基于三级数法的高耸结构弛振分析

Analysis and Three-Series Solution to High-Rise Structure's Galloping Oscillation

应用三级数法求解横风向的弛振的非线性运动微分方程,得到了三维结构的简明的稳态响应和临界风速表达式.从理论上阐述了可能发生弛振的关键因素:即升力线斜率为较大的负值,也就是只有非流线形的剖面,形成气流分离的结构才可能出现.形成不稳定的充分条件是结构的质量轻、刚度小、阻尼小、或是高度(长度)大、长细比大.非线性速度平方项不影响临界风速值,但它使弛振的稳态响应加大,使频率减小,临界风速只取决于速度的一次项.而且弛振响应在最初的几分钟也几乎完全取决于速度的一次项.算例表明,该方法是有效的,可以很方便的应用到工程实际当中.

The three-series solution is taken up to the nonlinear differential equation of the galloping movement caused by the cross wind force acting on a high-rise structure, thus giving a reduced 3D expression in terms of steady-state response and critical wind speed. Analyzes theoretically the vital factors which may lead to the occurrence of galloping oscillation as follows. The structure may form an airflow breakaway only if the slope of airflow lifting line is of a great negative value, i.e. , the structure has a non-streamlined cross-section. The sufficient conditions to an instable structure are heavy mass, small stiffness and damping and tall with high aspect ratio. The equations derived shows that the nonlinear quadratic term of wind speed does not affect the value of critical wind speed but intensify the steady-state response and decrease the response frequency. It implies that the critical wind speed just depend on the first degree term of the speed, on which the initial few minutes to response to galloping oscillation almost depend. A numerical example indicates that the approach proposed is effective and easy to apply to engineering practice.