锥形剖面径向复合超声换能器的机电等效电路

Electromechanical equivalent circuit of conical section radial composite ultrasonic transducer

研究了一种锥形剖面径向复合超声换能器。该换能器由一个等截面内金属圆环、一个轴向极化的压电陶瓷圆环和一个锥形剖面外金属圆环沿径向复合而成,且换能器的径向尺寸远大于高度。锥形剖面外金属圆环满足关系式h=h0r,h0为厚度变化常数。基于平面应力径向振动理论,推导了换能器的机电等效电路,得到了共振频率方程和反共振频率方程,进而研究了换能器的振动特性。并将理论计算的第1阶、第2阶径向共振频率和反共振频率与数值仿真结果相比较,二者结果一致。研究表明:锥形剖面换能器第1阶、第2阶径向共振频率、反共振频率、有效机电耦合系数不仅与换能器各部分的材料、径向几何尺寸有关,还与h0有关。h0越大,第1阶径向共振频率、反共振频率越大,有效机电耦合系数先增大后减小。与等截面相比,锥形剖面换能器沿径向向外辐射声波,辐射面积更大,辐射声功率更高,指向性更好。

A kind of radial composite ultrasonic transducer with a conical section was studied.The transducer is composed of a metal ring with equal section,an axially polarized piezoelectric ceramic ring and a metal ring with conical section and the radial dimension of the transducer is much larger than the height.The metal ring with conical section satisfies the equation h=h0r,and h0 is a constant.Based on the plane stress radial vibration theory,the electromechanical equivalent circuit of the transducer was derived,the resonance frequency equation and anti-resonance frequency equation were obtained and then the vibration characteristics of the transducer were studied.The firstorder,second-order radial resonance frequencies and anti-resonance frequencies calculated by theory were compared with the numerical simulation results,and the results were consistent.The studies show that the first-order,second-order radial resonance frequencies and anti-resonance frequencies,and effective electromechanical coupling coefficients of the transducer with a conical section are not only related to the material and radial geometry of each part of the transducer,but also to h0.The greater h0,the greater the first-order radial resonance frequencies and anti-resonance frequencies,and the effective electromechanical coupling coefficient increases first and then decreases.Compared with the constant section,the conical section transducer radiates sound waves radially outward,with a larger radiation area,higher radiated sound power,and better directivity.