Vibration Analysis of Cracked Cantilever Beam for Various Crack Depths, Crack Locations and Crack Opening Size by Finite Element Method

International Journal of Mechanical Engineering

© 2025 by SSRG - IJME Journal

Volume 12 Issue 6

Year of Publication : 2025

Authors : Malay Quila

10.14445/23488360/IJME-V12I6P101

How to Cite?

Malay Quila, "Vibration Analysis of Cracked Cantilever Beam for Various Crack Depths, Crack Locations and Crack Opening Size by Finite Element Method," SSRG International Journal of Mechanical Engineering, vol. 12,  no. 6, pp. 1-14, 2025. Crossref, https://doi.org/10.14445/23488360/IJME-V12I6P101

Abstract:

Any structure with the presence of a crack is responsive to collapse due to a change in dynamic behaviour as the crack introduces flexibility, and thus, mode shape natural frequency is reduced due to the reduction of structural stiffness value. Change in dynamic behaviour leads to resonance formation. Hence, it is very crucial to govern the natural frequency of vibration. In this vibration analysis paper, mode shapes and natural frequencies of lateral vibration are extracted for cracked, free-cracked cantilever beams for five mode shapes. Euler-Bernoulli’s beam theory is considered to govern both natural frequencies and the shape of a cracked free cantilever beam. The natural frequency values of cracked free beam obtained from the Finite Element Method (FEM) and Euler-Bernoulli’s Beam Theory are compared. Transverse vibration analysis is expanded to analyse the effect of crack depth, position and opening size on natural frequency. As the cracked beam’s modal analysis is difficult to solve using an analytical method, software based on Finite Element Analysis (FEA) “Ansys Workbench 17.0” is taken into account for numerical analysis. The study analyses how the cracked beam’s natural frequencies for different mode shapes alter due to different situations, such as variations of crack depth, location, and opening size during vibration.

Keywords:

Cantilever beam, Modal natural frequency, Free vibration, Crack identification, FEA.

References:

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