Reduced order modeling of vibration localization in a rotating toroidal shell for angular rate sensors applications

Free and forced vibrations of a thin toroidal shell rotating along its principal axis of symmetry are considered. The motivation is a general research effort to explore new architectures in order to enhance the performance of resonant shell-type microsensors in general and shell-type angular rate sensors (micro gyros) in particular. Reduced order (RO) model of the structure along with the finite element analysis collectively indicates that certain vibrational modes are strongly localized along the internal, negative Gaussian curvature, part of the torus. We show that the RO model is an efficient tool for identification of the localized eigenmodes, as well as assessment of the gyroscopic Coriolis-induced split of associated eigenfrequencies and energy transfer between the degenerated eigenmodes pairs, which can be used for the rotational rate sensing. The vibration localization demonstrated in the paper can be beneficial for the reduction of the anchoring losses and enhancement of the quality factors, making toroidal shell to be an attractive candidate for the implementation in Coriolis vibrating micro gyroscopes.