中文摘要：

用瑞利法对三叠片弯振圆盘换能器在三种不同边界条件下的振动特性进行理论研究,推导了谐振频率及有效机电耦合系数的表达式,通过数值计算分析了复合换能器的谐振频率及有效机电耦合系数随换能器各结构参数的变化规律并进行比较研究,同时将计算结果与有限元模拟结果比较,结果表明不同边界条件下换能器的结构参数对谐振频率和有效机电耦合系数影响不同：在换能器结构参数一定时,自由边界条件下谐振频率最大,简支边界条件下最小,固定边界条件下次之;有效机电耦合系数随着金属片厚度、陶瓷片厚度和陶瓷片半径变化时,分别有一个最大值;其他参数一定时,有效机电耦合系数在简支边界条件下最大,自由边界条件下的值稍大于固定边界条件下的值。上述研究结果可为三叠片弯曲振动换能器的设计和实际应用提供一定的理论支持。

英文摘要：

Three laminated plate transducer is studied under three different boundary conditions and the expressions of the resonant frequency and the effective electromechanical coupling coefficient are derived by using Rayleigh method. Transducer resonant frequency and effective electromechanical coupling coefficient are analyzed and compared with the variation of the structure parameters of the transducer by means of numerical calculation, and the calculated results are compared with the results of finite element simulation. The results show that the effects of structural parameters under different boundary conditions of the transducer on the resonance frequency and the effective electromechanical coupling coefficient are different： for fixed structural parameters of the transducer, the resonant frequency is the greatest in free boundary condition, the next in fixed boundary condition and the minimum in simply supported boundary condition; the effective electromechanical coupling coefficient varies with the thickness of sheet metal and the thickness and radius of ceramic piece, and each has a maximum value; when other parameters are certain, the effective electromechanical coupling coefficient is the greatest in simply supported boundary condition, and the coefficient value in the free boundary condition is slightly larger than that in the fixed boundary condition. The above-mentioned results provide a theoretical support for the design and application of three laminated bending vibration transducer.