Investigation of Crack Effects on the Nonlinear Vibrations of Microbeams with a Tip Mass in a Magnetic Field

Microelectromechanical systems (MEMS) are critical members of modern technological devices, due to their applications in various industrial fields. In the physical applications of MEMS, cracks are a common structural problem, affecting the static and dynamic behavior of the system. In this paper, the effects of cracks on microbeams with a tip mass under the influence of a magnetic field have been investigated. The micro-size effect of the beam has been involved into the model by using the modified couple stress theory. The crack has been modeled by using a torsional spring, with the spring coefficient corresponds to the severity of the crack. Thus, the beam has been modeled as consisting of two segments connected by a torsional spring. The equations of motion have been formulated using Hamilton’s principle. The obtained equations have been solved by using the method of multiple scales, a perturbation technique. Frequencies regarding both linear and nonlinear vibrations of the microbeams have been examined. The results obtained in this study have been validated by using available numerical results in the literature. The effects of parameters such as crack severity, crack location, tip mass and the magnetic field force on linear and nonlinear vibrations have been presented. The results indicate a significant decrease in the natural frequencies and nonlinear frequencies of microbeams with increasing crack severity.