Numerical Analysis of Dynamical Processes in Inhomogeneous Piezoceramic Cylinders (Review)*
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International Applied Mechanics, Vol. 56, No. 5, September, 2020
NUMERICAL ANALYSIS OF DYNAMICAL PROCESSES IN INHOMOGENEOUS PIEZOCERAMIC CYLINDERS (REVIEW)* A. Ya. Grigorenko1*, Ya. M. Grigorenko1, and I. A. Loza2
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. Keywords: 3D theory of electroelasticity, dynamical process, piezoelectric circular waveguide, finite-length cylinder, coupled electroelastic fields, discrete-continuum methods, inhomogeneous piezoceramic materials Introduction. As noted in [65], the development of methods of numerical analysis and mechanics of coupled fields is one of basic trends in modern solid mechanics of deformable solids. The present review is devoted to the important class of electroelastic problems including dynamical processes in inhomogeneous piezoceramic cylinders. The solution of this class of problems involves severe mathematical difficulties. Therefore, it is necessary to use numerical methods. The studies described here represent an important problem of modern solid mechanics. One of the important areas of the mechanics of coupled fields is electroelasticity, which studies problems lying at the confluence of such two classical research areas as solid mechanics and continuum electrodynamics (electrostatics). The term “elecroelasticity” has been coined relatively recently (in the 1960s) and has been widely used in solid mechanics. Physicists traditionally employ the term “piezoelectricity.” The publications [10, 17, 26, 66, 74, 94] are fundamental in this field. An important stage in the evolution of electroelasticity is the development of segnetoelectric piezoceramics in the lat 1940s in several countries simultaneously. The first piezoceramic material was based on BaTiO titanium-barium powder. Noteworthy are other piezoelectric materials such as ZnO, CdS, BiGtO, TeO, LiNbO, LiTaO, BaNaNbO, and GaAs. 1
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St., Kyiv, Ukraine 03057, *e-mail: ayagri
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