混联Ⅰ型惯容系统基于李鸿晶谱的地震响应分析

针对设有混联Ⅰ型惯容系统的耗能结构基于李鸿晶谱的响应分析较为繁琐的问题，提出求解地震响应的简明封闭解法，并研究了惯容系统基本参数对减震性能的影响。首先，建立惯容系统和结构之间的微分型本构关系，并运用复模态法和虚拟激励法获得结构系列响应的统一解。其次，将结构系列响应的功率谱密度函数精确转化为复特征值及结构自振频率平方和表示的二次分解式，进而获得响应0阶～2阶谱矩的简明封闭解。最后，通过数值算例验证了所提方法的正确性及计算的高效性，对惯容系统参数的研究表明，当惯容系数和阻尼系数越大，结构减震效果越好，而刚度系数对结构的减震效果取决于惯容系统名义圆频率与结构自振圆频率的比值，当两者比值为0.9时减震效果最好。

Seismic response analysis of series-parallel-I inerter system subjected to Li Hongjing spectrum excitation

To address the problem that the response analysis of energy-dissipating structures with a series-parallel-I inerter system (SPIS-I) under the random excitation based on Li Hongjing spectrum,a concise closed solution of the response spectral moment is proposed,and the influence of the main parameters of the SPIS-I on the damping performance is studied.Firstly,the differential relation between the SPIS-I and the structure is established,and the complex modal method (CMM) and the Pseudo-excitation method (PEM) are applied to obtain a unified solution for the series response of the structure.Secondly,the power spectral density function (PSDF) of the structural series response is accurately transformed into a quadratic decomposition expressed as a sum of complex eigenvalues and the square of the natural frequency of the structure,and then a concise closed solution of the 0~2 order spectral moments of the response is obtained.Finally,the correctness and computational efficiency of the proposed method are verified by numerical simulations.The study of the parameters of the SPIS-I shows that the larger the inertial capacity coefficient and damping coefficient the better the damping effect of the structure,but the vibration reduction effect of the stiffness coefficient on the structure depends on the ratio of the nominal circular frequency of SPIS-I to the natural frequency of the structure,and the damping effect is best when this ratio is 0.9.