Ritz-POD法的原理及应用

Principle and application of Ritz-POD method

提出一种在频域内分析大跨度屋盖结构的风振响应的Ritz-POD法。该方法用本征正交分解法(POD法)分解脉动风压场,得到占优的前几阶本征模态作为荷载的空间分布形式;根据此荷载空间分布形式生成Ritz向量,用Ritz向量直接叠加法分析结构风振响应,以解决大跨度屋盖结构多振型参与振动且高阶振型对结构响应贡献可能较大这一问题。运用该方法分析一单层球面网壳的风振响应,并与振型分解法对比,结果表明Ritz-POD法仅用少量的Ritz向量进行结构风振响应分析便可达到较高精度。

Large span roofs are usually characterized as the dense distribution of natural frequencies and the remarkable coupling effects among the natural modes. Therefore, those traditional model superposition methods are not effective to analyze the wind-induced response of these structures. Based on proper orthogonal decomposition （POD） technique and Ritz vector superposition method, this paper presents a new method, which is named Ritz-POD method, to analyze wind-induced response of long span roof structures in frequency domain. The eigenvectors of fluctuating wind with POD are regarded as spatial distribution of the loading to generate Ritz vectors, and the wind-induced response is analyzed with Ritz vector superposition method. So, it can take into account multi-mode buffeting response and the case that structures vibrate in those modes with high frequencies. Moreover, the dominating modes to the dynamic response can be found, and coupling effects between these modes are discussed. According to this method, the wind-induced response of a single layer reticular shell is analyzed, and compared to the results achieved with model superposition method. It shows that Ritz-POD method is more accurate and efficient with fewer Ritz vectors.