An approach to characterize the structural stability of inertial instrument subjected to vibration hybridizing frequency- and time-domain analysis

The gyroscope is a pivotal component of inertial navigation systems. Its centroid shift, which is strongly influenced by vibration, may lead to significant drift errors. However, there was no an approach to evaluate the vibration resistance of the structure because the nanoscale centroid shift is not possible to measure, and difficult to compute through finite element method (FEM) due to various nonlinearity. Therefore, a novel approach that combines time- and frequency-domain analysis was developed in this study to decouple the dynamic effect and the hysteresis effect. This involves a random vibration analysis to derive the power spectral density (PSD) of the motor center displacement. Subsequently, the expectation of the maximum dimensionless amplitude is calculated and a displacement history curve is constructed for the motor center, facilitating a translation from frequency domain to time domain. Finally, the motor center is reciprocally pushed according to the constructed displacement history in a static analysis, yielding the residual displacement of the motor center. The stable value of the residual displacement serves as a key indicator of the vibration resistance. Analysis of random vibration and reciprocal push were performed for a prototype and compared with experimental results to validate the proposed approach, which was then applied to a gyroscope, enabling a quantitative evaluation of its vibration resistance.