基于小波-Galerkin方法的结构随机动力响应功率谱的确定

在最近发展的周期广义谐和小波PGHW(Periodic Generalized Harmonic Wavelet)的基础上,通过小波-Galerkin方法推导得到了线性单自由度结构的随机动力响应功率谱密度。在此过程中,利用PGHW的解析形式及其在频域内的特殊性:(1)推导得出了PGHW的联系系数(Connection Coefficient)的解析形式;(2)基于PGHW及其联系系数,利用小波-Galerkin方法推导得到了线性单自由度系统在确定性激励下的响应;(3)得到了在具有演变功率谱的随机动力激励下单自由度线性振子的随机响应功率谱解答。数值算例表明,无论是确定性响应解答,还是随机动力响应的功率谱密度,小波-Galerkin法的计算结果均能较好地吻合数值解。

Power spectrum determination of system response via the Wavelet-Galerkin technique

This paper presents a wavelet-Galerkin technique based approach for the determination of the power spectrum density (PSD) of the response of the SDOF system subject to stochastic excitation.Specifically,first the Periodic Generalized Harmonic Wavelet (PGHW) is presented and the connection coefficients of the PGHW are derived,based on the analytical form and the orthogonality of the wavelets.Further,the deterministic response of the system is obtained via the wavelet-Galerkin technique and the connection coefficients.Next,based on the relationship between the mean square value of the wavelet coefficients and the power spectrum density of the stochastic process,the excitation-response PSD relationship is derived.Finally,the numerical example demonstrates the reliability of the approach over the pertinent Monte Carlo simulation.