A unified approach to the analysis of the nonstationary vibrations of piezoelectric ceramic plane layers, cylinders, and spheres taking into account the functional inhomogeneity and viscoelasticity of the material is proposed. The standard model of vibration damping and the Kelvin–Voigt viscoelastic model are considered. The proposed approach makes it possible to study the transition of the transducer to a static state or to a steady-state vibration mode under nonstationary perturbations. The effect of functional inhomogeneity on the nonstationary vibrations of a piezoelectric element is analyzed. The damping of the vibrations and viscoelastic axisymmetric vibrations of a radially polarized cylinder under electrical and mechanical perturbation using the Heaviside function is calculated. The dynamics of damping is analyzed, and the obtained results are compared with the static solution to validate the results. The generation of voltage by a piezoceramic cylinder under mechanical axisymmetric loading is also studied taking into account the viscoelastic properties of the material. It was found that the time to reach the steady-state mode for mechanical and electrical loads is almost the same.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. O. Hryhorieva and I. V. Yanchevskyi, “Nonstationary vibrations of piezoelectric transducers made of functionally graded materials,” Probl. Obch. Mekh. Mits. Konstr., No. 35, 29–41 (2022).
I. F. Kirichok, Y. A. Zhuk, and T. V. Karnaukhova, “Damping of the resonant axisymmetric vibration of an infinitely long viscoelastic cylindrical shell containing piezoelectric sensor and actuator, with allowance for self-heating,” Visn. Kyiv. Nats. Univ. im. Tarasa Shevchenka, No. 1, 35–40 (2015).
V. M. Sharapov, J. V. Sotula, and L. G. Kunitskaya, Electroacoustic Transducers, Tekhnosfera, Moscow (2013).
M. O. Shul’ga and V. L. Karlash, Resonant Electromechanical Vibrations of Piezoelectric Plates [in Ukrainian], Naukova Dumka, Kyiv (2008).
I. V. Yanchevskyi, Nonstationary Vibrations of Bimorphic Electrically Elastic Bodies, KPI im. Igorya Sikorskogo, Kyiv (2023).
I. J. Busch-Vishniac, Electromechanical Sensors and Actuators, Springer, New York (1999).
C. F. Chazal and R. Moutou Pitti, “An incremental constitutive law for ageing viscoelastic materials: a three-dimensional approach,” Compt. Rend. Mécan., 337, No. 1, 30–33 (2009).
H. L. Dai, Y. M. Fu, and J. H. Yang, “Electromagnetoelastic behaviors of functionally graded piezoelectric solid cylinder and sphere,” Acta Mech. Sinica, 23, No. 1, 55–63 (2007).
D. Fang, F. Li, B. Liu, and Y. Zhang, “Advances in developing electromechanically coupled computational methods for piezoelectrics/ferroelectrics at multiscale,” Appl. Mech. Reviews, 65, No. 6, 52 (2013).
A. Y. Grigorenko, W. H. Müller, and I. A. Loza, Selected Problems in the Elastodynamics of Piezoceramic Bodies, Springer, Cham (2021).
L. Grigoryeva, “Transient responses in piezoceramic multilayer actuators taking into account external viscoelastic layer,” Strength Mater. Theor. Struct., No. 105, 255–266 (2020).
L. O. Hryhorieva and I. V. Yanchevskyi, “Influence of material functional heterogeneity on non-stationary oscillations of piezoceramic bodies,” Strength Mater. Theor. Struct., No. 109, 359–368 (2022).
V. I. Kozlov, L. P. Zinchuk, and T. V. Karnaukhova, “Nonlinear vibrations and dissipative heating of laminated shells of piezoelectric viscoelastic materials with shear strains,” Int. Appl. Mech., 57, No. 6, 669–686 (2021).
J. Li, Y. Xue, F. Li, and Y. Narita, “Active vibration control of functionally graded piezoelectric material plate,” Comp. Struct., No. 207, 509–518 (2019).
S. J. Rupitsch, Piezoelectric Sensors and Actuators, Springer Berlin Heidelberg, Heidelberg–Berlin (2019).
K. Uchino, Y. Zhuang, and S. O. Ural, “Loss determination methodology for a piezoelectric ceramic: new phenomenological theory and experimental proposals,” J. Adv. Dielect., 1, No. 1, 17–31 (2011).
H. M. Wang, H. J. Ding, and Y. M. Chen, “Transient responses of a multilayered spherically isotropic piezoelectric hollow sphere,” Arch. Appl. Mech., No. 74, 581–599 (2005).
C. Ying and S. Zhi-fei, “Analysis of a functionally graded piezothermoelastic hollow cylinder,” J. of Zhejiang University, Science A, 6, No. 9, 956–961 (2005).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prykladna Mekhanika, Vol. 59, No. 6, pp. 84–94, November–December 2023
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Yanchevskyi, I.V., Hryhorieva, L.O. Nonstationary Vibrations of a Viscoelastic Functionally Graded Cylinder. Int Appl Mech 59, 708–717 (2023). https://doi.org/10.1007/s10778-024-01253-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-024-01253-1