[en] The objective of this paper is to examine nonlinear normal modes and their bifurcations in cyclic periodic structures. The nonlinear normal modes are computed using a numerical technique that combines shooting and pseudoarclength continuation. Unlike perturbation techniques, the resulting algorithm can investigate strongly nonlinear regimes of motion. This study reveals that modal interactions may occur without necessarily having commensurate natural frequencies in the underlying linear system. In addition, a countable infinity of such modal Q2 interactions are shown to exist in the system.
Disciplines :
Mechanical engineering
Author, co-author :
Georgiades, Fostios
Peeters, Maxime ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS - Vibrations et identification des structures
Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Golinval, Jean-Claude ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS - Vibrations et identification des structures
Ruzzene, M.; Georgia Institute of Technology, Atlanta, Georgia 30332
Language :
English
Title :
Modal Analysis of a Nonlinear Periodic Structure with Cyclic Symmetry
Publication date :
2009
Journal title :
AIAA Journal
ISSN :
0001-1452
eISSN :
1533-385X
Publisher :
American Institute of Aeronautics and Astronautics, Reston, United States - Virginia
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Bibliography
Ewins, D. J., Modal Testing: Theory, Practice and Application, 2nd ed., Research Studies Press, Hertfordshire, England, U.K., 2000.
Pierre, C., and Dowell, E. H., "Localization of Vibrations by Structural Irregularity," Journal of Sound and Vibration, Vol. 114, 1987, pp. 549-564. doi:10.1016/S0022-460X(87)80023-8
Bendiksen, O. O., "Localization Phenomena in Structural Dynamics," Chaos, Solitons and Fractals, Vol. 11, 2000, pp. 1621-1660. doi:10.1016/S0960-0779(00)00013-8
Castanier, M. P., and Pierre, C., "Using Intentional Mistuning in the Design of Turbomachinery Rotors," AIAA Journal, Vol. 40, 2002, pp. 2077-2086. doi:10.2514/2.1542
Wei, S. T., and Pierre, C., "Effects of Dry Friction Damping on the Occurrence of Localized Forced Vibrations in Nearly Cyclic Structures," Journal of Sound and Vibration, Vol. 129, 1989, pp. 397-416. doi:10.1016/0022-460X(89)90432-X
Vakakis, A. F., "Dynamics of a Nonlinear Periodic Structure with Cyclic Symmetry," Acta Mechanica, Vol. 95, 1992, pp. 197-226. doi:10.1007/BF01170813
Vakakis, A. F., and Cetinkaya, C., "Mode Localization in a Class of Multidegree-of-Freedom Nonlinear Systems with Cyclic Symmetry," SIAM Journal on Applied Mathematics, Vol. 53, 1993, pp. 265-282. doi:10.1137/0153016
Vakakis, A. F., Nayfeh, T., and King, M. E., "A Multiple-Scales Analysis of Nonlinear, Localized Modes in a Cyclic Periodic System," Journal of Applied Mechanics, Vol. 60, 1993, pp. 388-397. doi:10.1115/1.2900806
King, M. E., and Vakakis, A. F., "A Very Complicated Structure of Resonances in a Nonlinear System with Cyclic Symmetry: Nonlinear Forced Localization," Nonlinear Dynamics, Vol. 7, No. 1, Jan. 1995, pp. 85-104.doi:10.1007/BF00045127
King, M. E., and Layne, P. A., "Dynamics of Nonlinear Cyclic Systems with Structural Irregularity," Nonlinear Dynamics, Vol. 15, 1998, pp. 225-244. doi:10.1023/A:1008291628528
Folley, C. N., "Bifurcation and Symmetry in Cyclic Structures," Ph.D. Thesis, Purdue University, West Lafayette, IN, 1999.
