Crack mathematical modeling to study the vibration analysis of cracked micro beams based on the MCST

In this paper, a new approach is presented to capture size effect on the dynamic behavior of a cracked micro beam based on the modified couple stress theory (MCST). Firstly, the stiffness of equivalent torsional spring at the crack location is obtained based on the MCST and also considering the stress intensity factor for different models of the open edge crack. To capture size dependency, the governing equations of motion of the system and also associated boundary conditions are derived based on the MCST and using Hamilton's principle and stress intensity factor at crack location. Then the natural frequencies of the cracked micro beam are determined. Finally, the variation of natural frequencies of the system are studied with respect to different values of the system parameters such as the material length scale parameter, crack depth, crack location, based on the MCST and considering the newly proposed modeling of the local stiffness at the crack location. The results show that the crack depth, crack location, and also the material length scale parameter are extremely effective on lateral vibrations characteristics of the system.