Dynamic Analysis of Cracked FGM Cantilever Beam

  • Sarada Prasad Parida
  • Pankaj C. Jena
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The development and presence of crack in engineering structures is a natural phenomenon. Now a day’s, FGMS being a modern class of material. Due to its physical and mechanical properties varying through a particular geometrical regions, it is utilized in many of the structural applications. These structures like other metallic and composites are exposed to dynamic conditions. Hence, an FGM structure with initial cracks when subjected to dynamic environment, the performance of the structure is remarkably affected. So the study of the performance of the structures with cracks has been kept as a great area of interest. In this work, the effect of initial cracks at different positions with variable severity on dynamic property as a function of natural frequency is determined. For the purpose, a FGM cantilever beam of size 500 × 20 × 20 mm made of SUS304 and Si3N4 is simulated for free vibration in finite element method using.


FGM Cantilever Crack Finite element 



The authors do hereby acknowledge the Department of Production Engineering, VSSUT, Burla, and TEQIP-III for providing the infrastructure facilities and financial support for carrying out this research work.


  1. 1.
    Rizos PF, Aspragathos N, Dimarogonas AD (1990) Identification of crack location and magnitude in a cantilever beam from the vibration modes. J Sound Vib 138:381–388CrossRefGoogle Scholar
  2. 2.
    Shen MHH, Pierre C (1990) Natural modes of Bernoulli-Euler beams with symmetric cracks. J Sound Vib 138:115–134CrossRefGoogle Scholar
  3. 3.
    Liang RY, Choy FK, Hu J (1991) Detection of cracks in beam structures using measurements of natural frequencies. J Franklin Inst 328(4):505–518CrossRefGoogle Scholar
  4. 4.
    Narkis Y (1994) Identification of crack location in vibrating simply supported beams. J Sound Vib 172(4):549–558CrossRefGoogle Scholar
  5. 5.
    Krawczuk M, Ostachowicz WM (1995) Modeling and vibration analysis of a cantilever composite beam with a transverse open crack. J Sound Vib 183:69–89CrossRefGoogle Scholar
  6. 6.
    Nandwana BP, Maiti SK (1997) Modeling of vibration of beam in presence of inclined edge or internal crack for its possible detection based on frequency measurements. Eng Fract Mech 58:193–205CrossRefGoogle Scholar
  7. 7.
    Erdogan F, Wu BH (1997) The surface crack problem for a plate with functionally graded properties. J Appl Mech 64:448–456Google Scholar
  8. 8.
    Hsu MH (2005) Vibration analysis of edge-cracked beam on elastic foundation with axial loading using the differential quadrature method. Comput Methods Appl Mech Eng 194:1–17CrossRefGoogle Scholar
  9. 9.
    Lin HP, Chang SC (2006) Forced responses of cracked cantilever beams subjected to a concentrated moving load. Int J Mech Sci 48:1456–1463CrossRefGoogle Scholar
  10. 10.
    Loya JA, Rubio L, Saez JF (2006) Natural frequencies for bending vibrations of Timoshenko cracked beams. J Sound Vib 290:640–653CrossRefGoogle Scholar
  11. 11.
    Kisa M, Gurel MA (2007) Free vibration analysis of uniform and stepped cracked beams with circular cross sections. Int J Eng Sci 45:364–380CrossRefGoogle Scholar
  12. 12.
    Aydin K (2007) Vibratory characteristics of axially loaded Timoshenko beams with arbitrary number of cracks. J Vib Acoust 129:341–354CrossRefGoogle Scholar
  13. 13.
    Aydin K (2008) Vibratory characteristics of Euler-Bernoulli beams with an arbitrary number of cracks subjected to axial load. J Vib Control 14:485–510CrossRefGoogle Scholar
  14. 14.
    Yang J, Chen Y (2008) Free vibration and buckling analyses of functionally graded beams with edge cracks. Compos Struct 83:48–60CrossRefGoogle Scholar
  15. 15.
    Ke LL, Yang J, Kitipornchai S, Xiang Y (2009) Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials. Mech Adv Mater Struct 16:488–502CrossRefGoogle Scholar
  16. 16.
    Matbuly MS, Ragb O, Nassar M (2009) Natural frequencies of a functionally graded cracked beam using differential quadrature method. Appl Math Comput 215:2307–2316Google Scholar
  17. 17.
    Yan T, Kitipornchai S, Yang J, He XQ (2011) Dynamic behaviour of edge-cracked shear deformable functionally graded beams on an elastic foundation under a moving load. Compos Struct 93:2992–3001CrossRefGoogle Scholar
  18. 18.
    Wei D, Liu YH, Xiang ZH (2012) An analytical method for free vibration analysis of functionally graded beams with edge cracks. J Sound Vib 331:1685–1700CrossRefGoogle Scholar
  19. 19.
    Sherafatnia K, Farrahi GH, Faghidian SA (2014) Analytic approach to free vibration and bucking analysis of functionally graded beams with edge cracks using four engineering beam theories. Int J Eng 27(6):979–990Google Scholar
  20. 20.
    Khiem NT, Huyen NN (2017) A method for crack identification in functionally graded Timoshenko beam. J Nondestr Test Eval 32(3)Google Scholar
  21. 21.
    Jena PC, Parhi DR, Pohit G (2016) Dynamic study of composite cracked beam by changing the angle of bidirectional fibres. Iran J Sci Technol Trans A 40Al:27–37Google Scholar
  22. 22.
    Jena PC, Parhi DR, Pohit G (2014) Theoretical, numerical (FEM) and experimental analysis of composite cracked beams of different boundary conditions using vibration mode shape curvatures. Int J Eng Technol 6.2:509–518Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Sarada Prasad Parida
    • 1
  • Pankaj C. Jena
    • 1
  1. 1.Department of Production EngineeringVeer Surendra Sai University of TechnologyBurlaIndia

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