多振源作用下结构耦合响应的复模态CQC法  

A complex mode CQC method for calculating coupled responses under multiple vibration sources

作　　者：冯旭光 徐建 王翠坤[1,2] 陈才华 FENG Xuguang;XU Jian;WANG Cuikun;CHEN Caihua(China Academy of Building Research,Beijing 100013,China;CABR Technology Co.,Ltd,Beijing 100013,China;China National Machinery Industry Corporation,Beijing 100080,China)

机构地区：[1]中国建筑科学研究院有限公司,北京100013 [2]中建研科技股份有限公司,北京100013 [3]中国机械工业集团有限公司,北京100080

出　　处：《建筑结构学报》2024年第11期80-91,共12页Journal of Building Structures

基　　金：中国建筑科学研究院有限公司院士工作站科研基金项目(20220122330730021),中国建筑科学研究院有限公司科研基金项目(20220122330730017);中建研科技股份有限公司科研项目(20221902977130039)。

摘　　要：工程结构在使用中可能受到多种振源激励,但现有计算方法尚未充分反映多振源作用下响应之间的耦合效应。为了解决该问题,可以将实际工程中的不确定性振源视作随机过程,并引入可以精确考虑响应耦合关系的CQC法。基于复模态叠加法和随机振动理论,提出了可以同时考虑多振源与非比例阻尼结构的广义CQC法,即多输入复模态CQC法,并给出了功率谱矩、协方差和矩阵乘法三种形式。理论推导与算例分析表明:相比于传统的CQC系列方法,多输入复模态CQC法的适用性更加广泛,在一致输入或比例阻尼条件下也可以退化为传统的CCQC法和CQC法;对于不同程度的非比例阻尼结构,多输入复模态CQC法均有良好的精度和稳定性;随着非比例阻尼程度的提高,基于实模态的强制解耦CQC法已无法反映结构的真实振动特性,导致多振源作用下的响应被严重低估。Engineering structures may be subjected to various vibration sources in service.However,current computational methods have not adequately captured the coupling effects between responses under multiple vibration sources.To address this issue,this study proposed to treat the uncertain vibration sources in practical engineering as stochastic processes and introduces the CQC method,which can accurately consider the coupling responses.Based on the complex mode superposition method and random vibration theory,a generalized CQC method that simultaneously accounts for multiple vibration sources and non-proportional damping structures was proposed,namely,the multi-input complex mode CQC method.Three forms of the formula were provided,including power spectral moment,covariance and matrix multiplication.Theoretical derivation and numerical examples demonstrate that the new approach exhibits broader applicability compared to traditional CQC series methods.The proposed method can also degenerate into the conventional CCQC and CQC methods for scenarios of synchronous inputs or proportional damping.For structures with different degrees of non-proportional damping,the multi-input complex mode CQC method achieves high accuracy and stability.As the degree of non-proportional damping increases,the real mode-based forced decoupling CQC method fails to reflect the true vibrational characteristics of structures,leading to a significant underestimation of responses under multiple excitation sources.

关 键 词：多振源 CQC 复模态 随机振动 多输入复模态CQC法 强制解耦 

分 类 号：TU973.23[建筑科学—结构工程] TU311.3