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HYDRODYNAMICS AND ACOUSTICS

2018 ◊ Volume 1 (91) ◊ Issue 2 ◊ p. 160-190

V. L. Karlash*

* S. P. Timoshenko Institute of Mechanics of NAS of Ukraine, Kyiv, Ukraine

Analysis of forced vibration of piezoceramic transducers at a non-uniform electric loading

Gidrodin. akust. 2018, 1(2):160-190

https://doi.org/10.15407/jha2018.02.160

TEXT LANGUAGE: Ukrainian

ABSTRACT

The influence of a non-uniform electric loading on the admittance and dynamic electromechanical coupling factor (EMCF) for transducers of mentioned type is studied considering the examples of the problems describing the forced vibration of narrow piezoceramic plates-bars with partially-electroded surfaces or divided electrodes. A wide retrospective of the researches in this area for recent century is represented on the basis of analysis of the domestic and foreign bibliographic sources. The basic relations of the linear theory of electroelasticity are presented in the following sections and boundary problems for the cases of steady forced vibration of the thin-walled piezoelectric resonators with transversal polarization are formulated. The expressions for calculation of energy characteristics of the process (in particular, the dynamic EMCF) are offered. The mathematical statements corresponding to various configurations of the surface electrodes are considered. The anti-phase vibration excitation is shown to be an effective instrument for selecting the overtones corresponding to high modes and, consequently, for increasing the operating frequency. The presence of the electrodeless areas may lead to a certain (still, insignificant) EMCF increase of the fundamental resonance. Partial short-circuiting of the electrodes is resulted in occurrence of both odd and even longitudinal modes, which cannot be excited with full electrodes. The calculations made for stress state and admittance are in good agreement with the experimental data on amplitude-frequency characteristics of the forced vibration of piezoelectric plates the surfaces of which are covered with the sectional electrodes.

KEY WORDS

piezoceramic transducers, electromechanical coupling factor, forced vibration, admittance, active and reactive components, stress state

