TMD结构基于双过滤白噪声随机地震激励的系列响应的简明解

针对既有方法在分析TMD结构基于双过滤白噪声激励下结构响应的解表达式复杂而导致计算效率低的问题，提出了一种简明封闭解法。首先，利用双过滤白噪声谱的滤波方程与TMD结构的地震动方程联立，可将TMD结构基于复杂的双过滤白噪声激励准确的表示为易于求解的运动方程；其次，基于复模态法获得TMD耗能结构位移、层间位移的系列响应的复特征值及复模态参与系数；然后基于随机振动理论获得了TMD结构随机地震动系列响应（相对于地面绝对位移和结构层间位移）的功率谱统一形式的二次正交解，进而获得了TMD结构系列随机响应的0-2阶谱矩和方差的简明封闭解。最后研究了基于首超破坏准、Markov过程假设及串联失效模式的TMD结构的体系动力可靠度。通过一算例分析，表明了本文方法的正确性和高效性。因此，本文方法可用于各类线性结构基于复杂的随机地震动响应的分析及其动力可靠度计算。

New explicit solutions for random response of structure equipped with TMD subjected to Clough-Penzien excitation

In order to solve the problem that the solution expressions of TMD structure response based on Clough-Penzien excitation are complex and lead to low computational efficiency, a concise closed-form solution is proposed. Firstly, the filtering equation of double filtered white noise spectrum is combined with the ground motion equation of TMD structure, and the complex random seismic motion spectrum of TMD structure is accurately transformed into the ground motion based on the concise white noise spectrum. Secondly, the complex modal vibration eigenvalues and corresponding modal participation coefficients of TMD structure are obtained by using the complex mode method. Then, based on the random vibration theory, the quadratic orthogonal solution of the power spectrum unified form of the random ground motion series response (the absolute displacement relative to the ground and the inter-story displacement of the structure) is obtained based on the random vibration theory, and the concise closed-form solution of 0-2 order spectral moments and variance of the structural series response are obtained. Finally, the dynamic reliability of TMD structure based on first passage failure criterion, Markov process hypothesis and series failure mode is studied. An example is given to show the correctness and efficiency of the presented method. So, the method presented in the paper can be used to analyze and calculate the dynamic reliability of all kinds of linear structures based on complex random ground motion response.