基于等效黏性阻尼模型的非比例阻尼体系反应谱CCQC法  

A RESPONSE SPECTRUM CCQC METHOD FOR NONPROPORTIONALLY DAMPED SYSTEMS BASED ON EQUIVALENT VISCOUS DAMPING MODEL

作　　者：孙攀旭 杨红[2,3] SUN Pan-xu;YANG Hong(School of Civil Engineering,Zhengzhou University,Zhengzhou 450001,China;School of Civil Engineering,Chongqing University,Chongqing 400045,China;Key Laboratory of New Technology for Construction of Cities in Mountain Area of the Ministry of Education,Chongqing University,Chongqing 400045,China)

机构地区：[1]郑州大学土木工程学院,郑州450001 [2]重庆大学土木工程学院,重庆400045 [3]重庆大学山地城镇建设与新技术教育部重点实验室,重庆400045

出　　处：《工程力学》2021年第10期160-172,180,共14页Engineering Mechanics

基　　金：国家自然科学基金项目(52078078)。

摘　　要：由不同材料组成的混合结构,其阻尼矩阵不再满足与质量矩阵、刚度矩阵的比例关系,具有非比例特性。我国设计规范中常用的振型分解反应谱法是基于比例阻尼建立的,并不严格适用于计算非比例阻尼体系的地震作用效应。该文在基于等效黏性阻尼模型的复模态叠加法基础上,结合虚拟激励法和平稳随机理论,推导了基于等效黏性阻尼模型的反应谱CCQC(Complex Complete Quadratic Combination)法实数表达式,建立了一种解决非比例阻尼混合结构的地震作用效应计算问题的理论方法。算例分析表明:与基于分块Rayleigh阻尼模型的反应谱CCQC法相比,该文建立的基于等效黏性阻尼模型的反应谱CCQC法直接依赖于结构的质量、刚度和阻尼参数,不受振型组合的影响,具有计算结果唯一的优点,且仅涉及位移相关系数的计算;与基于能量法的反应谱CQC法相比,基于等效黏性阻尼模型的反应谱CCQC法可有效考虑结构的非比例特性,适用于非比例特性较强的混合结构。The damping matrix of a hybrid structure no longer satisfies the proportional relationship with its mass matrix and its stiffness matrix,which has non-proportional characteristics.Therefore,the common seismic design method of the design code,which assumes of proportional damping,is not strictly applicable to the calculation of the structural earthquake effects of non-proportionally damped systems.On the basis of the complex mode superposition method based on the equivalent viscous damping model,combined with the virtual excitation method and the stationary random theory,the corresponding real value form formulas are derived for the response spectrum complete quadratic combination(CCQC).Then a theoretical method is proposed,which could be used directly to calculate the earthquake effects of non-proportionally damped hybrid structures composed of different materials.The cases show that:compared with the response spectrum CCQC method based on the Rayleigh damping model of the substructures,the response spectrum CCQC method based on the equivalent viscous damping model directly depends on the quality,on stiffness,and on damping parameters,which is not influenced by the mode combination.The corresponding calculation results are unique,and the calculation of the displacement correlation coefficient is only involved.Compared with the response spectrum CQC method based on the energy method,the response spectrum CCQC method based on the equivalent viscous damping model can effectively consider the non-proportional characteristics of the hybrid structures and is suitable for the hybrid structures with significant non-proportional damping characteristics.

关 键 词：非比例阻尼 等效黏性阻尼 反应谱CCQC法 相关系数 地震作用效应 

分 类 号：TU311.3[建筑科学—结构工程]