考虑边界条件的弹性长方体封闭结构腔辐射声场分析

在弹性板边界施加假想的弹簧系统模拟板的不同边界条件,利用汉密尔顿函数和瑞利-李兹方法,建立由2块四边弹性支承的弹性板及4块刚性板构成的封闭矩形腔外的辐射声场模型,推导腔体外辐射声场的解析解.该模型考虑两弹性板之间以及弹性板与腔体内声场之间的耦合.算例表明,低频段时两弹性板之间为弱耦合,辐射声场主要由受到外激励的结构所决定;支承板的线弹簧的刚度变化对辐射声场的影响较旋转弹簧大.同时,运用有限元法计算腔体内的声模态和弹性板的振动模态及其耦合系数,结合边界元法计算出腔体外的声压响应,并将此数值仿真结果与前面导出的解析结果进行比较,理论推导的正确性得到验证.

ANALYSIS OF SOUND RADIATION OF ELASTIC RECTANGULAR ENCLOSURE WITH CONSIDERING BOUNDARY CONDITIONS

The model of sound radiated from a rectangular enclosure consisted of two elastic supported flexible panels and four rigid panels is deduced by using Hamiltonian function and Rayleigh-Ritz method. By means of continuous distributions of artifical springs along boundary of flexible panels, this model allows the consideration of a wide variety of boundary condi-tions and structure joint conditions. Analytical results on the radiation of sound are presented. These results are intended to investigate two main issues: one is the coupling of the com- bined structure is relatively weak, so the radiation of sound is controlled by panel which is directly excited, the other is the translational stiffness affects the radiation of sound more than the rotational stiffness does. Then, modes of sound pressure and flexible panel are obtained by FEM. Modal coupling coeffici- ents are synthesized. Finally, the responses of sound pressure is worked out by BEM. The result of the simulation method coin- cides well with the analytical result, and is satisfactory.