可压缩流体中封闭薄球壳的自由振动

FREE VIBRATIONS OF ATHIN COMPLETE SPHERICAL SHELL SUBMERGED IN A COMPRESSIBLE FLUID MEDIUM

通过引入位移函数，成功地研究了薄球壳在可压缩流体中的自由振动。发现存在两类自由振动：第一类与外界流体无关；第二类则受到流体性质的影响．证明了第二类振动的频率方程具有多项式形式并只存在复频率（除ｎ＝１时有Ω＝０）．求解ｎ＝０，１和２时的频率方程，并讨论参数的影响及给出根轨迹图。最后就小阻尼系数法作了对比分析。

By the introduction of two displacement functions,the non-axisymmetric free vibrations of a complete thin isotropic spherical shell submerged in a compressible fluid medium are successfully investigated.It is found that there are two classes of free vibrations:the first class is not affected by the ambient fluid while the second is.It is further proved that the frequency equations can be expressed in terms of polynomial.For the second class of vibration of submerged spherical shell,it is also demonstrated that only complex frequencies exist except for the case of n=1,for which the trivial solution Ω=0 emerges。For n=0,1 and 2,the root-loci plots of frequency equations of the second class are given in the paper and the effects of various relative parameters are discussed.The method of small damping coefficient is discussed finally.