Abstract
Piezoelectric ceramic resonators are discussed in details including calculation of impedance/admittance for each resonator type, resonance and antiresonance conditions and parameters of equivalent electronic circuit parameters. Resonators of bar, plate, disc and ring shape with various electrode pattern and poling directions are covered for all common one-dimensional as well as special vibration modes in detailed calculations. Some of the miscellaneous resonators (cylindrical or spherical shape) are reviewed from literature references. All resonators are demonstrated by experimental data of impedance spectra with identified and calculated vibration mode parameters. Example of higher order mode theory for coupled vibration is also given for reference.
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References
Adelman NT, Stavsky Y (1975) Vibrations of radially polarized composite piezoceramic cylinders and disks. J Sound Vib 43(1):37–44
Adelman NT, Stavsky Y (1977) Equivalent electrical circuit of a multielectrode composite piezoceramic bar. J Acoust Soc Am 61(2):422–427
Adelman NT, Stavsky Y, Segal E (1975a) Radial vibrations of axially polarized piezoelectric ceramic cylinders. J Acoust Soc Am 57(2):356–360
Adelman NT, Stavsky Y, Segal E (1975b) Axisymmetric vibrations of radially polarized piezoelectric ceramic cylinders. J Sound Vib 38(2):245–254
Ballato A (2001) Modeling piezoelectric and piezomagnetic devices and structures via equivalent networks. IEEE Trans UFFC 48(5):1189–1240
Berlincourt DA, Curran DR, Jaffe H (1964) Piezoelectric and piezomagnetic materials and their function in transducers. In: Mason WP (ed) Physical acoustics — principles and methods, vol 1 — A Methods and devices. Academic Press, New York, pp 169–270
Ebenezer DD, Abraham P (1997) Eigenfunction analysis of radially polarized piezoelectric cylindrical shells of finite length. J Acoust Soc Am 102(3):1549–1558
Erhart J, Sebastian T (2015) Effective Electromechanical coupling for the partially electroded ceramic resonators of different geometries. The Annals of “Dunarea de Jos” University of Galati. Fascicle IX. Metallurgy and Materials Science, vol XXXIII, no 2. pp 7–16
Ghosh AK, Agrawal MK (1994) Radial vibrations of spheres. J Sound Vib 171(3):315–322
Graff KF (1991) Wave motion in elastic solids. Dover Publications, New York
Haskins JF, Walsh JL (1957) Vibrations of ferroelectric cylindrical shells with transverse isotropy. I. Radially polarized case. J Acoust Soc Am 29(6):729–734
Holland R (1967a) Representation of dielectric, elastic and piezoelectric losses by complex coefficients. IEEE Trans Sonics Ultrason SU-14(1):18–20
Holland R (1967b) The equivalent circuit of a symmetric N-electrode piezoelectric disk. IEEE Trans Sonics Ultrason SU-14(1):21–33
Huang CH (2005) Theoretical and experimental vibration analysis for a piezoceramic disk partially covered with electrodes. J Acoust Soc Am 118(2):751–761
Huang R, Lee PCY, Lin WS, Yu JD (2002) Extensional, thickness-stretch and symmetric thickness-shear vibrations of piezoceramic disks. IEEE Trans UFFC 49(11):1507–1515
Huang CH, Lin YC, Ma CC (2004) Theoretical analysis and experimental measurement for resonant vibration of piezoceramic circular plates. IEEE Trans UFFC 51(1):12–24
Huang N, Zhang R, Cao W (2007) Electromechanical coupling coefficient of 0.70Pb(Mg1/3Nb2/3)O3–0.30PbTiO3 single crystal resonator with arbitrary aspect ratio. Appl Phys Lett 91:122903
Ivina NF (2001) Analysis of the natural vibrations of circular piezoceramic plates with partial electrodes. Acoust Phys 47(6):714–720
Karlash VL (1979) Nonsymmetric vibrations of piezoelectric ceramic rings polarized along the thickness. Int Appl Mech 14:1303–1308
Karlash VL (2008) Resonant electromechanical vibrations of piezoelectric shells of revolution (Review). Int Appl Mech 44(4):361–387
Kim JO, Lee JG (2007) Dynamic characteristics of piezoelectric cylindrical transducers with radial polarization. J Sound Vib 300:241–249
Kim JO, Hwang KK, Jeong HG (2004) Radial vibration characteristics of piezoelectric cylindrical transducers. J Sound Vib 276:1135–1144
Kim M, Kim J, Cao W (2005a) Aspect ratio dependence of electromechanical coupling coefficient of piezoelectric resonators. Appl Phys Lett 87:132901
Kim JO, Lee JG, Chun HY (2005b) Radial vibration characteristics of spherical piezoelectric transducers. Ultrasonics 43(7):531–537
