Harmonic oscillations of a piezoceramic functional-graded sectional cylinders with account of energy dissipation





sectioned piezoceramic cylinder; functional-gradient material; harmonic response; FEM; Rayleigh damping; electrical resonance and antiresonance


Harmonic oscillations of piezoceramic functional-gradient sectioned hollow cylinders are studied, taking into account energy dissipation. A cylinder of finite length is considered, consisting of an even number of sections polarized in the circular direction, which are connected to each other by similar sides. The material is considered to be functionally heterogeneous in the direction of the previous polarization. The cylinder is loaded by the potential difference applied to the flat faces of the sections. The calculation is performed by the finite element method. The forming of damping matrix and determining the coefficients corresponding to the four ways of introducing Rayleigh damping into the FEM is described. Amplitude-frequency responses taking into account damping are built for displacements, charge on the electrodes, electrical admittance and its logarithm. The consideration of energy dissipation according to the Rayleigh damping model is related to the experimental data due to the Q factor of the piezo element. The frequencies of electrical resonances, anti-resonances and the corresponding electromechanical coupling coefficients for functionally inhomogeneous and homogeneous cylinders are determined. For the functional-gradient piezoelectric element of the considered configuration, the maximum CEMC occurs at the frequency of the second electrical resonance. At this frequency, the dynamic stress-strain state of the cylinder is investigated. Forms of oscillations and distribution of stress amplitude values are constructed. The largest normal stresses according to the Coulomb-Mohr strength theory are determined and compared with the von Mises strength theory. FEA allows three-dimensional calculation of harmonic oscillations of functional-gradient piezo elements of complicated geometry. The determined frequencies of electrical resonance and anti-resonance and the corresponding CEMC make it possible to choose the most effective operating mode of the piezo element. The FEM mathematical apparatus makes it possible to quickly and qualitatively evaluate the strength, determine the charge on the electrodes, the current in the circuit, build the amplitude-frequency characteristics of admittance and impedance, and evaluate the efficiency of energy conversion.


