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Harmonic oscillations of an electroelastic semi-infinite medium, caused by a periodic action in space. (English. Russian original) Zbl 0693.73074

J. Appl. Math. Mech. 51, No. 5, 664-667 (1987); translation from Prikl. Mat. Mekh. 51, No. 5, 845-848 (1987).
Summary: A two-dimensional boundary value problem of the harmonic oscillations of a semi-infinite piezoelectric medium with one flat boundary on which a normal displacement and an electrical field potential are given periodically, is considered. This problem occurs in the design of a number of surface acoustic wave devices. Such devices consist of a piezoelectric crystal of rectangular planform and cross-section on one of whose faces a periodic system of rectangular electrodes is superimposed. The presence of the periodically arranged electrodes on the boundary exerts an influence on the surface acoustic waves by two means: 1) electrical shorting of the surface, and 2) mechanical action on the oscillating medium because of electrode inertia. The contribution of the mechanical action here grows as the operating frequencies of the device increase.
The boundary value problem reduces to a system of periodic convolution equations. The properties of the kernels of the integral equations are established. A theorem is presented that enables one to transfer to the solution of systems of algebraic equations. A solution is constructed for the wave fields at any point of the medium. An example is considered for calculating the wave fields on the boundary of the medium.

MSC:

74F15 Electromagnetic effects in solid mechanics
78A40 Waves and radiation in optics and electromagnetic theory
74J15 Surface waves in solid mechanics
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
74B99 Elastic materials
74H99 Dynamical problems in solid mechanics
31A35 Connections of harmonic functions with differential equations in two dimensions
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References:

[1] (Matthews, H., Surface Acoustic Wave Filters (1981), Radio i Svyaz: Radio i Svyaz Moscow), /Russian translation/
[2] Viktorov, I. A., Acoustic Surface Waves in Solids (1981), Nauka: Nauka Moscow
[3] Tamm, I. E., Principles of the Theory of Electricity (1966), Nauka: Nauka Moscow
[4] Finkel’shtein, A. B., Waves in an electroelastic semi-infinite medium with a periodic system of electrodes, (Tsentra Vyssh. Shk. Estestv. Nauki, 1 (1986), Izv. Sev.-Kavk. Nauch)
[5] Evgrafov, M. A., Asymptotic Estimates and Entire Functions (1979), Nauka: Nauka Moscow · Zbl 0447.30016
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