5GREENSPON J E. Vibrations of a thick walled cylindrical shell-comparison of the exact theory with approximate theories[J]. Acoustical Society of America, 1960,32 (5) : 571-578.
6EBENEZER D D, ABRAHAM P. Eigenfunction analysis of radially polarized piezoelectric cylindrical shell[s of finite length[J]. Acoustical Society of America, 1997,102(3):1 549-1 558.
7aEBENEZER D D, ABRAHAM P. Piezoelectric thin shell theoretical model and eigenfunction analysis of radially polarized piezoelectric ceramic cylinders [J]. Acousticalsociety of America, 1999,105(1):154-163.
8Horito R E. Free-flooding unidirectional resonators for deep-ocean transdueers [J]. The Journal of the Acous- tical Society of America, 1967,41 : 158-166.
9Peshkovsky S L, Peshkovsky A S. Matching a trans- ducer to water at cavitation acoustic horn design princi- ples[J]. Ultrasonics Sonochemistry, 2007, 14 : 314-322.
10Mindlin R D, Medick M A. Extensional vibration of e- lastic plates[J].Journal of Applied Mechanics, 1959, 26:511 -569.
