Commenced in January 2007
Paper Count: 30831
Vibration and Parametric Instability Analysis of Delaminated Composite Beams
Authors: A. Szekrényes
Abstract:This paper revisits the free vibration problem of delaminated composite beams. It is shown that during the vibration of composite beams the delaminated parts are subjected to the parametric excitation. This can lead to the dynamic buckling during the motion of the structure. The equation of motion includes time-dependent stiffness and so it leads to a system of Mathieu-Hill differential equations. The free vibration analysis of beams is carried out in the usual way by using beam finite elements. The dynamic buckling problem is investigated locally, and the critical buckling forces are determined by the modified harmonic balance method by using an imposed time function of the motion. The stability diagrams are created, and the numerical predictions are compared to experimental results. The most important findings are the critical amplitudes at which delamination buckling takes place, the stability diagrams representing the instability of the system, and the realistic mode shape prediction in contrast with the unrealistic results of models available in the literature.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1125055Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 940
 J.-F. Zhu, Y. Y Gu, and LTong, “Formulation of reference surface element and its applications in dynamic analysis of delaminated composite beams,” Composite Structures, vol. 68, no. 4, pp. 481–490, 2005.
 B. G. Kiral, “Free vibration analysis of delaminated composite beams,” Science and Engineering of Composite Materials, vol. 16, no. 3, pp. 209–224, 2009.
 N. H. Erdelyi and S. M. Hashemi, “A dynamic stiffness element for free vibration analysis of delaminated layered beams,” Modelling and Simulation in Engineering, vol. Article ID 492415, 8 pages, 2012.
 P. Mujumdar and S. Suryanarayan, “Flexural vibration of beams with delaminations,” Journal of Sound and Vibration, vol. 125, no. 3, pp. 441–461, 1988.
 M.-H. Shen and J. Grady, “Free vibrations of delaminated beams,” AIAA Journal, vol. 30, no. 5, pp. 1361–1370, 1992.
 M. H. Kargarnovin, M. T. Ahmadian, R. A. Jafari-Talookolaei, and M. Abedi, “Semi-analytical solution for the free vibration analysis of generally laminated composite Timoshenko beams with single delamination,” Composites Part B: Engineering, vol. 45, no. 1, pp. 587- 600, 2013.
 H. Luo and S. Hanagud, “Dynamics of delaminated beams,” International Journal of Solids and Structures, vol. 37, pp. 1501–1519, 2000.
 S. Lee, T. Park, and G. Z. Voyiadjis, “Vibration analysis of multidelaminated beams,” Composites Part B - Engineering, vol. 34, pp. 647–659, 2003.
 T. Park and a. G. Z. V. S Lee, “Recurrent single delaminated beam model for vibration analysis of multidelaminated beams,” Journal of Engineering Mechanics, vol. 130, no. 9, pp. 1072–1082, 2004.
 R.-A. Jafari-Talookolaei and M. Abedi, “Analytical solution for the freevibration analysis of delaminated Timoshenko beams,” The Scientific World Journal, 2014, article ID: 280256.
 J. Lee, “Free vibration analysis of delaminated composite beams,” Computers and Structures, vol. 74, pp. 121–129, 2000.
 H. Tang, C. Wu, and X. Huang, “Vibration analysis of a coupled beam sdof system by using the recurrence equation method,” Journal of Sound and Vibration, vol. 311, pp. 912–923, 2008.
 N. Hu, H. Fukunaga, M. Kameyama, Y. Aramaki, and F. Chang, “Vibration analysis of delaminated composite beams and plates using a higher-order finite element,” International Journal of Mechanical Sciences, vol. 44, pp. 1479–1503, 2002.
 A. Chakraborty, D. R. Mahapatra, and S. Gopalakrishnan, “Finite element analysis of free vibration and wave propagation in asymmetric composite beams with structural discontinuities,” Composite Structures, vol. 55, pp. 23–26, 2002.
 E. Manoach, J. Warminski, and A. Warminska, “Large amplitude vibrations of heated timoshenko beams with delamination,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 230, no. 1, pp. 88–101, 2016.
 A. Szekrényes, “Coupled flexural-longitudinal vibration of delaminated composite beams with local stability analysis,” Journal of sound and vibration, vol. 333, pp. 5141–5164, 2014.
 A. Szekrényes, “The system of exact kinematic conditions and application to delaminated first-order shear deformable composite plates,” International Journal of Mechanical Sciences, vol. 77, pp. 17–29, 2013.
 Z. Szabó, “Nonlinear vibrations of parametrically excited complex mechanical systems,” Ph.D. dissertation, Budapest University of Technology and Economics, Department of Applied Mechanics, Budapest, 2001.
