Investigating the vibration of cracked micro-cantilever beam with concentrated mass and rotary inertia based on MCST

The current paper proposes the vibrational behavior of a cracked micro-cantilever Euler-Bernoulli beam with a concentrated mass and its moment of inertia at the free-end boundary condition based on the Modified Couple Stress Theory (MCST). We model the open-edge crack and calculate its stiffness. We also consider The Stress Intensity Factor (SIF). Using Hamilton’s principle, the associated boundary conditions followed by the system’s dynamic equations are derived based on MCST. Afterward, the natural frequencies of the cracked micro-cantilever beam are semi-analytically determined. In the numerical results, we obtain the first three natural frequencies of the system versus various parameters containing the crack depth and location changes and the material length scale parameter with the different mass ratios. The results are verified with similar previous research. The calculated results indicate that increasing the crack depth, approaching the crack location to the concentrated mass and the node points, and increasing the mass ratio cause a decrease in frequencies. However, increasing the material length scale parameter causes an increase in the natural frequencies due to raising the total strain energy of the system.

Keywords:

crack , Micro-cantilever Beam , MCST , Mass Ratio , natural frequency