Abstract
Linear vibration absorbers are a valuable tool used to suppress vibrations due to harmonic excitation in structural systems. While limited evaluation of the performance of nonlinear vibration absorbers for nonlinear structures exists in the literature for single mode structures, none exists for multi-mode structures. Consequently, nonlinear multiple-degrees-of-freedom structures are evaluated. The theory of nonlinear normal modes is extended to include consideration of modal damping, excitation and small linear coupling, allowing estimation of vibration absorber performance. The dynamics of the N + 1-degrees-of-freedom system are shown to reduce to those of a two-degrees-of-freedom system on a four-dimensional nonlinear modal manifold, thereby simplifying the analysis. Quantitative agreement is shown to require a higher-order model which is recommended for future investigation.
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References
Sun, J. Q., Jolly, M. R., and Norris, M. A., `Passive, adaptive, and active tuned vibration absorbers’, ASME Combined Anniversary Issue Journal of Mechanical Design and Journal of Vibration and Acoustics 117 (B), 1995, 234–242.
Von Flotow, A. H., Beard, A., and Bailey, D., `Adaptive tuned vibration absorbers: Tuning laws, tracking agility, sizing, and physical implementations’, in Proceedings Noise-Con 94, 1994.
Roberson, R. E., `Synthesis of a nonlinear vibration absorber’, Journal of the Franklin Institute 254, 1952, 205–220.
Arnold, F. R., `Steady-state behavior of systems provided with nonlinear dynamic vibration absorbers’, Journal of Applied Mechanics 22, 1955, 487–492.
Pipes, L. A., `Analysis of a nonlinear dynamic vibration absorber’, Journal of Applied Mechanics 20, 1953, 515–518.
Miller, H. M. and Gartner, J. R., `Tunable, non-linear vibration absorber’, ASME Paper No. 75-DET-9, 1975.
Hunt, J. B. and Nissen, J. C., `The broadband dynamic vibration absorber’, Journal of Sound and Vibration 83, 1982, 573–578.
Kojima, H. and Saito, H., `Forced vibrations of a beam with a non-linear dynamic vibration absorber, Journal of Sound and Vibration 88 (4), 1983, 559–568.
Jordanov, 1. N. and Cheshankov, B. 1., `Optimal design of linear and non-linear dynamic vibration absorbers’, Journal of Sound and Vibration 123 (1), 1988, 157–170.
Nissen, J.-C., Popp, K., and Schmalhorst, B., `Optimization of a non-linear dynamic vibration absorber’, Journal of Sound and Vibration 99 (1), 1985, 149–154.
Shaw, J., Shaw, S. W., and Haddow, A. G., `On the response of the nonlinear vibration absorber’, International Journal of Non-Linear Mechanics 24, 1989, 281–293.
Rice, H. J. and McCraith, J. R., `Practical non-linear vibration absorber design’, Journal of Sound and Vibration 116 (3), 1987, 545–559.
Natsiavas, S., `Steady state oscillations and stability of non-linear vibration absorbers’, Journal of Sound and Vibration 156 (2), 1992, 227–245.
Agnes, G. S. and Inman, D. J., `Nonlinear piezoelectric vibration absorbers’, Smart Materials and Structures 5, 1996, 704–714.
Agnes, G. S., `Performance of nonlinear mechanical, resonant-shunted piezoelectric, and electronic vibration absorbers for multi-degree-of-freedom structures’, Ph.D. Thesis, Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA, 1997.
Agnes, G. S. and Inman, D. J., `Nonlinear vibration absorbers for nonlinear structures, Part I: Theory’, Journal of Sound and Vibration,to appear.
Agnes, G. S. and Inman, D. J., `Nonlinear vibration absorbers for nonlinear structures, Part II: Experiments’, Journal of Sound and Vibration, to appear.
Slater, J. C., `Nonlinear modal control’, Ph.D. Thesis, State University of New York at Buffalo, 1993.
Slater, J. C. and Inman, D. J., `Nonlinear modal control method’, Journal of Guidance, Control and Dynamics 18 (3), 1995, 433–440.
Shaw, S. W. and Pierre, C., Non-linear normal modes and invariant manifolds’, Journal of Sound and Vibration 150, 1991, 170–173.
Rosenberg, R. M., `The normal modes of nonlinear N-degree-of-freedom systems’, Journal of Applied Mechanics 30, 1962, 7–14.
Rosenberg, R. M. and Kuo, J. K., `Nonsimilar normal mode vibrations of nonlinear systems having two degrees of freedom’, Journal of Applied Mechanics 31, 1964, 283–290.
Rosenberg, R. M., `On nonlinear vibrations of systems with many degrees of freedom’, in Advances in Applied Mechanics, G. Kuerti, (ed.), Academic Press, New York, 1966, pp. 155–242.
Shaw, S. W. and Pierre, C., `Normal modes for non-linear vibratory systems’, Journal of Sound and Vibration 164, 1993, 85–124.
Nayfeh, A. H. and Nayfeh, S. A., `On nonlinear modes of continuous systems’, Journal of Vibrations and Acoustics 116, 1994, 129–136.
Nayfeh, A. H., Nayfeh, S. A., and Chin, C., `On nonlinear normal modes of systems with internal resonance’, Journal of Vibration and Acoustics 118 (3), 1996, 340–345.
Nayfeh, A. H. and Balachandran, B., Applied Nonlinear Dynamics, Wiley, New York, 1995.
Vakakis, A. F., Manevitch, L. I. Mikhlin, Y. V., Pilipchuk, V. N., and Zevin, A. A., Normal Modes and Localization in Nonlinear SystemsWiley, New York, 1996.
Vakakis, A. F., `Nonlinear normal modes (NNMs) and their applications in vibration theory: An overview’, Mechanical Systems and Signal Processing 11 (1), 1997, 3–22.
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© 2001 Springer Science+Business Media Dordrecht
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Agnes, G.S., Inman, D.J. (2001). Performance of Nonlinear Vibration Absorbers for Multi-Degrees-of-Freedom Systems Using Nonlinear Normal Modes. In: Vakakis, A.F. (eds) Normal Modes and Localization in Nonlinear Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2452-4_15
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DOI: https://doi.org/10.1007/978-94-017-2452-4_15
Publisher Name: Springer, Dordrecht
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