This study investigates the forced vibration characteristics of functionally graded material (FGM) beams with square cross-sections featuring V-shaped cracks. FGMs, characterized by a gradual transition in mechanical composition from a ceramic to a metallic surface, offer unique advantages in various engineering applications due to their non-uniform microstructure, which imparts varying material properties throughout the structure. This research employs ANSYS Workbench to conduct a comprehensive numerical analysis, focusing on evaluating the frequencies and mode shapes of cracked FGM beams under simply supported boundary conditions. The analysis delves into the impact of three critical crack parameters: crack opening width, crack depth, and crack location. The findings highlight that the crack opening width significantly influences the vibrational frequencies of the FGM beam. Specifically, as the crack opening width increases from 0.002 meters to 0.01 meters, the frequencies decrease across all mode shapes, indicating that wider cracks introduce greater flexibility and reduce the stiffness of the beam. For instance, the frequency for the first mode drops from 172.19 Hz for a 0.002-meter crack to 165.87 Hz for a 0.01-meter crack. This trend is consistent across higher modes, reflecting the sensitivity of the beam's dynamic behaviour to changes in crack width. Conversely, the study finds that variations in crack depth and crack location have relatively minor effects on the dynamic behaviour of the cracked FGM beam within the examined ranges. The frequencies remain largely consistent as the crack depth varies from 0.05 meters to 0.15 meters, and as the crack location shifts from 0.5 meters to 2.5 meters along the length of the beam. These observations suggest that while the presence of a crack is a critical factor, its depth and specific location along the beam length are less influential on the overall vibrational characteristics compared to the width of the crack opening. The study offers valuable insights into the dynamic behaviour of cracked FGM beams, which can inform the design and structural health monitoring of these advanced materials. By understanding how different crack parameters affect the vibrational properties, engineers can better predict and mitigate potential failures in structures utilizing FGMs.
Keywords: Functionally graded material, simply supported, numerical analysis, frequencies, crack parameters, dynamic behavior, structural health monitoring.