Abstract

A detailed study of one-, two-, and three-impact per period motion of a vibro-impacting, pinned beam is presented involving experimental results, as well as one- and multi-degree-of-freedom theoretical models. The details of the impact event are examined and correlated to the qualitative appearance of the frequency response. In addition, it is noted that the multi-degree-of-freedom model is necessary in order to predict response at high frequencies. This study is unique in that the model system includes a pinned boundary condition, the forcing frequency is considerably lower than the fundamental in-contact natural frequency, and the frequency analysis extends into a range important for acoustic predictions.

1.
Shaw
,
S. W.
, and
Holmes
,
P. J.
,
1983
, “
A Periodically Forced Piecewise Linear Oscillator
,”
J. Sound Vib.
,
90
, pp.
129
155
.
2.
Nordmark
,
A. B.
,
1991
, “
Non-Periodic Motion Caused by Grazing Incidence in an Impact Oscillator
,”
J. Sound Vib.
,
145
, pp.
279
297
.
3.
Fang
,
W.
, and
Wickert
,
J. A.
,
1994
, “
Response of a Periodically Driven Impact Oscillator
,”
J. Sound Vib.
,
170
, pp.
397
409
.
4.
Todd
,
M. D.
, and
Virgin
,
L. N.
,
1996
, “
Natural Frequency Considerations of an Impact Oscillator
,”
J. Sound Vib.
,
194
, pp.
452
460
.
5.
Todd
,
M. D.
, and
Virgin
,
L. N.
,
1997
, “
An Experimental Impact Oscillator
,”
Chaos, Solitons Fractals
,
8
, pp.
699
714
.
6.
Shaw
,
S. W.
,
1985
, “
Forced Vibrations of a Beam with One-sided Amplitude Constraint: Theory and Experiment
,”
J. Sound Vib.
,
99
, pp.
199
212
.
7.
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.
8.
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
.
9.
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
.
10.
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
.
11.
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
.
12.
Personal conversation with Rick Powell of Polytec PI, August 1999.
You do not currently have access to this content.