Three displacement functions are introduced to represent each mechanical displacement according to the three-dimensional theory. After expanding these functions and the electric potential with orthogonal series, the free vibration equation of piezoelectric cylindrical shells satisfying SS edge conditions can be obtained. The equation was solved by utilizing Bessel functions with complex arguments. The effects of compressible fluid on shells are considered and some new phenomena which are exclusive for piezoelectric cylindrical shells are reported. Results of empty infinite piezoelectric cylindrical shells are compared to those presented in relative references. Some lowest frequencies that were missed by Paul and Venkatesan [Paul, H. S. and Venkatesan, M. (1987). Vibrations of hollow circular cylinder of piezoelectric ceramics. Journal of the Acoustic Society of America 82, 852-856] were discovered. (C) 1997 Elsevier Science Ltd. [References: 17]
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机译：根据三维理论，引入了三个位移函数来表示每个机械位移。将这些函数和电势按正交级数展开后，可获得满足SS边缘条件的压电圆柱壳的自由振动方程。该方程是通过利用带有复杂参数的贝塞尔函数来求解的。考虑了可压缩流体对壳体的影响，并报道了压电圆柱壳所独有的一些新现象。将空无穷大压电圆柱壳的结果与相关参考文献中给出的结果进行比较。 Paul和Venkatesan错过了一些最低的频率[Paul，H. S. and Venkatesan，M.（1987）。压电陶瓷空心圆柱体的振动。发现了美国声学学会杂志82，852-856]。 （C）1997 Elsevier Science Ltd. [引用：17]
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