Aronov Boris
Department of Electrical and Computer Engineering, University of Massachusetts Dartmouth, BTech Acoustic LLC, Acoustics Research Laboratory, Advanced Technology and Manufacturing Center, Massachusetts 02723, USA.
J Acoust Soc Am. 2009 Feb;125(2):803-18. doi: 10.1121/1.3056560.
Analysis of electromechanical transducers employing axially symmetric vibrations of piezoelectric ceramic thin-walled tubes of arbitrary aspect ratio is presented based on application of the energy method [B. S. Aronov, J. Acoust. Soc. Am. 117, 210-220 (2005)]. The suggestion made by Giebe and Blechshmidt [Ann. Physik, Ser. 5 18, 417-485 (1933)] regarding representation of a tube vibration as a coupled vibration of two partial systems is used to choose the assumed modes of the piezoceramic tube vibration, and the energy of the flexural deformations accompanying the extensional vibration of a tube is also taken into consideration. The Lagrange type equations describing the transducer vibrations are derived, and the equivalent electromechanical circuit is introduced that conveniently represents the solution. The resonance frequencies, effective coupling coefficients, and velocity distributions for differently poled piezoceramic tubes as functions of their height-to-diameter aspect ratio are calculated. The validity of the equivalent circuit is extended to the case that a piezoceramic tube is mechanically and acoustically loaded on the ends and acoustically loaded on its outer surface. The results of calculations are in good agreement with the results of experimental investigations.
基于能量法[B. S. 阿罗诺夫，《美国声学学会杂志》117, 210 - 220 (2005)]，对采用任意纵横比的压电陶瓷薄壁管轴对称振动的机电换能器进行了分析。吉贝和布莱希施密特[《物理学纪事》，第5辑18, 417 - 485 (1933)]提出的将管振动表示为两个子系统耦合振动的建议，被用于选择压电陶瓷管振动的假定模式，并且还考虑了伴随管纵向振动的弯曲变形能量。推导了描述换能器振动的拉格朗日型方程，并引入了能方便表示解的等效机电电路。计算了不同极化的压电陶瓷管的共振频率、有效耦合系数以及速度分布与它们的高径比的函数关系。等效电路的有效性扩展到压电陶瓷管两端受到机械和声学负载且其外表面受到声学负载的情况。计算结果与实验研究结果吻合良好。
