基于Rayleigh阻尼模型的竖向混合结构设计阻尼比研究

RESEARCH ON EQUIVALENT DAMPING RATIO OF VERTICALLY MIXED STRUCTURES BASED ON RAYLEIGH DAMPING MODEL

由两种或两种以上不同材料串联组成的竖向混合结构,结构阻尼特征空间分布存在明显差异,这使得整体结构地震作用下的动力响应难以估计。对于结构初步抗震设计,特别是采用常规商用软件进行分析时,往往需要确定结构的阻尼比系数,这就需要引入等效阻尼比的概念。该文基于Rayleigh阻尼模型,推导了竖向混合结构在谐振荷载下的近似解耦位移响应误差函数,由随机地震动激励下位移响应误差最小,得到最佳等效阻尼比计算公式。将竖向混合结构等效成两自由度结构模型,每一自由度的动力特性由对应子结构的主频确定,对该两自由度模型进行不同子结构特性下最佳等效阻尼比分布和位移响应误差分析。结果表明:采用该文给出的最佳等效阻尼比,能更合理地预测结构在地震作用下的位移响应;而简单地采用单一材料结构阻尼比进行分析,可能会过高或过低估计结构耗能能力。

Damping property of vertically mixed structure, which vertically consists of two or more types of materials, is difficult to identify due to the difference in energy dissipation of different parts of the structure. To perform fundamental structure design, especially using commercial software, the damping ratio is essential, and the concept of equivalent uniform damping ratio is commonly accepted. In this paper, based on the Rayleigh damping model, a formula was proposed for calculating the relative steady-state error of vertically mixed structure by means of decoupling approximation. And then, the optimum equivalent damping ratio was obtained under random ground motion. A vertically mixed structure was typically represented by an equivalent two degree-of-freedom （DOF） oscillator. Its dynamic characteristics were determined by those of sub-structures. The distribution of equivalent damping ratio and the displacement error of this 2-DOF oscillator were plotted as the function of structural parameters. Numerical results demonstrate that the procedure proposed in this paper generates more accurate displacement responses under seismic excitations, while in contrast, the use of single material damping ration may usually lead to a under- or over-estimate of the capability of energy dissipation.