Free vibration analysis of circular and annular thin plates based on crack characteristics
DOI:
https://doi.org/10.31181/rme20016032022gKeywords:
Circular Plate, Annular Plate, Crack, Finite Element Method, Free Vibration.Abstract
This study presents the effect of vertical and horizontal oriented cracks on free vibration response for circular and annular thin plates. To investigate the dynamic behavior of the damaged circular structures the cracks are modeled separately considering horizontal/vertical orientations, ten different locations, and four crack sizes. For annular thin plates, vertical and horizontal oriented cracks are placed in the middle between the outer and inner edges to investigate the effect of crack directions. The first five resonant frequencies, and the corresponding mode shapes of the cracked circular and annular plates, are obtained by employing the Finite Element Method. The free vibration analyses are conducted considering clamped boundary conditions for circular plates and clamped-clamped, clamped-free, and free-clamped boundary conditions for annular plates. The results are presented and interpreted considering the differences in the non-dimensional frequencies and the mode shapes of those structures. According to the findings, it is seen that depending on its location and size, a crack can change the mode shapes by accumulating the bending regions around it. Besides, a crack may also change the number of bending regions that occurred in the mode shapes of the circular or annular structures.
References
Arshad, S.H., Naeem, M.N., & Soutis, C. (2016). Influence of ring support on free vibration of sandwich functionally graded cylindrical shells with middle layer of isotropic material. Journal of Engineering Research, 4(1), 159-186.
Bisheh, H., Alibeigloo, A., Safarpour, M., & Rahimi, A.R. (2019). Three-Dimensional static and free vibrational analysis of graphene reinforced composite circular/annular plate using differential quadrature method. International Journal of Applied Mechanics, 11(8), 1950073.
Blevins, R.D. (1993). Formulas for Natural Frequency and Mode Shape. Florida: Krieger Publishing Company.
Chakraverty, S., Bhat, R.B., & Stiharu, I. (2001). Free vibration of annular elliptic plates using boundary characteristic orthogonal polynomials as shape functions in the Rayleigh-Ritz method. Journal of Sound and Vibration, 241(3), 524-539.
Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H. & Abdel-Wahab, M. (2021). A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA. Composite Structures, 259, 113216.
Gonenli, C. & Das, O. (2021). Effect of crack location on buckling and dynamic stability in plate frame structures. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 43, 311.
Gonenli, C., Ozturk, H., & Das, O. (2022). Effect of crack on free vibration of a pre-stressed curved plate. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 236(2), 811-825.
Han, J.B., & Liew, K.M. (1999). Axisymmetric free vibration of thick annular plates. International Journal of Mechanical Sciences, 41, 1089-1109.
He, D., Shi, D., Wang, Q., & Ma, C. (2021). A unified power series method for vibration analysis of composite laminate conical, cylindrical shell and annular plate. Structures, 29, 305-327.
Huang, C.H., & Ma, C.C. (2000). Vibration of cracked circular plates at resonance frequencies. Journal of Sound and Vibration, 236(4), 637-656.
Jaiman, Y., & Singh, B. (2019). Free vibration of circular annular plate with different boundary conditions. Vibroengineering Procedia, 29, 82-86.
Khare, S., & Mittal, N.D. (2015). Free vibration analysis of thin circular and annular plate with general boundary conditions. Engineering Solid Mechanics 3: 245-252.
Leissa, A.W. (1969). Vibration of Plates. Washington: Office of Technology Utilization.
Liew, K.M., & Yang, B. (1999). Three-dimensional elasticity solutions for free vibrations of circular plates: a polynomials-Ritz analysis. Computer Methods in Applied Mechanics and Engineering, 175, 189-201.
Shi, X., Shi, D., Li, W.L., & Wang, Q. (2014). A unified method for free vibration analysis of circular, annular and sector plates with arbitrary boundary conditions. Journal of Vibration and Control, 22(2), 442-456.
Sun, X., Zhang, P., Qiao, H., & Lin, K. (2021). High-order free vibration analysis of elastic plates with multiple cutouts. Archive of Applied Mechanics, 91, 1837-1858.
Xie, K., Chen, M., Zhang, L., & Xie, D. (2017). Wave based method for vibration analysis of elastically coupled annular plate and cylindrical shell structures. Applied Acousics, 123, 107-122.
Zhang, H., Zhu, R., Shi, D., & Wang, Q. (2019. A simplified plate theory for vibration analysis of composite laminated sector, annular and circular plate. Thin-Walled Structures 143, 106252.
Zhou, Z.H., Wong, K.W., Xu, X.S., & Leung, A.Y.T. (2011). Natural vibration of circular and annular thin plates by Hamiltonian approach. Journal of Sound and Vibration, 330, 1005-1017.
