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http://dx.doi.org/10.12989/aas.2016.3.1.095

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)
Publication Information
Advances in aircraft and spacecraft science / v.3, no.1, 2016 , pp. 95-112 More about this Journal
Abstract
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.
Keywords
Carrera unified formulation; beam; finite element; advanced models; damage analysis;
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  • Reference
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.   DOI
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.   DOI
6 Carrera, E. (2002), "Theories and finite elements for multilayered, anisotropic, composite plates and shells", Arch. Comput. Meth. Eng., 9(2), 87-140.   DOI
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.   DOI
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.   DOI
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.   DOI
13 Carrera, E., Pagani, A. and Petrolo, M. (2012b), "Component-wise method applied to vibration of wing structures", J. Appl. Mech., 80(4), 041012.   DOI
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.   DOI
15 Carrera, E. and Petrolo, M. (2012a), "Refined beam Elements with only displacement variables and plate/shell capabilities", Meccanica, 47(3), 537-556.   DOI
16 Carrera, E. and Petrolo, M. (2012b), "Refined one-dimensional formulations for laminated structure analysis", AIAA J., 50(1), 176-189.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
29 Salawu, O.S. and Williams, C. (1995), "Bridge assessment using forced-vibration testing", J. Struct. Eng., 121(2), 161-173.   DOI
30 Schardt, R. (1994), "Generalized beam theory - An adequate method for coupled stability problems", Thin Wall. Struct., 19(2-4), 161-180.   DOI
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.   DOI
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.   DOI
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.   DOI
34 Zhao, J. and Zhang, L. (2012), "Structural damage identification based on the modal data change", Int. J. Eng. Manuf., 4, 59-66.