  1. N. A. Shulha and A. M. Bolkysev, Kolebanyia pezokeramycheskykh tel. K: Nauk. dumka, 1990.
  2. Y. Grigorenko, W. H. Müller and I. A. Loza, Selected Problems in the Elastodynamics of Piezoceramic Bodies. Cham: Springer Int. Publishing, 2021. https://doi.org/10.1007/978-3-030-74199-0
  3. V. Yanchevskyi, Nestatsionarni kolyvannia bimorfnykh elektropruzhnykh til. Kyiv: KPI im. Ihoria Sikorskoho, 2023.
  4. O. Leiko, N. Bogdanova, O. Bogdanov, O. Drozdenko and K. Drozdenko, “Possibilities of Controlling the Dynamic Properties of a Cylindrical Piezoceramic Acousto-electronic Device with Two-frequency Resonance Excitation”, J. Nano- Electron. Phys., V. 12, № 6, p. 06003–1–06003–6, 2020. https://doi.org/10.21272/jnep.12(6).06003
  5. S. J. Rupitsch, Piezoelectric Sensors and Actuators. Berlin, Heidelberg: Springer, 2019. https://doi.org/10.1007/978-3-662-57534-5
  6. F. Kirichok and O. A. Cherniushok, “Forced Vibration and Self-Heating of a Thermoviscoelastic Cylindrical Shear Compliant Shell with Piezoelectric Actuators and Sensors*”, Int. Appl. Mechanics, January 2021. https://doi.org/10.1007/s10778-021-01049-7
  7. F. Kyrychok, Y. O. Zhuk, O. A. Chernyushok and A. P. Tarasov, “Axisymmetric Resonant Vibrations and Vibration Heating of an Inelastic Cylindrical Shell Compliant to Shear with Piezoelectric Actuators and Rigidly Fixed End Faces”, J. Math. Sci., May 2023. https://doi.org/10.1007/s10958-023-06480-4
  8. V. M. Zaika, “Metody ta zasoby proektuvannia piezokeramichnykh peretvoriuvachiv dlia kompiuternykh akustychnykh vymiriuvalnykh system”, Dysertatsiia na zdobuttia naukovoho stupenia kandydata tekhnichnykh nauk, Cherkasy, 2016.
  9. J. Kocbach, “Finite Element Modeling of Ultrasonic Piezoelectric Transducers”, a dr. scient. project., Univ. Bergen, Bergen, 2000.
  10. V. T. Rathod, “A Review of Electric Impedance Matching Techniques for Piezoelectric Sensors, Actuators and Transducers”, Electronics, V. 8, pp. 169, February 2019. https://doi.org/10.3390/electronics8020169
  11. V. Dubenets, O. Savchenko ta O. Derkach, “Active damping of nonstationary vibrations in a beam with electro-viscoelastic patches”, Visn. Chernih. derzh. tekhnol. un-tu, V. 71, pp. 43–49, January 2014.
  12. R. D. Yershov, O. V. Savchenko, A. P. Zinkovskii and O. L. Derkach, “Electronic System for Calculation-Experimental Determination of the Modal and Damping Characteristics of Active Viscoelastic Beams”, in 2020 IEEE 40th Int. Conf. Electron. Nanotechnol. (ELNANO), Kyiv, Ukraine, 22–24 of april. 2020. IEEE, 2020. https://doi.org/10.1109/elnano50318.2020.9088927
  13. J. Li, Y. Xue, F. Li and Y. Narita, “Active vibration control of functionally graded piezoelectric material plate”, Composite Struct., V. 207, Pp. 509–518, January 2019. https://doi.org/10.1016/j.compstruct.2018.09.053
  14. V. G. Karnaukhov, I. F. Kirichok and V. I. Kozlov, “Thermomechanics of Inelastic Thin-Walled Structural Members with Piezoelectric Sensors and Actuators Under Harmonic Loading (Review)”, Int. Appl. Mechanics, V. 53, pp. 6–58, January 2017. https://doi.org/10.1007/s10778-017-0789-3
  15. I. A. Guz, Y. A. Zhuk and C. M. Sands, “Analysis of the vibrationally induced dissipative heating of thin-wall structures containing piezoactive layers”, Int. J. Non-Linear Mechanics, V. 47, pp. 105–116, March 2012. https://doi.org/10.1016/j.ijnonlinmec.2011.03.004
  16. O. Ishchenko and M. Kryshchuk, “Safety margin determination of the nuclear power plant reactor pressure vessel with taking into account warm pre-stress effect”, Mechanics Adv. Technol., vol. 6, no. 3, Dec. 2022. https://doi.org/10.20535/2521-1943.2022.6.3.268515
  17. K. Rudakov, “Procedure of the updated calculations of disks of aero – engines with removable blades a finite element method in three – dimensional statement in the environment of Femap/Nastran”, Mechanics Adv. Technol., vol. 5, no. 1, pp. 22–32, Jun. 2021. https://doi.org/10.20535/2521-1943.2021.5.1.226931
  18. O. Krivenko, Y. Vorona, and A. Kozak, “Finite element analysis of nonlinear deformation, stability and vibrations of elastic thin-walled structures”, Strength Mater. Theory Struct., no. 107, pp. 20–34, Oct. 2021. https://doi.org/10.32347/2410-2547.2021.107.20-34
  19. M. O. Shulha and V. L. Karlash, Rezonansni elektromekhanichni kolyvannia piezoelektrychnykh plastyn. Kyiv: Nauk. dumka, 2008.
  20. K. Uchino, Y. Zhuang and S. O. Ural, “Loss determination methodology for a piezoelectric ceramic: new phenomenological theory and experimental proposals”, J. adv. dielectrics, V. 01, pp. 17–31, January 2011. https://doi.org/10.1142/s2010135x11000033



How to Cite

L. Hryhorieva and I. Yanchevskyi, “Harmonic oscillations of a piezoceramic functional-graded sectional cylinders with account of energy dissipation”, Mech. Adv. Technol., vol. 8, no. 1(100), pp. 98–107, Mar. 2024.