum Density (PSD) and the wavelet coefficients, response PSD is therefore obtained. Pertinent numerical simulations demonstrate the reliability of the proposed technique.