摘要
本文从理论上研究了用有限模型和无限模型模拟无限域中的波动问题时所存在的差异。文中给出的有关分析结果表明:(1)在弹性介质情况下,无限摸型可对系统给出复数形式的复频响应函数或位移分布,这与无限域中波动问题的解析解相吻合;而有限模型只能对系统给出实数形式的复频响应函数,这与无限域中波动问题的解析解不相符合。说明在弹性介质情况下,有限模型不能反映无限域中的波动特性。(2)在粘弹性介质情况下,即使有限地基范围取得较大,有限模型所给出的数值结果与解析解的误差仍然很大,说明在用有限元法对无限域问题进行动力计算时,一般不宜采用有限模型,而应采用无限地基模型。
The theoretical analysis on the differences between finite model and infinite one in the infinite domain wave problems is studied in this paper. Some analytical results given here illustrate the conclusions as follows: (1) In the case of elastic media, the complex frequency response functions or displacements of the complex forms can be obtained by using infinite models. These have good coincidances with theoretical solutions. But the complex frequency response functions of the complex forms can not be got by using finite models. These facts show that the finite models can not represent the wave propagation characteristics in the infinite domain foundations. (2)In the case of viscoelastic media, althongh the large range modelled by finite elements is taken, great errors still exist between the finite model results and the analytical ones. These facts show that we should use infinite models instead of finite ones for modelling infinite domain wave problems.
