背景响应、共振响应定义及其相关性分析方法

Definitions and correlation analyses for background response and resonant response

以模态加速度法为基础，推导了脉动风响应中背景响应和共振响应的严密数学定义；在此基础上，根据随机振动理论，推导了频域内的背景响应、共振响应，以及两者间相关性的分析方法；指出脉动风响应谱包括背景响应谱、共振响应谱和两者间的耦合谱三部分，并给出了背景响应和共振响应的精确组合方法。将该方法用于一单层球面网壳，结果表明：对于该结构，背景响应和共振响应的相关系数在[-0．3，-0．1]之间，若忽略该相关性时，将高估该结构的实际响应，比例在3％～10％范围内。

It is an important problem in wind engineering to define background response, resonant response, and to analyze the correlation between their components for multi-degrees-of-freedom system. On the basis of modal acceleration method, background response and resonant response are strictly defined. Furthermore, it is deduced to calculate background response and resonant response and the correlation coefficient between these two components in frequency domain. It is found that response spectrum under fluctuating wind consists of background response spectrum, resonant response spectrum and the coupling spectrum, and the exact method is deduced to combine these three components. According to the method, three response components of wind-induced response of a single layer reticular shell is analyzed, and the results show that the correlation coefficients between background response and resonant response for all nodal displacements are around [-0.3,-0. 1], and it will overestimate the exact response 3%-10% if this correlation is neglected.