径向极化厚壁压电陶瓷管径向振动研究

Research on the radial vibration of thick piezoelectric hollow cylinder with radial olarization

应用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圆管径向振动特性进行研究.利用分离变量法,求解振子径向位移函数的微分方程,得到了位移函数精确解.推导出其机电类比等效电路,得出其等效电阻抗.在此基础上,推出振子共振反共振频率方程,得到了振子的阻抗特性曲线,探讨了振子的共振反共振频率和有效机电耦合系数与其几何尺寸之间的依赖关系.利用数值法得到了不同几何尺寸圆管振子的共振反共振频率,结果与数值分析一致.通过对两个压电圆管振子谐振频率的理论计算与实验测试,表明了理论的准确性与精确性,这为压电陶瓷复合管换能器的理论研究及设计提供了依据.

Combined with piezoelectric plane strain and three-dimensional piezoelasticity theory,the radial vibration characteristics of a piezoelectric ceramic thick hollow cylinder with radial polarization has been investigated.By virtue of the separation of variables technique,the integral equation of radial displacement can be solved analytically the and closed form solutions are obtained. Its electro-mechanical equivalent circuit and equivalent impedance are derived. Based on the equivalent circuits and using the boundary conditions,the resonance and anti-resonance frequency equations are also obtained.The impedance curve displayed as a function of the frequency is given,the relations between the resonance frequency,the anti-resonance frequency,the effective electromechanical coupling coefficient and the radius ratio are analyzed.The resonance and anti-resonance frequencies of different radius tubes are calculated by use of numerical method,which are consistent with that of the finite element analysis.The accuracy of this theory are verified by theoretical and experimental tests about resonance frequency of two piezoelectric ceramic thick hollow cylinder.All these provide the basis for the composite pipe piezoelectric ultrasonic transducer theoretical research and design.