Advances in aircraft and spacecraft science

  • 제3권1호
  • /
  • Pages.95-112
  • /
  • 2016
  • /
  • 2287-528X(pISSN)
  • /
  • 2287-5271(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Free vibration analysis of damaged beams via refined models

  • Petrolo, Marco (Department of Mechanical and Aerospace Engineering, Politecnico di Torino) ;
  • Carrera, Erasmo (Department of Mechanical and Aerospace Engineering, Politecnico di Torino) ;
  • Alawami, Ali Saeghier Ali Saeed (School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University)
  • 투고 : 2015.04.30
  • 심사 : 2015.07.10
  • 발행 : 2016.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents the free vibration analysis of damaged beams by means of 1D (beam) advanced finite element models. The present 1D formulation stems from the Carrera Unified Formulation (CUF), and it leads to a Component-Wise (CW) modelling. By means of the CUF, any order 2D and 1D structural models can be developed in a unified and hierarchical manner, and they provide extremely accurate results with very low computational costs. The computational cost reduction in terms of total amount of DOFs ranges from 10 to 100 times less than shell and solid models, respectively. The CW provides a detailed physical description of the real structure since each component can be modelled with its material characteristics, that is, no homogenization techniques are required. Furthermore, although 1D models are exploited, the problem unknown variables can be placed on the physical surfaces of the real 3D model. No artificial surfaces or lines have to be defined to build the structural model. Global and local damages are introduced by decreasing the stiffness properties of the material in the damaged regions. The results show that the proposed 1D models can deal with damaged structures as accurately as a shell or a solid model, but with far lower computational costs. Furthermore, it is shown how the presence of damages can lead to shell-like modal shapes and torsional/bending coupling.