Samaranayake, S., Samaranayake, G., and Bajaj, A. K., "Resonant Vibrations in Harmonically Excited Weakly Coupled Mechanical Systems with Cyclic Symmetry," Chaos, Solitons and Fractals, Vol. 11, 2000, pp. 1519-1534. doi:10.1016/S0960-0779(99)00075-2
Kerschen, G., Peeters, M., Golinval, J. C., and Vakakis, A. F., "Nonlinear Normal Modes, Part I: A Useful Framework for the Structural Dynamicist," Mechanical Systems and Signal Processing, Vol. 23, 2009, pp. 170-194. doi:10.1016/j.ymssp. 2008.04.002
Peeters, M., Viguié, R., Sérandour, G., Kerschen, G., andGolinval, J.C., "Nonlinear Normal Modes, Part II: Practical Computation Using Numerical Continuation Techniques," Mechanical Systems and Signal Processing, Vol. 23, 2009, pp. 195-216. doi:10.1016/j.ymssp. 2008.04.003
Rosenberg, R. M., "On Nonlinear Vibrations of Systems with Many Degrees Of Freedom," Advances in Applied Mechanics, Vol. 9, Academic Press, New York/London/Orlando, FL, 1966, pp. 155-242.
Vakakis, A. F., "Analysis and Identification of Linear and Nonlinear Normal Modes in Vibrating Systems," Ph.D. Dissertation, California Inst. of Technology, Pasadena, CA, 1990.
Vakakis, A. F., Manevitch, L. I., Mikhlin, Y. V., Pilipchuk, V. N., and Zevin, A. A., Normal Modes and Localization in Nonlinear Systems, Wiley, New York, 1996.
Vakakis, A. F., "Non-Linear Normal Modes and Their Applications in Vibration Theory: An Overview," Mechanical Systems and Signal Processing, Vol. 11, 1997, pp. 3-22. doi:10.1006/mssp. 1996.9999
Shaw, S. W., and Pierre, C., "Non-Linear Normal Modes and Invariant Manifolds," Journal of Sound and Vibration, Vol. 150, 1991, pp. 170-173. doi:10.1016/0022-460X(91)90412-D
Shaw, S. W., and Pierre, C., "Normal Modes for Non-Linear Vibratory Systems," Journal of Sound and Vibration, Vol. 164, 1993, pp. 85-124. doi:10.1006/jsvi.1993.1198
Lee, Y. S., Kerschen, G., Vakakis, A. F., Panagopoulos, P. N., Bergman, L. A., and McFarland, D. M., "Complicated Dynamics of a Linear Oscillator with a Light, Essentially Nonlinear Attachment," Physica D, Vol. 204, 2005, pp. 41-69. doi:10.1016/j.physd.2005.03.014
Vakakis, A. F., Gendelman, O., Bergman, L. A., McFarland, D. M., Kerschen, G., and Lee, Y. S., Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems, Solid Mechanics and Its Applications, Springer, Vol. 156, 2009.
Slater, J. C., "A Numerical Method for Determining Nonlinear Normal Modes," Nonlinear Dynamics, Vol. 10, 1996, pp. 19-30. doi:10.1007/BF00114796
Pesheck, E., "Reduced-Order Modeling of Nonlinear Structural Systems Using Nonlinear Normal Modes and Invariant Manifolds," Ph.D. Thesis, Univ. of Michigan, Ann Arbor, MI, 2000.
Arquier, R., Bellizzi, S., Bouc, R., and Cochelin, B., "Two Methods for the Computation of Nonlinear Modes of Vibrating Systems at Large Amplitudes," Computers and Structures, Vol. 84, 2006, pp. 1565-1576. doi:10.1016/j.compstruc.2006.01.011
Doedel, E., AUTO, Software for Continuation and Bifurcation Problems in Ordinary Differential Equations, 2007.
Seydel, R., Practical Bifurcation and Stability Analysis, from Equilibrium to Chaos, 2nd ed., Springer-Verlag, Berlin, 1994.
Ewins, D. J., "Structural Dynamics Characteristics of Bladed Assemblies," Lecture Series 1992-06 on Vibration and Rotor Dynamics, Von Karman Institute for Fluid Dynamics, 1992.
Castanier, M. P., and Pierre, C., "Modeling and Analysis of Mistuned Bladed Disk Vibration: Status and Emerging Directions," Journal of Propulsion and Power, Vol. 22, 2006, pp. 384-396. doi:10.2514/1.16345
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