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提出了两种基础振动分析的高阶集中参数模型。首先将近似基础频率响应的复频率有理函数展开为连分式;然后与模型动力刚度方程的连分式表达对比获得模型参数。相比于现有的高阶集中参数模型,两类模型容易扩展到高阶,其物理结构简洁并与所分析的问题无关。此外,由于模型的动力方程具有二阶时间导数项,因而应用本文模型的结构–基础–土系统可以采用显式时间积分求解。通过分析弹性地基表面半无限杆问题,并与Wu-Lee集中参数模型的结果进行比较,验证了本文模型的有效性。
Two kinds of high-order lumped parameter models of fundamental vibration analysis are proposed. Firstly, the complex frequency rational function of approximate fundamental frequency response is expanded into continuous fraction. Then the model parameters are obtained by comparing with the continuous fractional expression of the dynamic stiffness equation of the model. Compared with the existing high-order lumped parameter models, the two types of models are easy to extend to higher order, and their physical structure is simple and has nothing to do with the analyzed problems. In addition, since the dynamic equation of the model has second-order time derivative terms, explicit time integral solution can be applied to the structure-foundation-soil system applying this model. The validity of this model is verified by analyzing the semi-infinite bar on the elastic foundation surface and comparing with the Wu-Lee lumped parameter model.