REFERENCES

  1. W. G. Cady, Piezoelectricity: An introduction to the theory and applications of electromechanical phenomena in crystals. New York: McGraw-Hill, 1946.
  2. D. E. Dye, “The piezoelectric quartz resonator and its equivalent circuit”, Proceedings of the Physical Society of London, vol. 38, pp. 399–453, 1926. https://doi.org/10.1088/1478-7814/38/1/344.
  3. C. A. Rosen, US Pat. 439 992, Jun. 1954.
  4. S. Butterworth, “On electrically maintained vibrations”, Proceedings of the Physical Society of London, vol. 27, pp. 410–424, 1914. https://doi.org/10.1088/1478-7814/27/1/330.
  5. W. G. Cady, “Piezo-electric standards of high frequency”, Journal of the Optical Society of America, vol. 10, pp. 475–489, 1925. https://doi.org/10.1364/JOSA.10.000475.
  6. W. G. Cady, “Theory of longitudinal vibrations of viscous rods”, Physical Review, vol. 19, no. 1, pp. 1–6, 1922. https://doi.org/10.1103/PhysRev.19.1.
  7. J. Erhart, “Parameters and design optimization of the ring piezoelectric ceramic transformer”, Journal of Advanced Dielectrics, vol. 5, no. 3, 1550022(1–8), 2015. https://doi.org/10.1142/S2010135X15500228.
  8. J. Erhart and T. Sebastian, “Effective electromechanical coupling for the partially electroded ceramic resonators of different geometries”, Annual DUNAREA DE JOS University of Galati Fascicle IX, Metallurgy and Material Science, no. 2, pp. 7–16, 2015.
  9. N. F. Ivina, “Analysis of the natural vibrations with partial electrodes”, Acoustical Physics, vol. 47, no. 6, pp. 714–720, 2001. https://doi.org/10.1134/1.1418899.
  10. N. N. Rogacheva, “The dependence of the electromechanical coupling coefficient of piezoelectric elements on the position and size of the electrodes”, Journal of Applied Mathematics and Mechanics, vol. 65, no. 2, pp. 317–326, 2001. https://doi.org/10.1016/S0021-8928(01)00036-3.
  11. V. O. Andrushchenko, O. V. Boriseiko, D. S. Nemchenko, and I. A. Ulitko, “An experimental study of energy conversion efficiency at resonant vibration of a piezoceramic rod with split electrodes under the controlled electric excitation”, 2009, pp. 38–43.
  12. V. L. Karlash, “Forced electromechanical vibrations of rectangular piezoceramic bars with sectionalized electrodes”, International Applied Mechanics, vol. 49, no. 3, pp. 360–368, 2013. https://doi.org/10.1007/s10778-013-0574-x.
  13. B. van der Veen, “The equivalent network of a piezoelectric crystal with divided electrodes”, Phillips Research Reports, vol. 11, pp. 66–79, 1956.
  14. V. M. Sharapov, I. G. Minaev, Y. Y. Bondarenko, T. Y. Kisil, M. P. Musienko, S. V. Rotte, and I. B. Chudaeva, Piezoelectric transducers: A tutorial, V. M. Sharapov, Ed. Cherkassy: Cherkassy State University of Technology, 2004.
  15. V. M. Sharapov, Y. Y. Bondarenko, M. P. Musiyenko, and T. Y. Kisil, “About the methods of a linearization of a peak-frequency characteristics of piezoceramic transducers”, Visnik Cherkas’kogo Derzhavnogo Tehnologichnogo Universitetu, Technical Sciences, no. 3, pp. 51–53, 2005.
  16. V. M. Sharapov, M. P. Musiyenko, and V. V. Tuz, “The research .of piezoelectric converters with two planimetric feedback with charge amplifiers”, Visnik Cherkas’kogo Derzhavnogo Tehnologichnogo Universitetu, Technical Sciences, pp. 281–283, 2006.
  17. A. F. Ulitko, “Theory of electromechanical energy conversion in nonuniformly deformable piezoceramics”, Soviet Applied Mechanics, vol. 13, no. 10, pp. 1055–1062, 1977. https://doi.org/10.1007/BF00883190.
  18. A. F. Ulitko, “On determination of the electromechanical coupling coefficient in the problems of steady oscillations of piezoceramic bodies”, Matematicheskie Metody i Fiziko-Mehanicheskie Polya, no. 7, pp. 77–81, 1978.
  19. V. L. Karlash, “Vibrational modes and efficiency of energy conversion in composite piezoelectric rods”, Soviet Applied Mechanics, vol. 23, no. 2, pp. 170–174, 1987. https://doi.org/10.1007/BF00889013.
  20. E. C. Munk, “The equivalent electrical circuit for radial modes of a piezoelectric ceramic disk with concentric electrodes”, Phillips Research Reports, vol. 20, pp. 170–189, 1965.
  21. I. F. Vovkodav, “The radial vibrations of thin piezoceramic plate with the split electrodes”, Thermal Stress in Structural Elements, vol. 15, pp. 99–103, 1975.
