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.

考虑了沿其对称主轴旋转的薄环形壳的自由振动和受迫振动。动机是探索新架构的一般研究工作，以提高谐振壳型微传感器的性能，特别是壳型角速率传感器（微型陀螺仪）的性能。结构的降阶 (RO) 模型以及有限元分析共同表明某些振动模式沿着内部负高斯曲率（环面的一部分）强烈局部化。我们表明 RO 模型是一种有效的工具，用于识别局部特征模态，以及评估由陀螺科里奥利引起的相关特征频率分裂和退化特征模态对之间的能量转移，可用于转速传感。论文中展示的振动定位有利于减少锚定损失和提高质量因素，使环形壳成为科里奥利振动微型陀螺仪中实施的有吸引力的候选者。