基于位移激励的高层结构地震反应分析高阶振型修正法

Due to the deletion of the long period component of the ground motion records, the seismic response of high-rise structures cannot be obtained accurately by the analysis method based on the acceleration excitation anymore. In other words, aseismic design has not been able to guarantee the seismic safety of the structure. To solve this problem, this project will develop an analysis method of the seismic response of high rise structures that was based on displacement excitation. The combination of theoretical analysis, numerical simulation and experimental verification will be applied to study the influence mechanism of the difference of dynamic equilibrium equation on the seismic response of structures. Then the high-rise structural earthquake response based on displacement excitation will be constructed to analyze higher order mode corrections. Which will reveal the influence mechanism of the higher order mode corrections on computational accuracy and the influence mechanism of long period component of seismic motion on seismic response of high rise structures. Meanwhile, the validity of the new method will be tested by the model dynamic test. In this study, the deletion of the long period component of the ground motion will be solved based on the seismic records to acquire displacement excitation. And the Ritz vector will be used to solve the differential equation of truncated mode, which will amend the effect of higher modes of dynamic and the pseudo static displacement of ground. Which will realize the great improvement of the analysis precision under the condition of less vibration mode, this provides the advanced and effective theory and method to get accurate seismic response of high-rise structures, and it also provides foundation to reveal the seismic response characteristics and failure mechanism of high rise structures and develop new reasonable aseismic design method for high-rise buildings.

受地震动记录长周期成分缺失的限制，基于加速度激励的分析方法不能准确地获得高层结构地震反应，抗震设计已无法保证结构的地震安全性。针对此问题，本项目发展基于位移激励的高层结构地震反应分析方法。采用理论分析，数值模拟和试验验证相结合的方法，研究动力平衡方程差异对结构地震反应差别影响机理，构建基于位移激励的高层结构地震反应分析高阶振型修正法，揭示高阶振型修正对计算精度影响机理，以及地震动长周期分量对高层结构地震反应影响机理，通过模型振动试验，验证方法的有效性。在本项目研究中，通过采用测震记录获取位移激励以解决地震动长周期分量缺失问题；通过Ritz向量求解截断振型对应微分方程，获得高阶振型动力效应和修正地面拟静力位移，实现在使用较少振型前提下大幅提升分析精度，为准确获得高层结构地震反应提供先进有效的理论和方法，也为揭示高层结构地震反应特性和破坏机理，发展合理的高层建筑抗震设计方法奠定基础。

结构地震反应分析是结构抗震设计的重要基础，受加速度记录中长周期成分缺失的限制，基于加速度激励计算的长周期结构地震反应计算结果精度不高。本项目从使用测震记录计算结构地震反应和求解基于位移激励的动力平衡方程方法两方面开展研究。基于加速度激励动力平衡方程和位移与速度激励动力平衡方程的杜哈梅尔积分解，建立忽略与地面速度相关阻尼项时位移与速度激励结构地震反应差别函数。利用空间状态法和Ritz向量，推导求解位移与速度激励动力平衡方程新方法，给出选取参与计算振型数量方法，降低截断振型对动力反应贡献。基于拉普拉斯变换和双线性变换，构建用于修正窄频速度地震记录的传递函数，实现从测震记录中获取用于计算结构地震反应的地震激励。以振动台实验中采集的加速度、速度和位移激励作为地震激励计算结构地震反应，验证本项目中推导的求解位移与速度激励动力平衡方程方法的准确性，以及测震记录用于计算结构地震反应的可行性。项目研究成果为提高位移与速度激励结构地震反应分析方法的计算精度提供理论支撑，为扩展地震激励来源，将测震记录用于结构地震反应分析奠定理论基础。在项目执行期间，发表高水平学术论文4篇，其中SCI检索期刊文章1篇，北大中文核心期刊文章3篇；申请国家发明专利1项；获批软件著作权6项；培养硕士研究生3名。