  22. V. A. Andrushchenko, I. F. Vovkodav, V. L. Karlash, and A. F. Ulitko, “Coefficient of electromechanical coupling in piezoceramic disks”, Soviet Applied Mechanics, vol. 11, no. 4, pp. 377–382, 1975. https://doi.org/10.1007/BF00882905.
  23. V. L. Karlash, V. A. Klyushnichenko, Y. A. Kramarov, and A. F. Ulitko, “Radial vibrations of thin piezoceramic disks under a nonuniform electric load”, Soviet Applied Mechanics, vol. 13, no. 8, pp. 784–789, 1977. https://doi.org/10.1007/BF00885009.
  24. V. L. Karlash, “Nonsymmetric vibrations of piezoelectric ceramic rings polarized along the thickness”, Soviet Applied Mechanics, vol. 14, no. 12, pp. 1303–1308, 1978. https://doi.org/10.1007/BF00883735.
  25. V. L. Karlash, “On the theory of non-symmetric vibration of piezoceramic round plates with split electrodes”, Transactions of AS of Armenian SSR, Mechanics, vol. 34, no. 6, pp. 60–65, 1981.
  26. A. Pyatrauskas, S. Prilagauskas, and A. Mazhons, “Studying the vibration of composite round piezotransducers”, Ultrasound. Research Proceedings of Universities of Lithuanian SSR, vol. 19, pp. 107–113, 1987.
  27. J. Ramanauskas, “An experimental study of the disk bimorphic elements under bending vibration”, Ultrasound. Research Proceedings of Universities of Lithuanian SSR, vol. 20, pp. 158–163, 1990.
  28. L. V. Borisenko and N. A. Shul’ga, “Electroelastic vibrations of a radially polarized piezoceramic cylinder with partially electrodeposited side surfaces”, Prikladnaya Mehanika, vol. 26, no. 6, pp. 115–118, 1990.
  29. N. A. Shul’ga and L. V. Borisenko, “Electroelastic vibrations of a sectioned piezoceramic cylinder with axial polarization”, Prikladnaya Mehanika, vol. 26, no. 2, pp. 126–130, 1990.
  30. I. A. Kartashev and N. V. Marchenko, Piezoelectric current transformers. Kiev: Tehnika, 1978.
  31. V. V. Lavrinenko, Piezoelectric transformers. Moscow: Energiya, 1975.
  32. Y. A. Kramarov and V. A. Klyushnichenko, “Non-uniformly polarized piezoelectric transducer”, in Acoustic Methods and Means of Ocean Research, vol. 2, Vladivostok, 1974, pp. 3–6.
  33. V. G. Karnaukhov, V. I. Kozlov, V. V. Mikhailenko, and S. V. Mikhailenko, “Planar vibrations of piezoceramic plates with account for material depolarization caused by vibratory heating”, International Applied Mechanics, vol. 30, no. 3, pp. 222–227, 1994. https://doi.org/10.1007/BF00847339.
  34. S. I. Rudnitskii, V. M. Sharapov, and N. A. Shul’ga, “Vibrations of a bimorphic disk transducer of the metal-piezoceramic type”, Soviet Applied Mechanics, vol. 26, no. 10, pp. 973–980, 1990. https://doi.org/10.1007/BF00888849.
  35. O. P. Chervinko and Y. O. Zhuk, “Relationships of a coupled dynamic problem of thermosplasticity for flexible shells with piezo-active layers”, Reports of the National Academy of Sciences of Ukraine, no. 1, pp. 68–74, 2002.
  36. V. T. Grinchenko, V. L. Karlash, V. V. Meleshko, and A. F. Ulitko, “Investigation of planar vibrations of rectangular piezoceramic plates”, Soviet Applied Mechanics, vol. 12, no. 5, pp. 483–488, 1976. https://doi.org/10.1007/BF00882456.
  37. W. P. Mason, “Location of hysteresis phenomena in Rochelle salt”, Physical Review, vol. 58, pp. 744–756, 1940.
  38. V. L. Karlash, “The transmission coefficient and oscillation modes of a plane transversely-longitudinal piezotransformer”, Elektrichestvo, no. 1, pp. 51–55, 2002.
  39. V. L. Karlash, “Electroelastic vibrations and transformation ratio of a planar piezoceramic transformer”, Journal of Sound and Vibration, vol. 277, pp. 353–367, 2004. https://doi.org/10.1016/j.jsv.2003.03.012.
  40. V. Karlash, “Longitudinal and lateral vibrations of a planar piezoceramic transformer”, Japanese Journal of Applied Physics, vol. 44, no. 4A, pp. 1852–1856, 2005. https://doi.org/10.1143/JJAP.44.1852.
  41. J. Hu, Y. Fuda, M. Katsuno, and T. A. Yoshiba, “Study on the rectangular-bar shaped multilayer piezoelectric transformer using length extensional vibration mode”, Japanese Journal of Applied Physics, vol. 38, pp. 3208–3212, 1999. https://doi.org/10.1143/JJAP.38.3208.
  42. J. Erhart, “Bulk piezoelectric ceramic transformers”, Advances in Applied Ceramics, vol. 112, no. 2, pp. 91–96, 2013. https://doi.org/10.1179/1743676112Y.0000000028.
  43. K. Nadal, F. Pigache, and J. Erhart, “Modeling of a ring Rosen-type piezoelectric transformer by Hamilton’s principle”, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 62, no. 4, pp. 709–720, 2015. https://doi.org/10.1109/TUFFC.2014.006719.
