中文摘要：

结合平面应变和三维压电弹性力学理论,对径向极化厚壁压电陶瓷细长管的径向振动进行了研究,得出位移函数、电势函数的精确解。利用振子静电电荷方程导出电位移及电场强度函数,解决了电压与电场强度非线性关系问题,进而辅助maple软件首次对厚壁管形振子等效电导纳进行研究,推出了精确的谐振反谐振频率方程。利用数值法得出了不同尺寸管形振子的谐振反谐振频率,并通过有限元分析,结果表明了本文理论的准确性与精确性,为压电陶瓷厚壁振子的理论研究及设计提供了依据。

英文摘要：

Combined with piezoelectric plane strain and three-dimensional piezoelasticity theory,the vibration characteristics of a piezoelectric ceramic thick hollow cylinder with radial polarization has been studied,and closed-type solutions are obtained for the mechanical radial displacement and electric potential.The electric displacement and electric field strength are derived form the charge equation of electrostatics（Gauss）,which solves the problems of nonlinear relationship between voltage and electric field strength.Based on maple software,the equivalent admittance of the thick hollow cylinder is studied for the first time,and corresponding exact resonance and anti-resonance frequency equations are also obtained.By means of numberical method,the resonance and anti-resonance frequencies of different size tubular oscillators are calculated.Accuracy and precision of this theory are verified by finite element analysis.All these provide the basis for theoretical research and design of the piezoelectric ceramic thick oscillators.