Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Free vibration analysis of functionally graded plates containing embedded curved cracks

  • Khalafi, Vahid (Aerospace Engineering Department, Shahid Sattari Aeronautical University of Science and Technology) ;
  • Fazilati, Jamshid (Department of Aeronautical Science and Technology, Aerospace Research Institute)
  • Received : 2021.02.14
  • Accepted : 2021.05.03
  • Published : 2021.07.25
⟨ Previous Next ⟩

Abstract

In the present paper, the free vibration behavior of functionally graded plates containing straight and curved embedded crack is investigated. A NURBS-based multi-patch isogeometric analysis formulation is utilized based on the first-order shear deformation plate theory. The Nitsche technique is implemented to meet the inter-patch connection constraints. The crack line is assumed as a narrow cut along a straight or free-shape curve path within the plate. The crack growth phenomena are overlooked. The accuracy and quality of the obtained results are compared to those available in the literature. Subsequently, the effect of various material and geometry parameters on the free vibration characteristics of cracked FG plate including the volume-fraction index, crack shape, crack length, crack orientation and, crack location are examined. It learned that the straight crack inclination angle mainly influences the fifth and fourth natural modes. Moreover, the FGM mixture index doesn't noticeably affect the frequency trends. No considerable impact is noted between the edge constraint setups on the fundamental frequency.

