地震作用下二维场地模态叠加等效线性化方法

MODAL-SUPERPOSITION-BASED EQUIVALENT LINEARIZATION METHOD FOR SEISMIC RESPONSE ANALYSIS OF TWO-DIMENSIONAL SITES

为快速进行多维场地地震反应分析,将模态摄动法和模态叠加法相结合,提出了一种非比例滞后阻尼二维场地的模态叠加等效线性化计算方法。在该方法中,根据原系统的模态分析结果,利用模态摄动法得到迭代刚度修正后新系统的模态,然后,采用模态叠加法实现非比例复阻尼体系运动方程中矩阵维数的降阶,形成广义坐标耦合和解耦的模态叠加等效线性化法,在此基础上,进一步讨论了阻尼矩阵耦合系数的影响。随后,以杭州某一工程场地为例,研究不同输入地震动幅值下,场地水平加速度动力放大系数随地震动幅值的变化规律,并与二维频域等效线性化计算结果比较,验证所提算法的精度和有效性。计算结果表明:采用广义坐标耦合的模态叠加法,不同地震动输入幅值下,计算误差均小于5%;广义坐标解耦方法所得地表加速度放大系数的计算误差随耦合因子的增大而增大;当地震动幅值小于0.1 g时,可采用强制解耦方法计算场地地震反应。从计算效率看,模态叠加等效线性化法和二维频域等效线性化法的迭代次数基本相同,但计算时间约为频域等效线性化法的一半。

A mode-superposition-based equivalent linearization method was proposed based on the mode perturbation method and mode superposition method for fast seismic response analysis of two-dimensional sites with non-proportional hysteresis damping.In this method,based on the modal analysis results of the original system,the eigenvalue of the new system can be obtained by the modal perturbation method with modified iterative stiffness.Based on the modal superposition method,the dimension of matrices in the motion equation of a non-proportional complex damping system is reduced,and the modal-superposition-based equivalent linearization method of generalized coordinate coupling and decoupling are formed.Then,the influence of coupling coefficients in a damping matrix is discussed.The variation law of the horizontal acceleration amplification factor under different input ground motion amplitudes is studied by an engineering site in Hangzhou.And the results are compared with the two-dimensional frequency domain equivalent linearization to verify the accuracy and effectiveness of the proposed method.The numerical analysis results show that:the calculation error is less than 5%under different input amplitudes with the generalized coordinate coupled method.But by the generalized coordinate decoupling method,the calculation errors increase with the increase of the coupling factor.Hence,when the ground motion amplitude is less than 0.1 g,the generalized coordinate decoupling method can be used to calculate the site seismic response.For the computational efficiency,the iterative times of mode-superposition-based equivalent linearization method is basically the same with that of the two-dimensional frequency-domain equivalent linearization method,but the computational time is about half that of the frequency-domain equivalent linearization method.