Properties of fixed resonators with non-spherical contours: application to the resonators having spherical contours

For the simplest case of totally electroded plano-convex resonator with a particular unspherical contour respecting the lateral anisotropy of the plate and for the usual boundary conditions (totally free edge, "infinite" plate, totally fixed edges, the mode shapes are very simple. But if some parts of the edge are clamped while others are free, the solution should include higher order terms and the mode shape can become more intricate. In a second part, from computed results obtained with a numerical model, we show that the same effects exist also, with a similar amplitude, for conventional resonators having a spherical contour. The third part reports experiments made to confirm the predicted effects of the fixation. Some cases presenting effects similar to those predicted were observed. Other features of plano-convex resonators with one or with two curvatures of bi-convex and of bevelled resonators were also observed.