非平稳随机激励下线性结构动力响应的小波多尺度分析

Wavelet multi-scale analysis of dynamic responses of linear structures under nonstationary excitations

为了能够有效地建立随机激励作用下结构动力响应均方值、频率与时间之间的关系,基于小波多尺度分析理论,探讨了非平稳随机激励下线性结构动力响应均方值的2种计算方法:(1)先采用显式时域法求解线性结构在不同激励样本下的动力响应样本,然后基于小波多尺度分析技术对各动力响应样本进行多尺度分析;(2)先将不同的激励样本进行小波多尺度分析得到不同尺度下的激励样本,然后再基于显式时域法高效求解线性结构在不同尺度激励样本下的响应样本。最后,基于导出的响应均方值多尺度计算公式得到总的响应均方值。在数值算例部分,采用Meyer小波对结构动力响应实施了小波多尺度分析。算例结果表明,位于结构基频共振区域的那部分激励能量对位移响应均方值有较大的贡献,而对速度响应均方值和加速度响应均方值影响较为复杂。同时,数值算例还表明所提计算方法不受非平稳激励形式的限制,且可以在频域空间高效地识别出激励不同频率区间的能量对结构动力响应均方值的贡献情况。

To establish the relationship among the mean-square values of the structural dynamic responses,the frequency range,and the time,two calculation methods are investigated for the mean-square values of the dynamic responses of structures under nonstationary excitations based on the wavelet multi-scale analysis theory.Firstly,the explicit time-domain method is used to solve the dynamic response samples of linear structure under different excitation samples,and then the multi-scale analysis of each dynamic response sample is carried out based on the wavelet multi-scale analysis technology.Secondly,the excitation samples at different scales are obtained by wavelet multi-scale analysis for different excitation samples,and then the response samples of linear structure under excitation samples at different scales are efficiently solved based on explicit time-domain method.Finally,the total response mean-square value is constructed based on the derived multi-scale calculation formula.In the numerical example,the Meyer wavelet is used for the multi-scale analysis of the dynamic responses.The results indicate that the energy of the excitation,which is located in the resonant region of the fundamental frequency of the structure,has a great contribution to the mean-square values of displacements,but the influence on the mean-square values of the velocity response and the acceleration response is more complex.In summary,the proposed method is not restricted by the types of the external excitations,and the frequency range of the excitations,which contributes to the mean-square values of responses more,can be effectively identified based on the proposed method.