Radial Vibration Analysis of Cylindrical Piezoelectric Transducers Considering Anisotrpy

이방성을 고려한 원통형 압전 변환기의 반경방향 진동 특성 해석

  • 이정구 (숭실대학교 대학원 기계공학과) ;
  • 김진오 (숭실대학교 공과대학 기계공학과)
  • Published : 2004.03.01


This paper presents the analysis fur the radial vibration characteristics of cylindrical piezoelectric transducers. Taking into account the piezoelectric anisotropy, the differential equations of piezoelectric radial motion have been derived in terms of radial displacement and electric potential. Applying mechanical and electric boundary conditions has yielded a characteristic equation for radial vibration. Numerical analysis also has been carried out by using the finite element method. Theoretical calculations of the fundamental natural frequency have been compared with the experimental observations for transducers of several sizes. Comparison with the previous report of theoretical analysis simplifying the piezoelectric anisotropy into isotropy concludes that isotropic analysis is a reasonable process to predict the vibration characteristics of piezoelectric transducers.


Piezoelectric Transducer;Cylindrical Transducer;Radial Vibration;Natural Frequency


  1. Berlincourt, D.A., Cmolik, C. Jaffe, H., 1960, 'Piezoelectric Properties of Polycrystalline Lead Titanate Zirconiate Compositions,' Proceeding of the IRE, pp. 220-229.
  2. Tae-Sung Inc., 1999, Introduction to Finite Element Analysis Using ANSYS, 3rd Ed., Tae-Sung, Seoul.
  3. Lazutkin, V.N. and Tsyganov, Y. V., 1972, Axisymmetric Modes and Electrical Impedance of Radially Polarized Piezoelectric Ceramic Rings,' Soviet Physics - Acoustics, Vol. 17, pp. 330-334.
  4. Wolfram. S., 1999, The Mathematica Book, Wolfram Media, Champaign.
  5. 岡騎淸, 1983, セラミック誘電體工學(第3版), 學獻社, 第8章.
  6. Miu, D. K., 1993, Mechatronics: Electromechanics and Contromechanics, Springer-Verlag, New York, Chap. 5.
  7. Achenbach, J. D., 1975, Wave Propagation in Elastic Solids, Elsevier Science Publishers, Amsterdam, Chap. 2.
  8. Hwang, K. K. Kim, J. O., 2003, 'Characteristics of the Radial Vibration of Cylindrical Piezoelectric Transducers,' Trans. of the Korean Society for Noise and Vibration Engineering, Vol. 13, No. 3, pp. 155-163.
  9. Kim, J.O., Jeong, H. G., 2001, 'Radial Vibration of Cylindrical Piezoelectric Transducers,' Trans. of the Korean Society for Noise and Vibration Engineering, Vol. 11, No. 7, pp. 247-252.
  10. Ebenezer, D. D., Abraham, P., 1977, 'Eigenfunction Analysis of Radially Polarized Piezoelectric Cylindrical Shells of Finite Length,' Journal of the Acoustic Society of America, vol. 102, No. 3, pp.1549-1558.
  11. Lee, J. G, Kim, J. O., 2003, 'A Study on Ultrasonic Sound Fields for Cleaning in a Pipe,' Journal of the Acoustical Society of Korea, in review.
  12. Kim, J.O., Hwang, K.K., Bau, H.H., 2003, 'A Study for the Measurement of a Fluid Density in a pipe Using Elastic Waves,' Journal of the Korean Society for Nondestructive Testing, Vol. 23, No. 6, pp. 583-593.
  13. Kim, J. O., Chun, H. Y., 2003, 'Interaction Between the Torsional Vibration of a Circular Rod and an Adjacent Viscous Fluid,' Trans. of ASME Journal of Vibration and Acousticsm Vol. 125, No. 1, pp. 39-45
  14. Chun, H.Y., Kim, J. O., 2002, 'A Study on the Measurement of the Fluid Viscosity by Using the Torsional Vibration of a Circular Rod,' Trans. of KSME(A), Vol. 26, No. 6, pp. 1016-1025.
  15. Kim, J.O., Kwon, O.S., 2003, 'Vibration Characteristics of Piezoelectric Torsional Transducers,' Journal of Sound and Vibration, vol. 264, No. 2, pp. 453-473.
  16. Kwon, O. S., Kim, J. O., 2001, 'Vibration Characteristics of Langevin-Type Piezoelectric Torsional Transducers,' Trans. of KSME (A), Vol. 25, No. 8, pp. 1197-1205.
  17. Ikeda,T., 1966, Fundamentals of Piezoelectricity, Oxford University Press, Oxford
  18. Busch-Vishniac, I. J., 1999, Electromechanical Sensors and Actuators, Springer, New-York, Chap. 5.