隔震结构基于Kanai-Tajimi平稳激励谱矩的简明解析解

Simple analytical solution for spectral moments of isolated structures based on Kanai-Tajimi stationary excitation

隔震结构基于Kanai-Tajimi激励下的地震动位移、层间剪力及其谱矩的分析,是计算其动力可靠度的前提,针对传统方法计算上述响应非常复杂的问题,提出了一种简明解析解法。由于Kanai-Tajimi谱可用基于白噪声随机激励的二阶滤波方程表示,提出将其与隔震耗能体系地震动方程联立,进而将基于Kanai-Tajimi随机激励的地震动转为基于白噪声激励的地震动响应。利用复模态方法并基于随机振动理论获得隔震体系随机地震动激励下的位移及速度、层间剪力及其速度的协方差简明表达式,利用Wiener-Khinchin定律,获得位移及层间剪力的功率谱简明表达式。最后基于平稳谱矩的定义,研究了可靠度分析的0阶~2阶谱矩的简明解析解。算例表明本文方法具有准确性及简洁性。

The analysis of seismic displacement, velocity and spectral moment of isolated structures based on Kanai-Tajimi spectrum is the premise of calculating their dynamic reliability. To solve the complex problem of calculating the above-mentioned response values by traditional methods, a concise analytical solution is proposed. Kanai-Tajimi seismic random excitation can be expressed as the response of white noise by a second-order differential equation, so the dynamic equations of isolated systems are established by combining Kanai-Tajimi seismic excitation with isolated structures. The response analysis of isolation system based on Kanai-Tajimi excitation is transformed into response analysis based on white noise excitation by complex mode method. Based on the concise characteristics of white noise excitation, the covariance expressions of displacement and velocity ofisolation system are obtained. The concise expression of power spectrum of displacement is expressed by using Wiener-Khinchin law, and the concise analytical solutions of 0-2-order spectral moments of reliability analysis are gained. An example is given to show the accuracy and simplicity of the proposed method.