基于随机模型的覆雪屋盖风致动力失稳机理研究

Millions of roofs have collapsed under snowstorms in China these years. Forensic engineering indicates that structural instability under non-uniform snow is the most important reason. Snow on the roof can be seen as a part of the variable mass system of the roof. Therefore, when snow on the roof drifts under strong wind actions, the dynamic characteristics of the roof, such as the distribution of structural mass and natural frequencies, will change, which may causes the roof to be subjected to the most unfavorable dynamically unstable state during the process of snow drifting. However, dynamic instability analysis under deterministic unsteady wind loads baffles the acquirement of minimum critical wind speed for dynamic instability because wind action is essentially a random process. In this study, non-uniform snow distribution on roofs are obtained by CFD simulation and stochastic model for dynamic instability of snowy roofs under random wind loads is built according to theory of nonlinear random vibration. Based on the stochastic model, influence of non-uniform snow distribution on the dynamic instability boundary of the roof is explored and the corresponding influence function is constructed. Subsequently, wind tunnel tests on the aeroelastic model of a real double-layer reticulated shell are carried out to verify the proposed theoretical method, and reasons leading to the difference between numerical and experimental dynamic instability critical wind speed are analyzed in detail. Based on the stochastic model and aeroelastic tests, the effects of structural dynamic parameters and wind loading properties on the structural dynamic instability region, and the nonlinear vibration characteristics of the roof in the process of dynamic instability are investigated deeply to reveal the dynamic instability mechanism of snowy roofs in strong wind environment. After this study, it's expected that the dynamic instability mechanism of roofs under simultaneous actions of wind and non-uniform snow be clearly understood, the theoretical basis for roof design considering both wind and snow loads be established, and the safety of roofs in snowstorms be guaranteed to some extent.

积雪漂移改变了屋盖结构的动力特性，使屋盖处于动力稳定最不利状态而发生动力倒塌。本项目首先基于非线性随机振动理论建立风场中覆雪屋盖动力失稳分析的随机模型，基于该模型构造积雪分布对屋盖动力稳定性的影响函数，从而建立随机风荷载下覆雪屋盖动力失稳分析的概率评价方法。然后以一实际双层柱面网壳为例，通过气弹模型风洞试验来验证所提出的理论分析方法的有效性。基于随机模型和试验方法来细致分析结构动力参数和风荷载特性等对屋盖动力稳定边界的影响规律，通过响应谱、相平面、HHT等方法分析屋盖动力失稳过程中的非线性振动特性，从而揭示覆雪屋盖的风致动力失稳机理。通过本项目将提出随机风场中覆雪屋盖动力失稳的分析方法，为屋盖结构的抗风雪设计提供理论依据，保障屋盖结构在雪灾中的安全使用。

本项目首先建立了梁、拱等构件在风荷载样本下的动力稳定性分析方法。基于Bolotin方法建立了表征结构系统动力稳定性的Mathieu-Hill方程，通过特征值方法求解边界频率方程获得了动力不稳定域的边界。并通过Runge-Kutta法计算结构的风振响应时程，以验证不稳定域结果的准确性。对于拱构件，还讨论了荷载形式、拱顶配重、阻尼等参数的影响。.为了验证动力稳定性数值结果的可靠性，本项目进行了动力稳定性试验研究。采用德国APS激振器来产生外部激励，采用丹麦B&K信号采集系统来记录结构的振动响应，并自主设计了激励传递装置。试验测试了模型的实际模态参数，通过扫频激励获得了动力不稳定域的边界，与数值计算结果基本一致。.进一步将风荷载看作随机荷载，获得了系统的必然稳定条件，并采用Schwarz不等式获得了随机稳定边界的计算公式。以双层柱面网壳屋盖为例，基于CQC法和LRC法讨论了其风压分布、风振响应和等效静力风荷载特性，进一步分析了该屋盖结构的风致随机稳定性。.基于CFD方法模拟拱形屋盖上的积雪漂移现象，获得了屋面积雪不均匀分布的形式。研究了均匀、不均匀雪荷载和随机风荷载共同作用下屋盖的动力稳定性，发现均匀积雪下动力失稳杆件的数量反而少于仅有风荷载的情况，但某些截面积较大的杆件发生了动力失稳。而在不均匀积雪下，失稳杆件数量多于仅有风荷载的情况。此外，结构阻尼的增加使失稳杆件数量减少，构件尺寸对不稳定域的范围产生显著影响。存在不均匀积雪时，屋盖动力稳定性随平均风速并不出现规律性变化，而失稳杆件总数随风荷载脉动分量的增加而显著增加。