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.

在这项工作中，基于格里菲斯（Griffith）的裂纹理论，同时结合了耦合应力和表面弹性，开发了一个数学模型，以检验裂纹的振动梁式微/电子显微镜的性能和可操作性。尺寸相关的裂纹严重性因子用于表示由于表面裂纹而增加的局部挠性。陀螺仪的尺寸从微米级减小到纳米级，以分析驱动侧表面裂纹对微型/纳米陀螺仪灵敏度的影响。将使用取决于尺寸的裂纹严重性计算出的静态吸合，固有频率，非线性频率响应和陀螺仪灵敏度与使用经典裂纹严重性因子获得的结果进行比较。这样可以确定长度刻度，在裂纹严重性中必须考虑尺寸依赖性。已经发现，尺寸依赖性效应显着增加了纳米陀螺仪中的裂纹严重性，与经典的裂纹严重性相比，导致传感器灵敏度的显着变化。