Eigenvibrations in trapped-energy contoured piezoelectric resonators with a one-sided arbitrarily oriented elliptical convexity

A mathematical model of a piezoelectric plate is discussed with a one-sided convex surface of an arbitrary shape. Generic relations are given to calculate the frequency spectrum and distributions of the vibration amplitudes with normal drive levels. A particular case of the ellipsoidal convexity is studied, that is arbitrarily oriented with respect to the plate axes. A numerical example for such a curvature is also given. Based upon this, we show that the frequency spectrum is critically dependent on the angle between the main ellipsoid axis and the rotated coordinates of a piezoelectric plate and to the ratio of the main radii of an ellipsoid. We notice that such a surface allows for a proper placement of the anharmonics in the frequency spectrum, avoiding their interaction caused by environment. It may also be useful to model the manufacturing imperfection and its influence upon the vibration spectra.