基于梯度投影法的高层建筑附加粘滞阻尼参数优化研究

Study on the Optimization of Additional Viscous Damping Parameters for Highrise Buildings Based on Gradient Projection Method

摘要:

基于有限元时程分析方法是高层结构振动控制优化设计的主要手段之一，但因其计算量大、耗时严重，应用于实际工程具有一定的局限性。为了克服这一缺陷，提出了一种高效的基于梯度投影法的粘滞阻尼器优化设计策略。考虑到地震动的不确定性，该策略以多条地震动作用结构得到的最大均值层间位移角为目标函数，限制总阻尼系数及各层阻尼系数上限值，通过振型分解法得到结构的层间位移响应，利用梯度投影法进行阻尼器参数优化。 在 8 度多遇地震作用下，分别采用振型分解法和有限元时程分析方法对 6 层剪切模型和 15 层平面框架结构进行粘滞阻尼器优化设计，模拟结果表明：两种方法得到的阻尼器优化参数基本一致。同时，对 6 层剪切模型进行敏感性分析及约束条件的参数分析，进一步验证了该优化策略的有效性。最后，将振型分解法得到的优化方案应用于 15 层平面框架，对无附加阻尼、三种工况优化前和优化后的结构进行弹塑性分析，并选取一条典型地震动对三种工况优化前和优化后的结构进行耗能分析，结果表明：该方案在 8 度罕遇地震作用下仍可靠有效；通过阻尼器参数优化， 可进一步降低结构最大层间位移角以及提高结构附加阻尼耗能占比。

Abstract:

Time-history analysis based on finite element models is a primary method for vibration control optimization design of high-rise structures. However, its application in practical engineering is limited due to high computational costs and time-consuming processes. To address this, this study proposes an efficient viscous damper optimization design based on the gradient projection method. Considering the uncertainty of earthquake ground motions, the strategy used the maximum mean inter-story drift angle obtained from multiple ground motions as the objective function, with constraints on the total damping coefficient and the upper limits of damping coefficients for each story. The inter-story drift response was obtained via the modal decomposition method, and damper parameters were optimized using the gradient projection method. Under frequent earthquakes of 8-degree intensity, a 6-story shear model and a 15-story planar frame structure were analyzed using both the modal decomposition method and finite element time-history analysis for viscous damper optimization. The simulation results showed that the optimized damper parameters obtained from the two methods were nearly identical. Additionally, sensitivity analysis and parameter analysis of constraint conditions were conducted on the 6-story shear model to further validate the effectiveness of the optimization strategy. Finally, the optimized scheme obtained from the modal decomposition method was applied to the 15-story planar frame. Elastic-plastic analyses were conducted for three cases: the structure without additional damping, and the structures before and after optimization under three working conditions. A typical earthquake ground motion is selected for energy dissipation analysis of the structures before and after optimization under the three conditions. The results confirmed the strategy's reliability under rare earthquakes (8-degree intensity). The optimized damper parameters can significantly reduce the maximum inter-story drift angle and increase the proportion of energy dissipated by additional damping.