Crack severity and size dependent effects on the effectiveness and operability of micro/nanogyroscopes

Abstract

In this work, a mathematical model is developed based on Griffith’s crack theory while incorporating couple stress and surface elasticity in order to examine the performance and operability of cracked vibrating beam micro/nanogyroscopes. A size dependent crack severity factor is used to represent increased local flexibility due to surface crack. The gyroscope size is decreased from micro- to nano-scale to analyze the effects of a driving side surface crack on the sensitivity of micro/nanogyroscopes. The static pull-in, natural frequencies, nonlinear frequency response, and gyroscope sensitivity that are calculated using the size dependent crack severity are compared to the results obtained using the classical crack severity factor. This allows for the determination of the length scale, in which size dependency must be considered in the crack severity. It is found that size dependent effects significantly increase the crack severity in nanogyroscopes leading to significant changes in the sensor’s sensitivity in comparison with the classical crack severity.