An improved model of the slant crack on a microbeam is presented. Based on fracture mechanics, the rotation coefficient for the slant crack is derived as a massless rotational spring accounting for the additional stress intensity factors generated by the orientation of the crack compared to the transverse crack. Comparisons between microbeams with a slant crack of different geometry parameters (slant angle, depth ratio, and crack position) are investigated with regard to the dynamic mechanical behaviors and nonlinear response. By presenting a mathematical modeling, the effects of the slant crack and the electric actuation of an electrostatically actuated fixed-fixed microbeam on the dynamic characteristics are examined in detail. It is shown that the crack position has more significant influence on the pull-in voltage value than the slant angle or the depth ratio. Approaching the slant crack to the fixed end or enlarging the external incentives amplifies the nonlinearity of the microbeam system, while the effects of depth ratio and slant angle are dependent on the crack position. The resonance frequency and the resonance amplitude are affected as well.
Zhou, H., Zhang, W. M., Peng, Z. K., & Meng, G. (2015). Dynamic Characteristics of Electrostatically Actuated Microbeams with Slant Crack. Mathematical Problems in Engineering, 2015. https://doi.org/10.1155/2015/208065