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Suppressing resonant vibrations using nonlinear springs and dampers. (English) Zbl 1273.70067

Summary: The transmitted force around the resonant region of a system can be significantly reduced by introducing designed nonlinearities into the system. The basic choice of the nonlinearity can be either a nonlinear spring element or a nonlinear damping element. A numerical algorithm to compute and compare the transmitted force reduction produced by these two types of designed elements is proposed in this study. Analytical results are used to demonstrate the procedure. The numerical results indicate that the designed nonlinear damping element produces low levels of higher-order harmonics and no bifurcations in the system output response. In contrast, the nonlinear spring-based designs induce significant levels of harmonics in the transmitted force and can produce bifurcation behaviour. The conclusions provide an important basis for the design of nonlinear materials and nonlinear engineering systems.

MSC:

70Q05 Control of mechanical systems
70K40 Forced motions for nonlinear problems in mechanics
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References:

[1] Alkhatib, R., Shock and Vibration Digest 35 pp 367– (2003) · doi:10.1177/05831024030355002
[2] Billings, S.A., International Journal of Control 75 pp 1066– (2002) · Zbl 1038.93064 · doi:10.1080/00207170210157575
[3] Brennan, M.J., Journal of Sound and Vibration 318 pp 1250– (2008) · doi:10.1016/j.jsv.2008.04.032
[4] Friswell, M., Journal of Sound and Vibration 169 pp 261– (1994) · Zbl 0925.70260 · doi:10.1006/jsvi.1994.1018
[5] Geldelman, O., Journal of Applied Mechanics 68 pp 34– (2001) · Zbl 1110.74452 · doi:10.1115/1.1345524
[6] Harris, C.M., Shock and Vibration Handbook (1996)
[7] Lang, Z.Q., Proceedings of the Sixth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications
[8] Liu, L., Journal of Computational Physics 215 pp 298– (2006) · Zbl 1089.65129 · doi:10.1016/j.jcp.2005.10.026
[9] Soong, T.T., Passive Energy Dissipation Systems in Structural Engineering (1997)
[10] Stoker, J.J., Nonlinear Vibration (1950)
[11] Tomlinson, G.R., Structural Control & Health Monitoring 13 pp 523– (2006) · doi:10.1002/stc.148
[12] Urabe, M., Archive for Rational Mechanics and Analysis 20 pp 120– (1965) · Zbl 0133.35502 · doi:10.1007/BF00284614
[13] Urabe, M., Journal of Mathematical Analysis and Applications 14 pp 107– (1966) · Zbl 0196.49405 · doi:10.1016/0022-247X(66)90066-7
[14] Vakakis, A.F., Journal of Vibration and Control 9 pp 79– (2003) · doi:10.1177/107754603030742
[15] Worden, K., Nonlinearity in Structural Dynamics: Detection, Identification and Modelling (2001) · Zbl 0990.93508 · doi:10.1887/0750303565
[16] Zhang, B., Journal of Sound and Vibration 317 pp 918– (2008) · doi:10.1016/j.jsv.2008.03.041
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