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Numerical Analysis of Dynamical Processes in Inhomogeneous Piezoceramic Cylinders (Review)*

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International Applied Mechanics Aims and scope

The review is devoted to the numerical solution of new problems of electroasticity, namely, determination of the dynamical characteristics of inhomogeneous piezoceramic waveguides of circular cross-section and inhomogeneous piezoceramic cylinders of finite length. To solve these problems, an effective numerical–analytical approach is used. The approach employs various transformations (special functions, Fourier series expansion, and spline-collocation method), which make it possible to reduce the original three-dimensional partial differential equations of electroelasticity to a boundary-value eigenvalue problem for a system of ordinary differential equations. The system is solved by the method of discrete orthogonalization. Using the results obtained, the features of spectral characteristics in an inhomogeneous structure are studied considering the coupled electric field of the piezoceramic layers. The effect of the inhomogeneity and coupled electric field on the dynamical characteristics of the bodies is studied as well. Much attention is paid to the reliability of the numerical results.

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St, Kyiv, 03057, Ukraine

    A. Ya. Grigorenko & Ya. M. Grigorenko

  2. National Transport University, 1 Omel’yanovicha-Pavlenko St, Kyiv, 01010, Ukraine

    I. A. Loza

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  1. A. Ya. Grigorenko
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Correspondence to A. Ya. Grigorenko.

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Translated from Prikladnaya Mekhanika, Vol. 56, No. 5, pp. 3–55, September–October 2020.

This study was sponsored by the budget program “Support for Priority Areas of Scientific Research” (KPKVK).

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Grigorenko, A.Y., Grigorenko, Y.M. & Loza, I.A. Numerical Analysis of Dynamical Processes in Inhomogeneous Piezoceramic Cylinders (Review)*. Int Appl Mech 56, 523–571 (2020). https://doi.org/10.1007/s10778-020-01034-6

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