结构高频振动模态密度的点导纳数值计算

Numerical Analysis of the Modal Density of the Structure Systems in High Frequency Region by the Driving-Point Functions

从测试模态密度的点导纳法原理出发,研究了结构模态密度的数值计算方法。通过有限元谐响应分析,得到结构的响应位移和响应速度,并计算出点导纳的实部,然后利用点导纳实部与模态密度的关系得到结构的模态密度。用这种方法对梁、平板、圆柱壳的模态密度进行计算,与理论值或AutoSEA2计算结果的比较表明了点导纳数值计算方法在高频范围内求解精度较高,且避免了复杂的解析计算过程,是一种简便有效的求解模态密度的方法。

Experimental procedures that are based on the theoretical relation between the modal density and the real part of a driving-point function, averaged in space and frequency, are the main method to define the modal density. Based on the experimental method , a numerical analysis of the modal density of the structure systems is discussed. Giving a certain driving force on the structure, the displacement and the velocity can be obtained by the harmonic response of the finite element analysis, then the driving-point function is certain by its definition. The modal densities of a simple beam, a flat plane and a thin-walled cylinder are discussed by this numerical method. The computed results are compared with the theoretical results. For higher frequencies the results are in fairly good agreement.