Abstract
We show that a linear oscillator with a vibro-impact attachment possesses a very complicated structure of periodic orbits. These periodic orbits can be studied numerically by depicting them in a frequency-energy plot (FEP), where the (conserved) energy of a periodic orbit is plotted against its fundamental frequency. The results reported herein are a brief summary of a more detailed study (Lee et al., 2008).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Babitsky, V.: Theory of Vibro-impact Systems. Springer, Berlin (1998)
Brogliato, B.: Non-smooth mechanics. Springer, Berlin (1999)
Georgiades, F., Vakakis, A., McFarland, D.M., Bergman, L.: Shock isolation through passive energy pumping caused by nonsmooth nonlinearities. J. Bif. Chaos 15(6), 1989–2001 (2005)
Georgiades, F.: Nonlinear localization and targeted energy transfer phenomena in vibrating systems with smooth and nonsmooth stiffness nonlinearities. PhD Thesis, National Technical University of Athens, Greece (2006)
Kerschen, G.Y., Lee, Y.S., Vakakis, A.F., McFarland, D.M., Bergman, L.A.: Irreversible passive energy transfer in coupled oscillators with essential nonlinearity. SIAM J. Appl. Math. 66(2), 648–679 (2006)
Lee, Y.S., Kerschen, G., Vakakis, A.F., Panagopoulos, P.N., Bergman, L.A., McFarland, D.M.: Complicated dynamics of a linear oscillator with an essentially nonlinear local attachment. Physica D 204, 41–69 (2005)
Lee, Y.S., Nucera, F., Vakakis, A., McFarland, D.M., Bergman, L.: Periodic orbits, damped transitions and targeted energy transfer in oscillators with vibro-impact attachments. Physica D (submitted, 2008)
Nucera, F., Vakakis, A., McFarland, D.M., Bergman, L., Kerschen, G.: Targeted energy transfers in vibro-impact oscillators for seismic mitigation. Nonlinear Dyn. 50(3), 651–677 (2007)
Nucera, F., LoIacono, F., McFarland, D.M., Bergman, L., Vakakis, A.: Application of broadband nonlinear targeted energy transfers for seismic mitigation of a shear frame: experimental results. J. Sound Vib. 313, 57–76 (2008)
Shaw, S., Rand, R.: The transition to chaos in a simple mechanical system. Int. J. Nonlinear Mech. 24, 41–56 (1989)
Vakakis, A.F., Gendelman, O., Bergman, L., McFarland, D.M., Kerschen, G., Lee, Y.S.: Passive Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems: I and II. Springer, Berlin (in press, 2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lee, Y.S., Nucera, F., Vakakis, A.F., McFarland, D.M., Bergman, L.A. (2009). Complex Structure of Periodic Orbits in an Oscillator with a Vibro-Impact Attachment. In: Ibrahim, R.A., Babitsky, V.I., Okuma, M. (eds) Vibro-Impact Dynamics of Ocean Systems and Related Problems. Lecture Notes in Applied and Computational Mechanics, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00629-6_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-00629-6_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00628-9
Online ISBN: 978-3-642-00629-6
eBook Packages: EngineeringEngineering (R0)