Shmaliy O. Mathematical modeling of self-vibrations of reso-nators with thin convex piezoelectric plates

The object is the self-vibrations of one-sided convex piezoelectric plates with thickness-shear vibrations, where the convexity is spherical, ellipsoidal or arbitrarily; the subjects are the mathematical models of the self-vibrations of one-sided convex piezoelec-tric plates with thickness-shear vibrations, where the convexity is spherical, ellipsoidal or arbitrarily; the purpose is to improve the existent and to develop new mathematical models of the self-vibrations of one-sided convex piezoelectric plates with thickness-shear vibrations; methods - differential equations theory, theoretic physics, perturbations theory, mathematical physics, differential geometry, theory of the special functions of mathematical physics; novelty - the mathematical model of the one-sided convex piezoelectric plate with one-sided electrodes assuming abrupt change in a potential at the electrode bounds is first developed; the method of the calculating of frequency spectrum of the one-sided convex piezoelectric plate with one-sided electrodes assuming small change in a potential at the electrode bounds is first developed; the method of modeling one-sided convex piezoelectric plate is improved by introducing new additional parameters in the plate geometry, where the convex surface has the arbitrary curvature and the direction of the main curvature; efficiency - branch; application - piezo-electric devices development.