基于Kanai-Tajimi谱六参数黏弹性耗能结构地震响应的简明封闭解

Concise and closed solution of the seismic responses of viscoelastic energy dissipation structures under Kanai-Tajimi spectrum excitation

频域法在计算线性系统随机响应时应用较广泛,但其显著缺点为:计算多自由度动力系统随机响应功率谱无显示封闭解;获得结构响应的方差和谱矩需要数值积分,分析精度和效率受积分步长和积分区间影响较大。基于以上问题,研究了六参数黏弹性耗能多自由度结构基于Kanai-Tajimi谱地震作用下平稳响应的解析解法。运用该方法对一榀5层建筑结构进行分析,获得了线性多自由度耗能结构地震动系列响应方差及0~2阶谱矩的简明封闭解,并将其与虚拟激励法进行对比分析。研究表明,简明封闭解法是一种非常有效的计算线性多自由度系统随机稳态响应的简明解法。

Frequency domain methods are widely used in the calculation of random responses of linear systems,but its significant disadvantages are as follows:there is no closed solution to calculate the power spectrums of random responses of multi degrees of freedom dynamic systems,numerical integration is needed to obtain the variances and spectral moments of structural responses,and the analysis accuracy and efficiency are greatly affected by the integration step and integration interval.Aiming at the above problems,the analytical solution of the steady response of a six parameters viscoelastic energy dissipation multi-degree-of-freedom structure under Kanai-Tajimi spectrum excitation was studied.A 5-story building structure was analyzed as an example,and the concise closed form solutions of a series of response variances and 0-2 order spectral moments of linear multi degrees of freedom energy dissipation structures were obtained.The results were compared with those by the pseudo excitation method.The results show that the simplified closed form method is a very effective method to calculate the stochastic steady state responses of linear multi degrees of freedom systems.