Abstract
This paper theoretically and experimentally deals with the vibration characteristics of a piezoelectric disk polarized in the thickness direction and laminated with an elastic disk. Axisymmetric vibration modes include radial and axial motions. Theoretically, in this study, the differential equations of piezoelectric motions were derived in terms of radial and axial displacements and electric potential. The differential equations of elastic motions were expressed in terms of radial and axial displacements. Solving the governing equations and boundary conditions for a coupled structure produced characteristic equations that provided natural frequencies and mode shapes. Experimentally, the natural frequencies were measured using an impedance analyzer and the radial in-plane motions of the fundamental mode were measured using an in-plane laser interferometer. The results of the theoretical analysis were compared with those of a finiteelement analysis and experiments; moreover, the theoretical analysis was verified on the basis of this comparison. It appeared that the natural frequencies of the radial modes of the piezoelectric disk were not affected by the elastic disk; however, those of the thickness modes were reduced by the elastic disk owing to the added mass effect.
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References
C. I. J. Busch-Vishniac, Electromechanical Sensors and Actuators, Springer, New York (1999) Chapter 5.
R T. Ikeda, Fundamentals of Piezoelectricity, Oxford University Press, Oxford (1996).
L. C. Lynnworth, Ultrasonic Measurements for Process Control, Academic Press, Boston (1989).
S.-B. Choi and Y.-M. Han, Piezoelectric Actuators: Control Applications of Smart Materials, Boca Raton: Taylor & Francis (2010).
J. O. Kim, S. Choi and J. H. Kim, Vibroacoustic characteristics of ultrasonic cleaners, Applied Acoustics, 58 (1999) 211–228.
D. K. Miu, Mechatronics: Electromechanics and Contromechanics, Springer, New York (1993) Chapter 6.
D. J. Kim, S. H. Oh and J. O. Kim, Measurements of radial in-plane vibration characteristics of piezoelectric disk transducers, Transactions of the Korean Society for Noise and Vibration Engineering, 25 (2015) 13–23.
S. Lin and H. Tian, Study on the sandwich piezoelectric ceramic ultrasonic transducer in thickness vibration, Smart Materials and Structures, 17 (2008) 1–9.
P. Harkness, A. Cardoni, J. Russeli and M. Lucas, Designing a hollow Langevin transducer for ultrasonic coring, Applied Mechanics and Materials, 24 (2010) 65–70.
B. Fu, C. Li, J. Zhang and Z. Huang, Modeling of piezoelectric Langevin transducers by using mixed transfer matrix methods, Journal of the Korean Physical Society, 57 (2010) 929–932.
J. O. Kim and O. S. Kwon, Vibration characteristics of piezoelectric torsional transducers, Journal of Sound and Vibration, 264 (2003) 453–473.
A. H. Meitzler, H. M. O’Bryan and H. F. Tiersten, Definition and measurement of radial mode coupling factors in piezoelectric ceramic materials with large variations in Poisson’s ratio, IEEE Transactions on Sonics and Ultrasonics, SU-20 (1973) 233–239.
N. Guo, P. Cawley and D. Hitchings, The finite element analysis of the vibration characteristics of piezoelectric discs, Journal of Sound and Vibration, 159 (1992) 115–138.
P. R. Heyliger and G. Ramirez, Free vibration of laminated circular piezoelectric plates and discs, Journal of Sound and Vibration, 229 (4) (2000) 935–956.
J. E. Kim, Dedicated algorithm and software for the integrated analysis of AC and DC electrical outputs of piezoelectric vibration energy harvesters, Journal of Mechanical Science and Technology, 28 (2014) 4027–4036.
J. D. Achenbach, Wave Propagation in Elastic Solids, North Holland, Amsterdam (1975) Chapter 2.
S. Wolfram, The Mathematica Book, 4th Ed., Wolfram Media Inc., Champaign (1999).
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Recommended by Associate Editor Ohseop Song
Chunguang Piao received the M.S. degree in Mechanical Engineering from Soongsil University in 2013. He is now a Ph.D. candidate. During his stay at Soongsil Univ. as a graduate student, he has been working on ultrasonic wave propagation and vibration characteristics of piezoelectric transducers.
Jin Oh Kim received the B.S. and M.S. degrees in Mechanical Engineering from Seoul National University in 1981 and 1983, respectively, and the Ph.D. degree from University of Pennsylvania in 1989. Since 1997, he has been with the Faculty of Soongsil University, where he is currently a Professor of Mechanical Engineering. His research interests are in the areas of ultrasonic sensors and actuators using mechanical vibrations and humanbody dynamics for rehabilitation robots.
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Piao, C., Kim, J.O. Vibration characteristics of a piezoelectric disk laminated with an elastic disk. J Mech Sci Technol 30, 5351–5362 (2016). https://doi.org/10.1007/s12206-016-1102-9
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DOI: https://doi.org/10.1007/s12206-016-1102-9