膜与不可压缩有界流体接触时的自由振动

圆形膜与流体接触时的振动被广泛应用于工业中．推导了圆形膜在与不可压缩有界流体接触时，非对称自由振动的自振频率．鉴于膜在不可压缩、非粘性流体中振动引起的小振幅，采用速度势函数来描述流体场．使用两种方法来推导系统的自由振动频率．它们包括变分法及一种近似解法——Rayleigh商法．在用两种方法求得的自由振动频率值之间具有良好的相关性．最后，研究了流体的深度、质量密度以及径向张力对耦合系统自由振动频率的影响．

Free vibration of membrane/bounded incompressible fluid

Vibration of circular membrane in contact with fluid had extensive applications in the industry. The natural vibration frequencies for asymmetric free vibration of circular membrane in contact with incompressible bounded fluid were derived. Considering small oscillations induced by the membrane vibration in incompressible and inviscid fluid, velocity potential function was used to describe the fluid field. Two approaches were used to derive the free vibration frequencies of the system. These included a variational formulation and an approximate solution employing the Rayleigh quotient method. Good correlation was found between free vibration frequencies evaluated using the two methods. Finally, the effects of the fluid depth and mass density, and radial tension on the free vibration frequencies of the coupled system were investigated.