Simulation of crack influence on the free vibration of a rectangular plate using the finite element method (FEM)
الموضوعات :
Ahmad Haghani
1
,
Soleyman Esmaeil zadeh
2
1 - Department of Mechanics, Faculty of Engineering, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran
2 - M.Sc. Student in Mechanical Engineering, Faculty of Engineering, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran
الکلمات المفتاحية: Free Vibration, Crack, Natural frequency,
ملخص المقالة :
Today, sheet metals are extensively utilized in various industries as one of the most crucial components. The presence of a crack in a structural element reduces local stiffness and consequently weakens the structure's resistance. Any change in local stiffness affects modal factors including mode shapes, natural frequencies, and structural damping. A major challenge in structural health monitoring is identifying the severity and location of potential cracks. Continuous evaluation is essential to ensure the proper functioning of many structures. This study presents an engineering perspective on the influence of cracks on vibration frequencies considering crack dimensions and locations. Finite element simulations, a widely accepted computational tool, were employed for this investigation. After verifying the convergence of the solution method, the simulation results were compared with those found in other sources, showing good agreement. Finally, the impact of crack orientation and position on the natural frequencies of the system was analyzed.
[1] Q. Xiong, H. Guan, H. Ma, Z. Wu, J. Zeng, W. Wang and H. Wang, “Crack propagation and induced vibration characteristics of cracked cantilever plates under resonance state: Experiment and simulation,” Mechanical Systems and Signal Processing, vol. 201, p.110674, 2023.
[2] T. Wang, C. Wang, Y. Yin, Y. Zhang, L. Li and D. Tan, “Analytical approach for nonlinear vibration response of the thin cylindrical shell with a straight crack,” Nonlinear Dynamics, vol. 111(12), pp.10957-10980, 2023.
[3] Z.Y. Wu, H. Yan, L.C. Zhao, G. Yan, Z.B. Yang, H.F. Hu and W.M. Zhang, “Axial-bending coupling vibration characteristics of a rotating blade with breathing crack,” Mechanical Systems and Signal Processing, vol. 182, p.109547, 2023.
[4] N.C. Tho, P.H. Cong, A.M. Zenkour, D.H. Doan, and P. Van Minh, “Finite element modeling of the bending and vibration behavior of three-layer composite plates with a crack in the core layer,” Composite Structures, vol. 305, p.116529, 2023.
[5] Z. Hu, Z. Ni, D. An, Y. Chen and R. Li, “Hamiltonian system-based analytical solutions for the free vibration of edge-cracked thick rectangular plates,” Applied Mathematical Modelling, vol. 117, pp.451-478, 2023.
[6] E.S. Khoram-Nejad, S. Moradi and M. Shishehsaz, “Effect of crack characteristics on the vibration behavior of post-buckled functionally graded plates,” Structures, vol. 50, pp. 181-199, 2023.
[7] M.S. Taima, T.A. El-Sayed, M.B. Shehab, S.H. Farghaly and R.J. Hand, “Vibration analysis of cracked beam based on Reddy beam theory by finite element method,” Journal of Vibration and Control, vol.29(19-20), pp.4589-4606, 2023.
[8] S. Wu, J. Pan, P.S. Korinko and M.J. Morgan, “Simulations of Crack Extensions in Arc-Shaped Tension Specimens of Uncharged and Tritium-Charged-and-Decayed Austenitic Stainless Steels Using Cohesive Zone Modeling,” In Pressure Vessels and Piping Conference, USA, 2020.
[9] R. Citarella and V. Giannella, “Advanced Numerical Approaches for Crack Growth Simulation,” Applied Sciences, vol. 13(4), p.2112, 2023.
[10] A.M. Alshoaibi, and A.H. Bashiri, “Adaptive finite element modeling of linear elastic fatigue crack growth,” Materials, vol. 15(21), p.7632, 2022.
[11] A.P. Singh, A. Tailor, C.S. Tumrate and D. Mishra, “Crack growth simulation in a functionally graded material plate with uniformly distributed pores using extended finite element method,” Materials Today: Proceedings, vol. 60, pp.602-607, 2022.
[12] E.E. Gdoutos, “Fracture mechanics: an introduction,” In Springer, 3rd ed., Switzerland AG 2020, ch. 2, p. 15.
[13] M. Krawczuk, A. Żak, and W., “Ostachowicz, Finite element model of plate with elasto-plastic through crack,” Computers & Structures, vol. 79(5), pp.519-532, 2001.
