中文摘要：

传统的不变流行降阶技术通过增加状态空间的方式将外荷载看成是附加状态,这种方法只适用于非线性较弱的结构。考虑到膜结构的较强非线性的特点,本文基于中心流形理论,通过模态转换的方式对风和膜结构形成的耦合体系进行降阶处理,将膜结构的模态分为主模态和次模态,将膜结构的风振状态表示为主模态的非线性函数,并将次模态表达为主模态的随时间变化的非线性函数,这里的不变流形依赖于主模态和风荷载,最后通过扩展不变流形方程获得体系的降阶模型。将该降阶模型用于计算膜结构的风振耦合响应,得到了膜结构风压系数、风振响应和功率谱等重要参数,结果与全阶模型计算结果符合良好。同时对比了本文降阶模型的计算效率,由此可见本文降阶模型耗费机时比全阶模型平均减少约55%,耦合迭代次数比全阶模型平均减少约60%。由此可见,基于模态转换的降阶模型适用于膜结构的风振耦合分析,且具有较高的准确性和计算效率。

英文摘要：

External loads are treated as an additional state by adding state space in traditional invariant manifold technique, which is applicable for structures with slight nonlinearity. Considering the strong nonlinearity of mem- brane structures, based on central manifold theory, modal transformation is applied to form reducing order models for wind-structure coupling system. The membrane modes are considered as dominant and non-dominant modes, and the wind-induced state non-dominant modes are expressed as the nonlinear function of dominant modes, respec- tively. The invariant manifold depends on dominant modes and wind loads. Reducing order models are obtained by expanding invariant manifold equations. The reducing order model is applied to compute the wind-induced coupling responses of a membrane structure and obtains the significant parameters, such as wind pressure coefficients, re- sponses and power spectra. The results are coincident with those from full order model. The computing efficiency is compared with that of full order model. The results show that CPU time decreases about 55% while coupling itera-tion time diminishes about 60%. Results show that the reducing order models based on modal transformation is ap- plicable in wind-membrane interaction of membrane structures, with fairly high accuracy and efficiency.