Keywords

Acknowledgement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References

  1. Azam, M.S., Ranjan, V. and Kumar, B. (2015), "Finite element modelling and analysis of free vibration of a square plate with side crack", Differ. Eq. Dyn. Syst., 1-13. https://doi.org/10.1007/s12591-015-0241-2.
  2. Bhardwaj, G., Singh, I.V., Mishra, B.K. and Bui, T.Q. (2015), "Numerical simulation of functionally graded cracked plates using NURBS based XIGA under different loads and boundary conditions", Compos. Struct., 126, 347-359. https://doi.org/10.1016/j.compstruct.2015.02.066.
  3. Doan, D., Do, T.V., Nguyen, N.X., Vinh, P.V. and Trung, N.T. (2021), "Multi-phase-field modelling of the elastic and buckling behaviour of laminates with ply cracks", Appl. Math. Model., 94, 68-86. https://doi.org/10.1016/j.apm.2020.12.038.
  4. Dornisch, W., Vitucci, G. and Klinkel, S. (2015), "The weak substitution method - an application of the mortar method for patch coupling in NURBS-based isogeometric analysis", Int. J. Numer. Meth. Eng., 103, 205-234. https://doi.org/10.1002/nme.4918.
  5. Du, X., Zhao, G., Wang, W. and Fang, H. (2020), "Nitsche's method for non-conforming multipatch coupling in hyperelastic isogeometric analysis", Comput. Mech., 65, 687-710. https://doi.org/10.1007/s00466-019-01789-x.
  6. Du, X., Zhao, G., Wang, W., Liu, B. and Fang, H. (2017), "Application of isogeometric method to free vibration of Reissner-Mindlin plates with non-conforming multi-patch", Comput. Aid. Des., 82, 127-139. https://doi.org/10.1016/j.cad.2016.04.006.
  7. Fazilati, J. and Khalafi, V. (2019), "Effects of embedded perforation geometry on the free vibration of tow steered variable stiffness composite laminated panels", Thin Wall. Struct., 144, 106287. https://doi.org/10.1016/j.tws.2019.106287.
  8. Fazilati, J. and Khalafi, V. (2020), "Dynamic analysis of the composite laminated repaired perforated plates by using multi-patch IGA method", Chin. J. Aeronaut., 34(1), 266-280. https://doi.org/10.1016/j.cja.2020.09.038.
  9. Gayen, D., Rajiv, T. and Chakraborty, D. (2019), "Static and dynamic analyses of cracked functionally graded structural components: a review", Compos. Part B, 173, 106982. https://doi.org/10.1016/j.compositesb.2019.106982.
  10. Gu, J., Yu, T., Lich Le, V., Nguyen, T. and Bui, T.Q. (2018), "Adaptive multi-patch isogeometric analysis based on locally refined B-splines", Comput. Meth. Appl. Mech. Eng., 339, 704-738. https://doi.org/10.1016/j.cma.2018.04.013.
  11. Huang, C., McGee, O.G. and Chang, M. (2011), "Vibrations of cracked rectangular FGM thick plates", Compos. Struct., 93, 1747-1764. https://doi.org/10.1016/j.compstruct.2011.01.005.
  12. Huang, C.S. and Leissa, A.W. (2009), "Vibration analysis of rectangular plates with side cracks via the Ritz method", J. Sound Vib., 323(3-5), 974-988. https://doi.org/10.1016/j.jsv.2009.01.018.
  13. Huang, C.S., Leissa, A.W. and Li, R.S. (2011), "Accurate vibration analysis of thick, cracked rectangular plates", J. Sound Vib., 330(9), 2079-2093. https://doi.org/10.1016/j.jsv.2010.11.007.
  14. Hughes, T.J.R., Cottrell, J.A. and Bazilevs, Y. (2005), "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Comput. Meth. Appl. Mech. Eng., 194, 4135-4195. https://doi.org/10.1016/j.cma.2004.10.008.
  15. Israr, A., Cartmell, P., Manoach, E., Trendafilova, I., Ostachowicz, W., Krawczuk, M. and Zak, A. (2009), "Analytical modeling and vibration analysis of partially cracked rectangular plates with different boundary conditions and loading", J. Appl. Mech., 76(1), 11005-11013. https://doi.org/10.1115/1.2998755.
  16. Lee, H.P. and Lim, S.P. (1993), "Vibration of cracked rectangular plates including transverse shear deformation and rotary inertia", Comput. Struct., 49(4), 715-718. https://doi.org/10.1016/0045-7949(93)90074-N.
  17. Li, K., Yu, T., Bui, T.Q. (2020), "Adaptive extended isogeometric upper-bound limit analysis of cracked structures", Eng. Fract. Mech., 235, 107131. https://doi.org/10.1016/j.engfracmech.2020.107131.
  18. Liew, K.M., Hung, K.C. and Lim, M.K. (1994), "A solution method for analysis of cracked plates under vibration", Eng. Fract. Mech., 48(3), 393-404. https://doi.org/10.1016/0013-7944(94)90130-9.
  19. Lynn, P. and Kumbasar, N. (1967), "Free vibrations of thin rectangular plates having narrow cracks with simply-supported edges", 10th Midwestern Mechanics Conference, Fort Colins, 911-928.
