摘 要：用有限元法计算出弹性支撑位于网格节点上时的结构固有频率后，可采用两种方法处理支撑位于单元内部时的情形。第一种是将弹性支撑等效到单元节点上再求解特征值，第二种是结合在单元节点处，频率关于支撑位置的一阶导数（即灵敏度）值，利用单元形函数进行插值计算。两种方法都可以在不重新划分网格的情况下，获得结构的固有频率。通过分析得出第一种方法适用性较好，但计算效率较低。第二种方法要求结构的振型保持不变。数值算例结果表明：当弹性支撑的刚度和位置变化不改变结构的振型时，两种方法都有较好的计算精度。

After computing the natural frequency of a beam or plate structure with attachment of an elastic support using the finite element method, two numerical methods are utilized to deal with the case of the support occurring in an element. The first approach is to solve eigenvalue problem with the equivalent stiffness matrix, while the other one interpolates the natural frequency with the sensitivities to the support position as well as the related element shape functions. Both methods can gain the frequency without re-meshing the structure. The former is more applicable but less efficient, whereas the latter has a limitation that the structural vibration mode should be unchanged when the support is changed. Illustrative examples show that both the methods have a high accuracy when the stiffness of the elastic support does not change the structural vibration mode in a region.