0
TECHNICAL PAPERS

Stability Analysis of a Levitated Droplet by Using Floquet Multipliers

[+] Author and Article Information
Bogdan O. Ciocirlan, Dan B. Marghitu

Department of Mechanical Engineering, Auburn University, Auburn, AL 36849

J. Vib. Acoust 122(4), 399-408 (Mar 01, 2000) (10 pages) doi:10.1115/1.1286215 History: Received September 01, 1999; Accepted March 01, 2000
Copyright © 2000 by ASME
Your Session has timed out. Please sign back in to continue.

References

Mestel,  A. J., 1981, “Magnetic levitation of liquid metals,” J. Fluid Mech., 117, pp. 27–43.
Busse,  F. H., 1984, “Oscillations of a rotating liquid drop,” J. Fluid Mech., 142, pp. 1–8.
Cummings,  D. L., and Blackburn,  D. A., 1989, “Oscillations of magnetically levitated aspherical droplets,” J. Fluid Mech., 224, pp. 395–416.
Chen, S.-F., and Overfelt, A., 1997, “Effects of Sample Size on Surface Tension Measurements of Nickel in Reduced Gravity Parabolic Flight,” in 13th Symposium on Thermophysical Properties, June 22–27, Boulder, CO.
Cusumano,  J. P., and Moon,  F. C., 1995, “Chaotic Non-Planar Vibrations of the Thin Elastica, Part I: Experimental Observation of Planar Instability,” J. Sound Vib., 179, No. 2, pp. 185–208.
Kang,  Y., Chang,  Y. P., and Jen,  S. C., 1998, “Strongly Non-Linear Oscillations of Winding Machines, Part I: Mode-Locking Motion and Routes to Chaos,” J. Sound Vib., 209, No. 3, pp. 473–492.
Nayfeh, A. H., and Balachandran, B., 1995, Applied Nonlinear Dynamics, Wiley, New York.
Farmer,  J. D., Ott,  E., and Yorke,  J. A., 1983, “The dimension of chaotic attractors,” Physica D, 7, pp. 153–180.
Abarbanel, H. D. I., 1996, Analysis of Observed Chaotic Data, Springer-Verlag, New York.
Packard,  N. H., Crutchfield,  J. P., Farmer,  J. D., and Shaw,  R. S., 1980, “Geometry from a time series,” Phys. Rev. Lett., 45, pp. 712–716.
Albano,  A. M., Muench,  J., Schwartz,  C., Mees,  A. I., and Rapp,  P. E., 1988, “Singular-value decomposition and the Grassberger-Procaccia algorithm,” Phys. Rev. A, 38, pp. 3017–3034.
Provanzale,  A., Smith,  L. A., Vio,  R., and Murante,  G., 1992, “Distinguishing between low-dimensional dynamics and randomness in measured time series,” Physica D, 58, pp. 31–49.
Cambel, A. B., 1993, Applied Chaos Theory, Academic Press, Boston.
Smith,  L. A., 1988, “Intrinsic limits on dimensional calculation,” Phys. Lett. A, 133, No. 6, pp. 283–288.
Grassberger,  P., and Procaccia,  I., 1984, “Dimensions and entropies of strange attractors from a fluctuating dynamics approach,” Physica D, 13, pp. 34–54.
Mandelbrot, B., 1983, The Fractal Geometry of Nature, Freeman, San Francisco.
Grassberger,  P., and Procaccia,  I., 1983, “Characterization of strange attractors,” Phys. Rev. Lett., 50, No. 5, pp. 346–349.
Wolf,  A., Swift,  J. B., Swinney,  H. L., and Vastano,  J. A., 1985, “Determining Lyapunov exponents from a time series,” Physica D, 16, pp. 285–317.
Eckermann,  J. P., Kamphorst,  S. O., Ruelle,  D., and Ciliberto,  S., 1986, “Lyapunov exponents from time series,” Phys. Rev. A, 34, No. 6, pp. 4971–4979.
Kapitaniak, T., 1991, Chaotic Oscillations in Mechanical Systems, Manchaster University Press, New York.
Moon, F. C., 1992, Chaotic and Fractal Dynamics, Wiley, New York.
Theiler,  J., 1991, “Some comments on the correlation dimension of 1/fα noise,” Phys. Lett. A, 155, Nos. 8–9, pp. 480–493.
Theiler,  J., Eubank,  S., Longtin,  A., and Galdrikian,  B., 1992, “Testing for nonlinearity in time series: The method of surrogate data,” Physica D, 58, pp. 77–94.
Chennaoui,  A., Pawelzik,  K., Liebert,  W., Schuster,  H. G., and Pfister,  G., 1990, “Attractor reconstruction from filtered chaotic time series,” Phys. Rev. A, 41, No. 8, pp. 4151–4159.
Agguirre,  L. A., Mendes,  E. M., and Billings,  S. A., 1996, “Smoothing data with local instabilities for the identification of chaotic systems,” Int. J. Control, 63, No. 3, pp. 483–505.
Broomhead,  D. S., and King,  G. P., 1986, “Extracting qualitative dynamics from experimental data,” Physica D, 20, pp. 217–236.
Vautard,  R., and Ghil,  M., 1989, “Singular spectrum analysis in nonlinear dynamics with applications to paleoclimatic time series,” Physica D, 35, pp. 395–424.
Casdagli,  M., 1989, “Nonlinear prediction of chaotic time series,” Physica D, 35, pp. 335–356.
Abarbanel,  D. I., Frison,  T. W., and Tsimring,  L. S., 1998, “Obtaining order in a world of chaos,” IEEE Signal Proc. Mag., 15, No. 3, pp. 49–65.
Marghitu,  D. B., 1997, “Quantitative Measure of Vehicle Stability,” Comput. Model. Simul. Eng., 2, No. 2, pp. 163–176.

Figures

Grahic Jump Location
(a) Electromagnetic levitation instrument at Space Power Institute, Auburn University (b) Levitation coil and suspended droplet
Grahic Jump Location
Sketch of the electromagnetic levitation instrument
Grahic Jump Location
(a) SUM voltage signal (b) Zoom in
Grahic Jump Location
Correlation dimension (d) versus embedding dimension (D)
Grahic Jump Location
Largest Lyapunov exponent (λ1) versus embedding dimension (D)
Grahic Jump Location
Example of surrogate signal generated from the SUM voltage signal
Grahic Jump Location
Probability distribution of SUM voltage signal
Grahic Jump Location
Probability distribution of the surrogate signal
Grahic Jump Location
Surrogate data test for the SUM voltage signal
Grahic Jump Location
(a) SUM voltage signal derivative (b) Zoom in
Grahic Jump Location
Example of surrogate signal generated from the SUM voltage signal derivative
Grahic Jump Location
Surrogate data test for the SUM voltage signal derivative
Grahic Jump Location
(a) Power spectrum of the original x signal (b) Power spectrum of the smoothed x signal
Grahic Jump Location
Return map for x position signal
Grahic Jump Location
Floquet multipliers for the third experiment (applied DC voltage of 200 Vdc)
Grahic Jump Location
Largest Floquet multiplier(s) for each experiment

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In