Free vibration analysis of size-dependent cracked microbeam based on the modified couple stress theory

This paper investigates the analysis for free transverse vibration of a cracked microbeam based on the modified couple stress theory within the framework of Euler-Bernoulli beam theory. The governing equation and the related boundary conditions are derived by using Hamilton's principle. The cracked beam is modeled by dividing the beam into two segments connected by a rotational spring located at the cracked section. This model invokes the consideration of the additional strain energy caused by the crack and promotes a discontinuity in the bending slope. In this investigation, the influence of diverse crack position, crack severity, material length scale parameter as well as various Poisson's ratio on natural frequencies is studied. A comparison with the previously published studies is made, in which a good agreement is observed. The results illustrate that the aforementioned parameters are playing a significant role on the dynamic behavior of the microbeam.