 Z. Szabó and G. Lóránt, “Parametric excitation of a single railway wheelset,” Vehicle System Dynamics, vol. 33, no. 1, pp. 49–55, 2000.
 D. Bachrathy and G. Stépán, “Efficient stability chart computation for general delayed linear time periodic systems,” in Proceedings of the ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2013, pp. 1–9, iDETC/CIE 2013, August 4-7, Portland, Oregon, USA, DETC2013-13660.
 D. Bachrathy and G. Stépán, “Improved prediction of stability lobes with extended multi frequency solution,” CIRP Annals – Manufacturing Technology, vol. 62, pp. 411–414, 2013.
 Z. Dombóvári, A. Iglesias, M. Zatarain, and T. Insperger, “Prediction of multiple dominant chatter frequencies in milling processes,” International Journal of Machine Tools and Manufacture, vol. 51, no. 6, pp. 457–464, 2011.
 M. Zatarain, J. Alvarez, I. Bediaga, J. Munoa, and Z. Dombóvári, “Implicit subspace iteration as an efficient method to compute milling stability lobe diagrams,” International Journal of Advanced Manufacturing Technology, vol. 77, no. 1-4, pp. 597–607, 2015.
 T. Insperger and G. Stépán, Semi-discretization of time-delay systems. New York, Dordrecht, Heidelberg, London: Springer, 2011.
 D. Lehotzky, T. Insperger, and G. Stépán, “Extension of the spectral element method for stability analysis of time-periodic delay-differential equations with multiple and distributed delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 35, pp. 177–189, 2016.
 W. W. Bolotin, Kinetische Stabilit¨at Elastischer Systeme. VEB Deutscher Verlag der Wissenschaften, Berlin, 1961.
 A. Szekrényes, “Bending solution of third-order orthotropic Reddy plates with asymmetric interfacial crack,” International Journal of Solids and Structures, vol. 51, pp. 2598–2619, 2014.
 L. Kollár and G. Springer, Mechanics of Composite Structures. Cambridge, New York, Melbourne, Madrid, Capetown, Sao Paolo: Cambridge University Press, 2002.
 J. N. Reddy, Mechanics of laminated composite plates and shells -Theory and analysis. Boca Raton, London, New York, Washington D.C.: CRC Press, 2004.
 M. Petyt, Introduction to Finite Element Vibration Analysis, 2nd ed. Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo, Mexico City: Cambridge University Press, 2010.
 K.-J. Bathe, Finite Element Procedures. New Jersey 17458: Prentice Hall, Upper Saddle River, 1996.
 A. Szekrényes, “A special case of parametrically excited systems: free vibration of delaminated composite beams,” European journal of Mechanics A/Solids, vol. 49, pp. 82–105, 2015.
 N. H. Erdelyi and S. M. Hashemi, “On the finite element free vibration analysis of delaminated layered beams: A new assembly technique,” Shock and Vibration, vol. Article ID 3707658, 14 pages, 2016.
 L. Briseghella, C. Majorma, and C. Pellegrino, “Dynamic stability of elastic structures: a finite element approach,” Computers and Structures, vol. 69, pp. 11–25, 1998.
 A. G. Radu and A. Chattopadhyay, “Dynamic stability analysis of composite plates including delaminations using a higher order theory and transformation matrix approach,” International Journal of Solids and Structures, vol. 39, pp. 1949–1965, 2002.
 A. Chattopadhyay and A. G. Radu, “Dynamic instability of composite laminates using a higher order theory,” Computers and Structures, vol. 77, pp. 453–460, 2000.
 C. M. Saravia, S. P. Machado, and V. H. Cortínez, “Free vibration and dynamic stability of rotating thin-walled composite beams,” European Journal of Mechanics A/Solids, vol. 30, pp. 432–441, 2011.
 F. Pápai, S. Adhikari, and B. Wang, “Estimation of modal dampings for unmeasured modes,” Slovak Journal of Civil Engineering, vol. XX, no. 4, pp. 17–27, 2012.
 G. Catania and S. Sorrentino, “Experimental evaluation of the damping properties of beams and thin-walled structures made of polymeric materials,” in Proceedings of the IMAC-XXVII. Society of Experimental Mechanics Inc., 2009, pp. 1–10, february 9-12, Orlando, Florida, USA.
 J. Peringer, “Dynamics of delaminated composite beams,” Master’s thesis, Budapest University of Technology and Economics, Department of Applied Mechanics, 2012.
 A. Szekrényes, “Natural vibration-induced parametric excitation in delaminated Kirchhoff plates,” Journal of Composite Materials, 2015, doi:10.1177/0021998315603111.