Kim M, Kim J, Cao W (2006a) Electromechanical coupling coefficient of an ultrasonic array element. J Appl Phys 99:074102
Kim M, Kim J, Cao W (2006b) Experimental technique for characterizing arbitrary aspect ratio piezoelectric resonators. Appl Phys Lett 89:162910
Kim H, Brockhaus A, Engemann J (2009) Atmospheric pressure argon plasma jet using a cylindrical piezoelectric transformer. Appl Phys Lett 95:211501
Lee PCY (1971) Extensional, flexural, and width-shear vibrations of thin rectangular crystal plates. J Appl Phys 42(11):4139–4144
Lee PCY, Edwards NP, Lin WS, Syngellakis S (2002) Second-order theories for extensional vibrations of piezoelectric crystal plates and strips. IEEE Trans UFFC 49(11):1497–1506
Lin S (2000) Thickness shearing vibration of the tangentially polarized piezoelectric ceramic thin circular ring. J Acoust Soc Am 107(5):2487–2492
Lin S (2004) Study on the equivalent circuit and coupled vibration for the longitudinally polarized piezoelectric ceramic hollow cylinders. J Sound Vib 275(3):859–875
Lin S, Zhang F (1993) Vibrational modes and frequency spectra in piezoelectric ceramic rectangular resonators. J Acoust Soc Am 94(5):2481–2484
Lin S, Fu Z, Zhang X, Wang Y, Hu J (2013) Radially sandwiched cylindrical piezoelectric transducer. Smart Mater Struct 22(1):015005
Mason WP (1948) Electrostrictive effect in barium titanate ceramics. Phys Rev 74(9):1134–1147
Meitzler AH, O’Brian HM, Tiersten HF (1973) Definition and measurement of radial mode coupling factors in piezoelectric ceramic materials with large variations in Poisson’s ratio. IEEE Trans Sonics Ultrason SU-20(3):233–239
Mezheritsky AV (2003) Invariants of electromechanical coupling coefficients in piezoceramics. IEEE Trans UFFC 50(12):1742–1751
Mindlin RD (1976) Low frequency vibrations of elastic bars. Int J Solids Struct 12:27–49
Onoe M (1956) Contour vibrations of isotropic circular plates. J Acoust Soc Am 28(6):1158–1162
Onoe M, Jumonji H (1967) Useful formulas for piezoelectric ceramic resonators and their application to measurement of parameters. J Acoust Soc Am 41(4):974–980
Potter DS, Leedham CD (1971) Antisymmetric vibrations of a circular plate. J Acoust Soc Am 49(5B):1521–1526
Pustka M, Nosek J, Burianová L (2011) Coupled extensional vibrations of longitudinally polarized piezoceramic strips. IEEE Trans UFFC 58(10):2139–2145
Rogacheva NN (2001) The dependence of the electromechanical coupling coefficient of piezoelectric elements on the position and size of the electrodes. J Appl Math Mech 65(2):317–326
Sadd MH (2005) Elasticity: theory, applications, and numerics. Elsevier, Amsterdam
Schwartz RW, Ballato J, Haertling GH (2004) Piezoelectric and electro-optic ceramics. In: Buchanan RC (ed) Ceramic materials for electronics, 3rd edn. Marcel-Dekker, New York, pp 207–322
Stavsky Y, Greenberg JB (2003) Radial vibrations of orthotropic laminated hollow spheres. J Acoust Soc Am 113(2):847–851
Stefan O (1970) Contour vibrations of circular ceramic resonators. Czech J Phys A 20(2):113–122 (in Czech)
Stephenson CV (1956) Radial vibrations in short, hollow cylinders of barium titanate. J Acoust Soc Am 28(1):51–56
Tasker R, Lukacs M, Sayer M, Sherrit S (1999) Techniques to determine the complex material constants of spherical and cylindrical ring resonators. In: IEEE Proceedings of Ultrasonic Symposium, pp 987–990
Tiersten HF (1969) Linear piezoelectric plate vibrations. Plenum Press, New York
Uchino K, Zhuang Y, Ural SO (2011) Loss determination methodology for a piezoelectric ceramic: New phenomenological theory and experimental proposals. J Adv Diel 1(1):17–31
Wang J, Yang J (2000) Higher-order theories of piezoelectric plates and applications. Appl Mech Rev 53(4):87–99
Weisstein EW (2016) Lommel function. In: Mathworld — A Wolfram web resource. http://mathworld.wolfram.com/LommelFunction.html. Accessed 20 Apr 2016
Yang J (2006) The mechanics of piezoelectric structures. World Scientific, Singapore
Zelenka J (1986) Piezoelectric resonators and their applications. Elsevier, Amsterdam
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Erhart, J., Půlpán, P., Pustka, M. (2017). Piezoelectric Ceramic Resonators (Resonance Frequency and Equivalent Electrical Circuit). In: Piezoelectric Ceramic Resonators. Topics in Mining, Metallurgy and Materials Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-42481-1_3
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DOI: https://doi.org/10.1007/978-3-319-42481-1_3
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