浸没圆柱壳低频自振频率计算中流固与声固耦合模型统一性分析

Unity analysis of the fluid-structure coupling model and the acoustic-structure coupling model in the natural frequency calculation of a submerged cylindrical shell

流固耦合与声固耦合模型是分析流场中圆柱壳自振特性的常用理论模型。现有的研究表明,基于这2种理论模型的流场中圆柱壳低频自振特性计算结果吻合较好,但尚未有关于二者本质联系方面的研究。分别基于这2种理论模型求解浸没圆柱壳的自由振动,基于圆柱壳自由振动的Flügge方程进行相关公式的推导,并提出利用Galerkin法求解特征方程的方法。结果显示,采用该方法既可求得各阶模态固有频率的精确解,又能显著提高运算效率。对2种理论模型进行统一性分析,从贝塞尔函数的性质出发,证实流固与声固耦合模型虽然是基于不同的理论基础,但在求解浸没圆柱壳低频自振特性上其本质上是一致的,且通过算例的对比,证明2种模型在低频段计算结果吻合较好。

The fluid-structure interaction model and the acoustic-structure interaction model are two commonly-used theoretical models to analyze free vibration characteristics of submerged cylindrical shells. It has already been confirmed that the results are consistent when dealing with low-frequency free vibration problems, but no study was conducted to explain the cause behind. In this paper, free vibration characteristics of a submerged cylindrical shell are investigated based on both the fluid-structure interaction model and the acoustic-structure interaction model. According to Flügge theory, free vibration equations are established as well as related formulas. In order to apply the Galerkin method to solve the characteristic equations, the accurate data of natural frequencies of the system is first obtained, and the calculation efficiency is improved. Consistency analysis of the two theoretical models is also carried out based on the characters of the Bessel function, which indicates that the nature and the calculation samples of the two models are indeed consistent when dealing low-frequency free vibration problems, though the two methods which are based on different theories.