  44. N. Y. Wong, Y. Zhang, H. L. W. Chan, and C. L. Choy, “A bilayer piezoelectric transformer operating in a bending vibration mode”, Materials Science and Engineering: B, vol. 99, no. 1–3, pp. 164–167, 2003. https://doi.org/10.1016/S0921-5107(02)00472-5.
  45. C. M. Leung, S. W. Or, F. Wang, S. L. Ho, and H. Luo, “Enhanced magnetoelectric effect in heterostructure of magnetostrictive alloy bars and piezoelectric single-crystal transformer”, Review of Scientific Instruments, vol. 82, no. 1, p. 013 903, 2011. https://doi.org/10.1063/1.3529439.
  46. T. Sebastian and J. Erhart, “Bar piezoelectric ceramic transformers working in longitudinal mode”, Ferroelectrics, vol. 486, no. 1, pp. 13–24, 2015. https://doi.org/10.1080/00150193.2015.1099413.
  47. P. Pulpan and J. Erhart, “Experimental verification of an analytical model for the ring shaped piezoelectric transformer”, Journal of Electrical and Electronics Engineering, vol. 8, no. 2, pp. 23–28, 2015.
  48. R. Holland, “Representation of dielectric, elastic and piezoelectric losses by complex coefficients”, IEEE Transactions on Sonics and Ultrasonics, vol. SU-14, pp. 18–20, 1967. https://doi.org/10.1109/T-SU.1967.29405.
  49. V. L. Karlash, “Resonant electromechanical vibrations of piezoelectric plates”, International Applied Mechanics, vol. 41, no. 7, pp. 709–747, 2005. https://doi.org/10.1007/s10778-005-0140-2.
  50. M. O. Shul’ga and V. L. Karlash, “Amplitude-phase characteristics of radial vibrations of a thin piezoceramic disk near resonances”, Reports of the National Academy of Sciences of Ukraine, no. 9, pp. 80–86, 2013.
  51. V. L. Karlash, “Energy losses in piezoceramic resonators and its influence on vibrations’ characteristics”, Electronics and Communication, vol. 19, no. 2(79), pp. 82–94, 2014.
  52. V. L. Karlash, “Modeling of energy-loss piezoceramic resonators by electric equivalent networks with passive elements”, Mathematical Modeling and Computing, vol. 1, no. 2, pp. 163–177, 2014.
  53. H. Xue, J. Yang, and Y. Hu, “Analysis of Rosen piezoelectric transformers with a varying cross-section”, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 55, no. 7, pp. 1632–1639, 2008. https://doi.org/10.1109/TUFFC.2008.837.
  54. M. O. Shul’ga and V. L. Karlash, Resonant electromechanic vibration of piezoceramic plates. Kyiv: Naukova Dumka, 2008.
  55. N. A. Shul’ga and A. M. Bolkisev, Vibration of piezoceramic bodies. Kiev: Naukova Dumka, 1990.
  56. B. Jaffe, W. R. Cook, and H. Jaffe, Piezoelectric ceramics. New York: Academic Press, 1971. https://doi.org/10.1016/B978-0-12-379550-2.X5001-7.
  57. G. V. Katz, Ed., Magnetic and dielectric devices. Part I. Moscow: Energiya, 1964.
  58. “IRE standards on piezoelectric crystals: Measurements of piezoelectric ceramics”, Proceedings of IRE, vol. 49, pp. 1161–1169, 1961.
  59. I. A. Glozman, Piezoceramics. Moscow: Energiya, 1972.
  60. O. I. Bezverkhyi, L. P. Zinchuk, and V. L. Karlash, “Effect of the electrical loading on forced vibrations of transversely polarized piezoceramic bars”, Electronics and Communication, vol. 20, no. 4(87), pp. 77–88, 2015.
  61. K. Uchino, J. H. Zheng, Y. H. Chen, X. H. Du, J. Ryu, Y. Gao, S. Ural, S. Priya, and S. Hirose, “Loss mechanisms and high power piezoelectrics”, Journal of Materials Science, vol. 41, pp. 217–228, 2006. https://doi.org/10.1007/s10853-005-7201-0.
  62. K. Uchino, Y. Zhuang, and S. O. Ural, “Loss detertmination methodology for a piezoelectric ceramic: New phenomenological theory and experimental proposals”, Journal of Advanced Dielectrics, vol. 1, no. 1, pp. 17–31, 2011. https://doi.org/10.1142/S2010135X11000033.
  63. S. Dong, “Review on piezoelectric, ultrasonic and magnetoelectric actuators”, Journal of Advanced Dielectrics, vol. 2, no. 1, 1230001(1–18), 2012. https://doi.org/10.1142/S2010135X12300010.
  64. V. L. Karlash, “Methods for determining of the coupling and energy loss coefficients at vibration of piezoceramic resonators”, Acoustic Bulletin, vol. 15, no. 4, pp. 24–38, 2012.
  65. K. Okadzahi and M. Umino, “Analysis of vibrations in thin piezoceramic resonators with annular electrodes”, Nippon Onkyo Gakkaishi, vol. 25, no. 6, pp. 325–334, 1969.