地震多点反应谱模型存在缺陷的改进与验证

推导出基于位移和位移 速度输入模型的多点反应谱。阐述了基于位移输入模型所导出反应谱的缺陷及其逻辑必然性，说明了基于加速度模型导出的多点反应谱计算结果有效的偶然性、必然性及其适用范围，并给出数值算例予以验证。分析表明：基于位移 速度导出的多点反应谱理论严格；基于位移输入模型导出的多点反应谱会导致底部单元内力不收敛，计算结果不合理；基于加速度输入模型导出的多点反应谱结果虽然有效，但适用于经典阻尼体系，在推导过程中的忽略项在理论上具有误差相互抵消的特点。

Defect,Improvement and Verification of Seismic Multi-supported Response Spectrum Model

The multiple support response spectrum (MSRS) theory formula based on displacement and the displacement velocity model are induced and given. Then, the irrationality and unconvergency of the responses, which are calculated from the displacement-multiple support response spectrum (D-MSRS) model and derived from the current displacement input model, are explained. This paper also addresses the accidence in deducing processing, and necessity in calculation results of MSRS deduced from the acceleration model. The deriving processing and numerical results show that the displacement velocity-multiple support response spectrum (DV-MSRS) is strict and logical. The D-MSRS can induce the unreasonable and unconvergent internal force of the bottom element. The reasonability of A-MSRS (acceleration-multiple support response spectrum) derived from the two negligible terms can be counteracted, but is suitable for a classic damping system.