关于结构振型参与系数和振型贡献的分析

Analysis of Mode Participation Factor and Modal Contribution of Structures

采用振型分解反应谱法求解多自由度弹性体系的地震反应时,为了在满足所需计算精度的前提下减少工作量,需要对振型数量进行合理的选择,而振型数的确定主要取决于结构各阶振型对总体反应的贡献。通过数学推导,对振型贡献及振型数量的选择问题进行了研究。首先,讨论了振型参与系数的性质,在此基础上给出了能够反映结构振型贡献参数的数学表达式,对这些参数的力学含义进行了解释,并给出了相关证明;其次,对有效质量法、振型位移控制法等基于不同振型贡献标准的确定振型数的方法进行了分析比较,指出了其合理性和不足。本文研究对进一步理解结构振型贡献和振型数的选择问题具有一定的理论意义。

In the earthquake response analysis of an elastic multi-degree-of-freedom structure, the modesuperposition response spectrum method can be applied. It is necessary to select an appropriate number of vibration modes in order to obtain satisfactory results with reduced computational work. The number of vibration modes to be included depends on the modal contribution to the total response of the structure due to earthquake excitation. By mathematical derivation, the problems of modal contribution and computational method on the reasonable mode number are analyzed and studied. First, the properties of modal participation factor are discussed. The mathematical expressions of several parameters for structural modal contribution are given and the mechanical meanings are interpreted by theoretical proof. Further, computation methods on the reasonable mode number including effective modal mass method and modal displacement control method are evaluated and compared with each other. This research can provide a theoretical basis and reference for further understanding the structural modal contribution and selecting the reasonable mode number for the earthquake response analysis of structures.