多自由度体系的动力放大系数解析研究  

Analytical research on dynamic amplification factor of multi-degree-of-freedom system

作　　者：张超[1] 周桢干 赖志超 付馨迪 杨晓强 ZHANG Chao;ZHOU Zhengan;LAI Zhichao;FU Xindi;YANG Xiaoqiang(College of Civil Engineering,Fuzhou University,Fuzhou 350108,China)

机构地区：[1]福州大学土木工程学院,福建福州350108

出　　处：《振动工程学报》2025年第3期550-557,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金面上项目(52178464)。

摘　　要：在结构动力冲击响应分析中,通常采用动力放大系数(DAF)简化计算结构的动力响应。但是,目前工程结构中对DAF的取值还存在争议。针对此问题,本文推导了多自由度(MDOF)体系的DAF解析表达式,分析了DAF大于2.0的前提条件;分别通过单自由度(SDOF)体系和MDOF体系算例模型验证了解析表达式的准确性,解释了MDOF体系的DAF大于2.0的原因。基于所提出的DAF解析表达式分析了张弦梁剩余结构在断索冲击作用下的DAF分布规律。分析结果表明:当某一阶模态振型的分量与静力响应值反向时,张弦梁的DAF可能会大于2.0;即使在有阻尼情况下,张弦梁的DAF也可能会大于2.0。In the dynamic impact response analysis of the structure,the dynamic amplification factor(DAF)is usually used to simplify the calculation of the dynamic response of the structure.However,the size of DAF in engineering structures is still controversial.In order to solve this problem,the analytical expression of DAF of multi-degree-of-freedom system(MDOF)is derived in this paper,and the precondition of DAF greater than 2.0 is analyzed.The accuracy of the analytical expression is verified by the single-degree-of-freedom(SDOF)and MDOF example models,and the reason why the DAF of the MDOF is greater than 2.0 is explained.Finally,based on the DAF analytical method proposed in this paper,the DAF distribution law of beam string under cable breaking impact is analyzed.The analysis results show that when the contribution of a first-order modal shape is opposite to the static response,the DAF of the beam string may be greater than 2.0.Even for the damping system,the DAF of the beam string may be greater than 2.0.

关 键 词：多自由度体系 张弦梁 动力放大系数 断索冲击 

分 类 号：TU311.3[建筑科学—结构工程]