키워드

참고문헌

  1. Allemang, R.J. and Brown, D.L. (1982), "A correlation coefficient for modal vector analysis", Proceedings of the 1st SEM International Modal Analysis Conference, Orlando, FL, November.
  2. Balsamo, L. and Mukhopadhyay, S., Betti, R. and Lus, H. (2013), "Damage Detection Using Flexibility Proportional Coordinate Modal Assurance Criterion", Topics in Modal Analysis, Volume 7: Proceedings of the 31st IMAC, A Conference on Structural Dynamics, 2013, Conference Proceedings of the Society for Experimental Mechanics Series 45.
  3. Berdichevsky, V.L., Armanios, E. and Badir, A. (1992), "Theory of anisotropic thin-walled closed-crosssection beams", Compos. Eng., 2(5-7), 411-432. https://doi.org/10.1016/0961-9526(92)90035-5
  4. Bernoulli, D. (1751), Commentarii Academiae Scientiarum Imperialis Petropolitanae, Petropoli. Chapter, De vibrationibus et sono laminarum elasticarum.
  5. Capozuzza, R. (2014), "Vibration of CFRP cantilever beam with damage", Compos. Struct., 116, 211-222. https://doi.org/10.1016/j.compstruct.2014.04.027
  6. Carrera, E. (2002), "Theories and finite elements for multilayered, anisotropic, composite plates and shells", Arch. Comput. Meth. Eng., 9(2), 87-140. https://doi.org/10.1007/BF02736649
  7. Carrera, E. (2003), "Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking", Arch. Comput. Meth. Eng., 10(3), 216-296.
  8. Carrera, E., Cinefra, M., Petrolo, M. and Zappino, E. (2014), Finite Element Analysis of Structures through Unified Formulation, John Wiley & Sons.
  9. Carrera, E. and Giunta, G. (2010), "Refined beam theories based on a unified formulation", Int. J. Appl. Mech., 2(1), 117-143. https://doi.org/10.1142/S1758825110000500
  10. Carrera, E., Giunta, G., Nali, P. and Petrolo, M. (2010a), "Refined beam elements with arbitrary crosssection geometries", Comput. Struct., 88(5-6), 283-293. https://doi.org/10.1016/j.compstruc.2009.11.002
  11. Carrera, E., Giunta, G. and Petrolo, M. (2011), Beam Structures: Classical and Advanced Theories, John Wiley & Sons.
  12. Carrera, E., Maiaru, M. and Petrolo, M. (2012a), "Component-wise analysis of laminated anisotropic composites", Int. J. Solid. Struct., 49(13), 1839-1851. https://doi.org/10.1016/j.ijsolstr.2012.03.025
  13. Carrera, E., Pagani, A. and Petrolo, M. (2012b), "Component-wise method applied to vibration of wing structures", J. Appl. Mech., 80(4), 041012. https://doi.org/10.1115/1.4007849
  14. Carrera, E., Pagani, A. and Petrolo, M. (2013a), "Classical, refined and component-wise analysis of reinforced-shell structures", AIAA J., 51(5), 1255-1268. https://doi.org/10.2514/1.J052331
  15. Carrera, E. and Petrolo, M. (2012a), "Refined beam Elements with only displacement variables and plate/shell capabilities", Meccanica, 47(3), 537-556. https://doi.org/10.1007/s11012-011-9466-5
  16. Carrera, E. and Petrolo, M. (2012b), "Refined one-dimensional formulations for laminated structure analysis", AIAA J., 50(1), 176-189. https://doi.org/10.2514/1.J051219
  17. Carrera, E., Petrolo, M. and Nali, P. (2010b), "Unified formulation applied to free vibrations finite element analysis of beams with arbitrary section", Shock Vib., 18(3), 485-502. https://doi.org/10.1155/2011/706541
  18. Carrera, E., Petrolo, M. and Zappino, E. (2012c), "Performance of CUF approach to analyze the structural behavior of slender bodies", J. Struct. Eng., 138(2), 285-297. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000402
  19. Carrera, E., Zappino, E. and Petrolo, M. (2013b), "Analysis of thin-walled structures with longitudinal and transversal stiffeners", J. Appl. Mech., 80(1), 011006. https://doi.org/10.1115/1.4006939
  20. El Fatmi, R. and Ghazouani, N. (2011), "Higher order composite beam theory built on Saint-Venant solution. Part-I: Theoretical developments", Compos. Struct., 93(2), 557-566. https://doi.org/10.1016/j.compstruct.2010.08.024
  21. Euler, L. (1744), De curvis elasticis, Lausanne and Geneva, Bousquet.
  22. Fayyadh, M.M., Razak, H.A. and Ismail, Z. (2011) "Combined modal parameters-based index for damage identification in a beamlike structure: theoretical development and verification", Arch. Civil Mech. Eng., 11(3), 587-609. https://doi.org/10.1016/S1644-9665(12)60103-4
  23. Gopalakrishnan, S., Ruzzene, M. and Hanagud, S. (2011), Computational Techniques for Structural Health Monitoring, Springer.
  24. Kapania, K. and Raciti, S. (1989a), "Recent advances in analysis of laminated beams and plates, Part I: shear effects and buckling", AIAA J., 27(7), 923-935. https://doi.org/10.2514/3.10202
  25. Kapania, K. and Raciti, S. (1989b), "Recent advances in analysis of laminated beams and plates, Part II: vibrations and wave propagation", AIAA J., 27(7), 935-946. https://doi.org/10.2514/3.59909
  26. Ladeveze, P., Sanchez, P. and Simmonds, J. (2004), "Beamlike (Saint-Venant) solutions for fully anisotropic elastic tubes of arbitrary closed cross-section", Int. J. Solid. Struct., 41(7), 1925-1944. https://doi.org/10.1016/j.ijsolstr.2003.11.006
  27. Mukhopadhyay, S., Lus, H., Hong, L. and Betti, R. (2012), "Propagation of mode shape errors in structural identification", J. Sound Vib., 331, 3961-3975. https://doi.org/10.1016/j.jsv.2012.04.012
  28. Perez, M.A., Gil, L., Sanchez, M. and Oller, S. (2014), "Comparative experimental analysis of the effect caused by artificial and real induced damage in composite laminates", Compos. Struct., 112, 169-178. https://doi.org/10.1016/j.compstruct.2014.02.017
  29. Salawu, O.S. and Williams, C. (1995), "Bridge assessment using forced-vibration testing", J. Struct. Eng., 121(2), 161-173. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:2(161)
  30. Schardt, R. (1994), "Generalized beam theory - An adequate method for coupled stability problems", Thin Wall. Struct., 19(2-4), 161-180. https://doi.org/10.1016/0263-8231(94)90027-2
  31. Timoshenko, S.P. (1921), "On the corrections for shear of the differential equation for transverse vibrations of prismatic bars", Philos. Mag., 41, 744-746. https://doi.org/10.1080/14786442108636264
  32. Wang, Y., Liang, M. and Xiang, J. (2014), "Damage detection method for wind turbine blades based on dynamics analysis and mode shape difference curvature information", Mech. Syst. Signal Pr., 48, 351-367. https://doi.org/10.1016/j.ymssp.2014.03.006
  33. Zhang, Z., Shankar, K., Morozov, E.V. and Tahtali. M. (2014), "Vibration-based delamination detection in composite beams through frequency changes", J. Vib. Control, DOI: 10.1177/1077546314533584.
  34. Zhao, J. and Zhang, L. (2012), "Structural damage identification based on the modal data change", Int. J. Eng. Manuf., 4, 59-66.

피인용 문헌

  1. Evaluation of energy and failure parameters in composite structures via a Component-Wise approach vol.108, 2017, https://doi.org/10.1016/j.compositesb.2016.09.085
  2. Effect of Localized Damages on the Free Vibration Analysis of Civil Structures by Component-Wise Approach vol.144, pp.8, 2018, https://doi.org/10.1061/(ASCE)ST.1943-541X.0002128
  3. Experimental and numerical dynamic analysis of laminate plates via Carrera Unified Formulation vol.202, pp.None, 2016, https://doi.org/10.1016/j.compstruct.2018.05.085