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TECHNICAL PAPERS

Dynamics of a Flexible Beam Contacting a Linear Spring at Low Frequency Excitation: Experiment and Analysis

[+] Author and Article Information
Karen J. L. Fegelman, Karl Grosh

Department of Mechanical Engineering, University of Michigan, 2350 Hayward St., Ann Arbor, MI 48109-2125

J. Vib. Acoust 124(2), 237-249 (Mar 26, 2002) (13 pages) doi:10.1115/1.1426073 History: Received June 01, 2000; Revised September 01, 2001; Online March 26, 2002
Copyright © 2002 by ASME
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References

Shaw,  S. W., and Holmes,  P. J., 1983, “A Periodically Forced Piecewise Linear Oscillator,” J. Sound Vib., 90, pp. 129–155.
Nordmark,  A. B., 1991, “Non-Periodic Motion Caused by Grazing Incidence in an Impact Oscillator,” J. Sound Vib., 145, pp. 279–297.
Fang,  W., and Wickert,  J. A., 1994, “Response of a Periodically Driven Impact Oscillator,” J. Sound Vib., 170, pp. 397–409.
Todd,  M. D., and Virgin,  L. N., 1996, “Natural Frequency Considerations of an Impact Oscillator,” J. Sound Vib., 194, pp. 452–460.
Todd,  M. D., and Virgin,  L. N., 1997, “An Experimental Impact Oscillator,” Chaos, Solitons Fractals, 8, pp. 699–714.
Shaw,  S. W., 1985, “Forced Vibrations of a Beam with One-sided Amplitude Constraint: Theory and Experiment,” J. Sound Vib., 99, pp. 199–212.
Sin, V. W. T., and Wiercigroch, M., 1996, “Experimental and Numerical Study of a Symmetrically Piecewise Linear Oscillator,” Proceedings of the 1996 ASME International Mechanical Engineering Congress and Exposition, 19961117-19961122 , Atlanta, GA, pp. 63–68.
Wiercigroch,  M., and Sin,  V. W. T., 1998, “Measurement of Chaotic Vibration in a Symmetrically Piecewise Linear Oscillator,” Chaos, Solitons Fractals, 9, pp. 209–220.
van Campen,  D. H., van deVorst,  E. L. B., van der Spek,  J. A. W., and de Kraker,  A., 1995, “Dynamics of a Multi-DOF Beam System with Discontinuous Support,” Nonlinear Dyn., 8, pp. 453–466.
van deVorst,  E. L. B., van Campen,  D. H., and de Kraker,  A., 1996, “Periodic Solutions of a Multi-DOF Beam System with Impact,” J. Sound Vib., 192, pp. 913–925.
van deVorst,  E. L. B., Heertjes,  M. F., van Campen,  D. H., and de Kraker,  A., 1998, “Experimental and Numerical Analysis of the Steady State Behavior of a Beam System with Impact,” J. Sound Vib., 212, pp. 321–336.
Personal conversation with Rick Powell of Polytec PI, August 1999.

Figures

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Vibro-impact beam test structure
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Experimental measurement of vibro-impacting beam at 50 Hz, 1.1 g (a) displacement time history (b) displacement frequency content (c) velocity time history (d) velocity frequency content (e) acceleration time history (f) acceleration frequency content
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Experimental measurement of vibro-impacting beam at 50 Hz, 1.2 g (a) displacement time history (b) displacement frequency content (c) velocity time history (d) velocity frequency content (e) acceleration time history (f) acceleration frequency content
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Experimentally measured phase portraits at 50 Hz. Motion to the left of the dashed line corresponds to in-contact motion, motion to the right of the line corresponds to out-of-contact motion. (a) 1.1 g case (b) 1.2 g case.
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Rigid model including effect of compromise stiffness
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Rigid body model prediction of motion for vibro-impacting beam at 50 Hz, 1.1 g (a) displacement time history (b) displacement frequency content (c) velocity time history (d) velocity frequency content (e) acceleration time history (f) acceleration frequency content
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Rigid body model prediction of motion for vibro-impacting beam at 50 Hz, 1.2 g (a) displacement time history (b) displacement frequency content (c) velocity time history (d) velocity frequency content (e) acceleration time history (f) acceleration frequency content
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Rigid model prediction of phase portraits at 50 Hz (a) 1.1 g case (b) 1.2 g case
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Flexible body model prediction of motion for vibro-impacting beam at 50 Hz, 1.1 g (a) displacement time history (b) displacement frequency content (c) velocity time history (d) velocity frequency content (e) acceleration time history (f) acceleration frequency content
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Flexible body model prediction of motion for vibro-impacting beam at 50 Hz, 1.2 g (a) displacement time history (b) displacement frequency content (c) velocity time history (d) velocity frequency content (e) acceleration time history (f) acceleration frequency content
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Flexible body model prediction phase portraits at 50 Hz (a) 1.1 g case (b) 1.2 g case
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Experimental measurement of vibro-impacting beam at 50 Hz, 1.02 g (a) velocity time history (b) velocity frequency content (c) acceleration time history (d) acceleration frequency content. Arrows in (f) indicate in-contact (ic) and out-of-contact (oc) natural frequencies.
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Flexible body model prediction of motion for vibro-impacting beam at 50 Hz, 1.02 g (a) displacement time history (b) displacement frequency content (c) velocity time history (d) velocity frequency content (e) acceleration time history (f) acceleration frequency content. Arrows in (f) indicate in-contact (ic) and out-of-contact (oc) natural frequencies.
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Line contact for vibro-impact beam experiment

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