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

Petoft, Hamed; Rahi, Abbas

doi:10.22064/tava.2023.556982.1208

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

Document Type : Research Article

Authors

Hamed Petoft ¹
Abbas Rahi ²

¹ Ph.D. Candidate, Faculty of Mechanical & Energy Engineering, Shahid Beheshti University, Tehran, Iran

² Associate Professor, Faculty of Mechanical & Energy Engineering, Shahid Beheshti University, Tehran, Iran

10.22064/tava.2023.556982.1208

Abstract

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.

Highlights

A cracked micro-cantilever beam with concentrated mass and its inertia is modeled.
The governing equations and boundary conditions are obtained based on MCST.
Material length scale parameter for the beam and SIF for the crack are considered.
Effect of mass ratio with inertia is investigated on the natural frequencies.
Changing the depth and location of the crack is considered

Keywords

Main Subjects

Vibration of mechanical structures and technical acoustics

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