Non-equidistant structure of a frequency spectrum of a piezoelectric resonator with an arbitrary convex surface

Frequency spectrum of piezoelectric resonator with an arbitrary convex surface concerning non-equidistance of spectrum to the frequency square is obtained. An analysis of obtained spectrum taking into consideration small curvature 1/R of convex surface is provided. It is show how non-equidistant spectrum depends on orientation of main directions of normal cuts relative to eigenaxes of anisotropic tensor and on relation of main radiuses of curvature of convex surface