用于固有振动分析的动态有限元阻抗矩阵

目前所用的动态有限元通常是以质量矩阵和刚度矩阵的频率展开式来表述的．本文提出单一的阻抗矩阵展式，从而无需分别导出质量阵和刚度阵的展开项，使建立动态有限元的工作大为简化，并可避免出现不正确的刚度阵展开项的矛盾。此外，还指出质量阵、刚度阵展开项和阻抗阵展开项之间存在一定的关系．对长方形弯曲板元，导出了直到二阶的阻抗阵展开项，并作为算例，计算了一个正方形悬臂板的固有频率。

THE IMPEDANCE MATRIX IN FINITE DYNAMIC ELEMENT METHOD FOR FREE VIBRATION ANALYSIS

Finite dynamic elements are usually expressed by frequency expansions of both mass and stiffness matrices. In the present paper a single impedance matrix expansion is proposed, hence there is no need to derive mass and sti- ffness matrix expansion terms separately and the formulation of a finite dy- namic element is simplified significantly. Furthermore, it is avoided that so- me incorrect term may be introduced in stiffness matrix expansion. In addit- ion. it is indicated that there are definite relations between the mass-stiffn- ess matrix pair and the impedance matrix expansion terms. For a rectangular bending plate element, the impedance matrix expansion terms to the second order are derived and, as an illustrative example, applied to the calculation of natural frequencies of a square cantilever plate.