基于有限元的有限板面导纳的数值计算

Calculation of Area Mobility of a Finite Plate Based on Finite Element Method

利用有限元方法对有限薄板结构在均布力作用下的二维面导纳进行数值计算的方法。根据有限元模型的特点,利用有效点导纳的原理,推导出均布力作用下面导纳的计算方法。并将通过有限元方法获得的计算结果与同样模型条件下根据理论公式计算获得的结果进行比较,证明有限元方法简单可行。还研究有限元计算中一些主要参数对计算结果的影响,为今后进行同类有限元计算提供参数设置的参考依据。

Area mobility is a new concept in the investigation of structural vibration, especially in that of the theory of vibration isolation. No matter in the theoretic calculations, experimental research and numerical calculations of area mobility, all of the work are just at the beginning. It is necessary to investigate the method of the numerical calculation to meet the requirements in engineering because it is very difficult to derive accurate analytical formulae for finite structures in practice. In this paper, the method of the numerical calculation is investigated for the two dimensional area mobility of a finite thin plate subject to a uniform force excitation by means of finite element method. A simple calculation method of area mobility is derived in the paper according to the principle of effective point mobility. And then the results obtained by finite element method are compared with that obtained from the theoretical calculation. It is verified that the numerical calculation of area mobility by FEM is correct and simple. The effects of some key parameters in the calculation are also analyzed for the calculation with identical model in the future.