  20. Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A. and Ford, R.G. (1999), "Functionally graded materials: design", Processing and Applications, Kluwer Academic Publisher, Boston, MA.
  21. Nasirmanesh, A. and Mohammadi, S. (2017), "An extended finite element framework for vibration analysis of cracked FGM shells", Compos. Struct., 180, 298-315. https://doi.org/10.1016/j.compstruct.2017.08.019.
  22. Natarajan, S., Baiz, P., Bordas, S., Rabczuk, T. and Kerfriden, P. (2011), "Natural frequencies of cracked functionally graded material plates by the extended finite element method", Compos. Struct., 93, 3082-3092. https://doi.org/10.1016/j.compstruct.2011.04.007.
  23. Natarajan, S., Baiz, P., Ganapathi, M. and Bordas, S. (2011), "Linear free flexural vibration of cracked functionally graded plates in thermal environment", Compos. Struct., 89, 1535-1546. https://doi.org/10.1016/j.compstruc.2011.04.002.
  24. Nguyen, K.D., Augarde, C.E., Coombs, W.M., AbdelWahab, M., Nguyen-Xuan, H. and Abdel-Wahab, M. (2020), "Nonconforming multipatches for NURBS-based finite element analysis of higher-order phase-field models for brittle fracture", Eng. Fract. Mech., 235, 107133. https://doi.org/10.1016/j.engfracmech.2020.107133.
  25. Nguyen, V., Kerfriden, P., Brino, M., Bordas, S. and Bonisoli, E. (2014), "Nitsche's method for two and three dimensional NURBS patch coupling", Comput. Mech., 53(6), 1163-1182. https://doi.org/10.1007/s00466-013-0955-3.
  26. Qian, G., Gu, S. and Jiang, J. (1991), "A finite element model of cracked plates and application to vibration problems", Comput. Struct., 39(5), 483-487. https://doi.org/10.1016/0045-7949(91)90056-R.
  27. Shahverdi, H. and Navardi, M. (2017), "Free vibration analysis of cracked thin plates using generalized differential quadrature element method", Struct. Eng. Mech., 62(3), 345-355. http://doi.org/10.12989/sem.2017.62.3.345.
  28. Sinha, G.P. and Kumar, B. (2021), "Review on vibration analysis of functionally graded material structural components with cracks", J. Vib. Eng. Technol., 9, 23-49. https://doi.org/10.1007/s42417-020-00208-3.
  29. Solecki, R. (1983), "Bending vibration of a simply-supported rectangular plate with a crack parallel to one edge", Eng. Fract. Mech., 18(6), 1111-1118. https://doi.org/10.1016/0013-7944(83)90004-8.
  30. Stahl, B. and Keer, L. (1972), "Vibration and stability of cracked rectangular plates", Int. J. Solid. Struct., 8, 69-91. https://doi.org/10.1016/0020-7683(72)90052-2.
  31. Su, R.K.L., Leung, A.Y.T. and Wong, S.C. (1988), "Vibration of cracked Kirchhoff's plates", Key Eng. Mater., 145-149, 167-172. https://doi.org/10.4028/www.scientific.net/KEM.145-149.167
  32. Valizadeh, N., Natarajan, S., Gonzalez-Estrada, O.A., Rabczuk, T., Bui, T.Q. and Bordas, S.P.A. (2013), "NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter", Compos. Struct., 99, 309-326. https://doi.org/10.1016/j.compstruct.2012.11.008.
  33. Xu, Z. and Chen, W. (2017), "Vibration analysis of plate with irregular cracks by differential quadrature finite element method", Shock Vib., 2017, 2073453. https://doi.org/10.1155/2017/2073453.
  34. Xue, Y., Jin, G., Ding, H. and Chen, M. (2018), "Free vibration analysis of in-plane functionally graded plates using a refined plate theory and isogeometric approach", Compos. Struct., 192, 193-205. https://doi.org/10.1016/j.compstruct.2018.02.076.
  35. Yang, H.S., Dong, C.Y., Qin, X.C. and Wu, Y.H. (2020), "Vibration and buckling analyses of FGM plates with multiple internal defects using XIGA-PHT and FCM under thermal and mechanical loads", Appl. Math. Model., 78, 433-481. https://doi.org/10.1016/j.apm.2019.10.011.
  36. Yang, J., Hao, Y., Zhang, W. and Kitipornchai, S. (2010), "Nonlinear dynamic response of a functionally graded plate with a through-width surface crack", Nonlin. Dyn., 59, 207-219. https://doi.org/10.1007/s11071-009-9533-9.
  37. Yin, S.H., Hale, J.S., Yu, T.T., Bui, T.Q. and Bordas, S.P.A. (2014), "Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates", Compos. Struct., 118, 121-138. https://doi.org/10.1016/j.compstruct.2014.07.028.
  38. Yu, T., Bui, T.Q., Yin, S., Doan, D.H., Wu, C.T., Do, T.V. and Tanaka, S. (2016), "On the thermal buckling analysis of functionally graded plates with internal defects using extended isogeometric analysis", Compos. Struct., 136, 684-695. https://doi.org/10.1016/j.compstruct.2015.11.002.