论理想流体与线弹性结构的耦联振动

本文对理想流体与线弹性结构的耦联振动问题作理论分析和数值分析.文中证明了耦联振动的固有频率存在并且均为正实数.将流-固耦合系统分析转化为单一结构物在真空中的自由振动分析后,频率方程中不再含有流体变元.使问题得以大大简化.给出了数值解的收敛性证明,以保证解的可靠性.文中还综合里兹法、边界元和有限元方法,提出一种分析转化后结构的混合算法.利用该算法,只需对现有结构分析程序稍作改进,就可分析那些理想流场与结构的耦合问题.一些数例说明了算法的有效性.

On the Coupled Vibration of an Ideal Fluid with a Linear Elastic Structure

The purpose of this paper is to analyse theoretically and numerically the coupled vibration of an ideal fluid with a linear elastic structure. It is proved in the papef that the natural frequencies of the coupled vibration do exist and are all real positive. The paper presents an efficient method to transform a coupled fluid-structure system to the structure with added mass and the vibrational analysis of the former is replaced by the latter in vacuum only. Numerical solution is outlined for the transformed problem and a compact frequency equation is derived in which fluid variables do not appear. This simplifies the analysis singnificantly. A convergent proof has been given to guarantee the reliability of the solution. The paper also offers a general algorithm combined with Ritz method, boundary element method, and finite element method to analyse the transformed problem. Based on this algorithm, one can apply a known structural analysing program, with a little modification, to solve many different kinds of fluid-structure coupling problems. Some numerical results are given to show the efficiency of the algorithm.