混合基础隔震耗能结构基于Clough-Penzien谱的地震动响应的简明解析解

在基础隔震层设置侧向黏弹性阻尼器组成混合基础隔震体系,可有效降低基础隔震结构过大的侧移,然而此类结构基于Clough-Penzien谱(C-P谱)的随机地震动响应解法较为复杂,提出了一种简明解析法。首先利用滤波方程,将混合基础隔震耗能结构基于C-P谱的地震动精确的转化为基于白噪声激励的地震动;其次运用复模态法获得耗能结构随机地震动系列响应(相对于地面位移及速度、层间位移及其变化率)协方差的统一简明表达式;然后基于随机振动理论,获得耗能结构地震动系列响应的方差及0-2阶谱矩的简明解析解;最后研究了基于首超破坏准的混合基础隔震结构的动力可靠度。将该方法应用于一算例,并与虚拟激励法进行对比分析,研究表明:该方法计算响应方差和谱矩为解析解,而虚拟激励法是数值解;同时也验证了混合基础隔震耗能结构能有效降低结构侧移及提高结构体系的可靠度。

Concise analytical solution to seismic response of hybrid base isolation energy-dissipation structure based on Clough-Penzien spectrum

The lateral viscoelastic damper is set at base isolation layer to form a hybrid base isolation system to effectively reduce excessive lateral displacement of the base isolation structure.However,this kind structure’s random seismic response solving method based on Clough-Penzien spectrum(C-P spectrum)is more complicated.Here,a simple analytical method was proposed.Firstly,using the filtering equation,the ground motion exerted on a hybrid base isolation energy-dissipation structure based on C-P spectrum was accurately converted into that based on white noise excitation.Secondly,the complex mode method was used to obtain the unified concise expression for the covariance of random seismic series responses of the hybrid base isolation structure including displacement and velocity relative to ground surface,inter-layer displacement and its change rate.Thirdly,based on the random vibration theory,the concise analytical solutions to variances and 0-2 order spectral moments of random seismic series responses of the hybrid base isolation structure were obtained.Finally,the dynamic reliability of the hybrid base isolation structure based on the first passing failure criterion was studied.The proposed method was applied in an example.The contrastive analysis was performed for this method and the virtual excitation method.Results showed that seismic response variances and spectral moments obtained with the proposed method are analytical solutions,while those gained with the virtual excitation method are numerical ones;the hybrid base isolation energy-dissipation structure can effectively reduce its lateral displacements,and improve its dynamic reliability.