A number of experiments on a physical system with clearance having combined parametric and external forcing excitation are presented. The data demonstrate several nonlinear phenomena that exist in periodically excited oscillators subject to clearance at a contact interface. Jump discontinuities in forced response curves are shown to exist and subharmonic resonances which are formed by period-n (nT) motions with n ≥ 2 are demonstrated. Long-period subharmonic motions with periods as long as nine times the excitation period are reported. Finally, several cases of measured chaotic motions are also illustrated through time-traces, phase portraits, Fourier spectra, and Poincare plots which form strange attractors.
Issue Section:
Technical Papers
1.
Bayly
P. V.
Virgin
L. N.
1993
, “An Experimental Study of an Impacting Pendulum
,” Journal of Sound and Vibration
, Vol. 164
, pp. 364
–374
.2.
Blankenship
G. W.
Kahraman
A.
1995
, “Steady State Forced Response of a Mechanical Oscillator With Combined Parametric Excitation and Clearance Type Nonlinearity
,” Journal of Sound and Vibration
, Vol. 185
, pp. 743
–765
.3.
Blankenship
G. W.
Singh
R.
1995
, “Analytical Solutions for Modulation Sidebands Associated with a Class of Mechanical Oscillators
,” Journal of Sound and Vibration
, Vol. 179
, pp. 13
–36
.4.
Choi
Y. S.
Noah
S. T.
Forced Periodic Vibration of Unsymmetric Piecewise-Linear Systems
,” Journal of Sound and Vibration
, Vol. 121
, pp. 117
–126
.5.
Comparin
R. J.
Singh
R.
1989
, “Nonlinear Frequency Response Characteristics of an Impact Pair
,” Journal of Sound and Vibration
, Vol. 134
, pp. 259
–290
.6.
Ehrich
F.
1992
, “Observations of Subcritical Superharmonic and Chaotic Response in Rotordynamics
,” ASME Journal of Vibration and Acoustics
, Vol. 114
, pp. 93
–100
.7.
Fang
W.
Wickert
J. A.
1994
, “Response of a Periodically Driven Impact Oscillator
,” Journal of Sound and Vibration
, Vol. 170
, pp. 397
–409
.8.
Hsu, C. S., and Cheng, W.-H., 1974, “Steady State Response of Dynamical System Under Combined Parametric and Forcing Excitations,” ASME JOURNAL OF APPLIED MECHANICS, pp. 371–378.
9.
Kahraman
A.
Singh
R.
1990
, “Nonlinear Dynamics of a Spur Gear Pair
,” Journal of Sound and Vibration
, Vol. 142
, pp. 49
–75
.10.
Kahraman
A.
Singh
R.
1991
, “Interactions Between Time-Varying Mesh Stiffness and Clearance Nonlinearity in a Gear System
,” Journal of Sound and Vibration
, Vol. 146
, pp. 135
–156
.11.
Kahraman
A.
Blankenship
G. W.
1996
, “Interactions Between Commensurate Parametric and Forcing Excitations in a System with Clearance
,” Journal of Sound and Vibration
, Vol. 194
, pp. 317
–336
.12.
Kahraman
A.
1992
, “On the Response of a Preloaded Mechanical Oscillator with a Clearance: Period Doubling and Chaos
,” Nonlinear Dynamics
, Vol. 3
, pp. 183
–198
.13.
Karagiannis
K.
Pfeiffer
F.
1991
, “Theoretical and Experimental Investigation of Gear-Rattling
,” Nonlinear Dynamics
, Vol. 2
, pp. 367
–387
.14.
Kim
Y. B.
Noah
S. T.
1991
, “Stability and Bifurcation Analysis of Oscillators with Piecewise-Linear Characteristics: A General Approach
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 58
, pp. 545
–553
.15.
Lau
S. L.
Zhang
W. -S.
1992
, “Nonlinear Vibrations of Piecewise Linear Systems by Incremental Harmonic Balance Method
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 59
, pp. 153
–160
.16.
Mahfouz
I. A.
Badrakhan
F.
1990
, “Chaotic Behavior of Some Piecewise-Linear Systems, Part II: Systems with Clearances
,” Journal of Sound and Vibration
, Vol. 143
, pp. 289
–328
.17.
Mevel
B.
Guyader
J. L.
1993
, “Routes to Chaos in Ball Bearings
,” Journal of Sound and Vibration
, Vol. 162
, pp. 471
–487
.18.
Moon, F. C., 1992, Chaotic and Fractal Dynamics, Wiley-Interscience, New York.
19.
Moon
F. C.
Shaw
S. W.
1983
, “Chaotic Vibrations of a Beam with Nonlinear Boundary Conditions
,” International Journal of Non-linear Mechanics
, Vol. 18
, pp. 465
–477
.20.
Natsiavas
S.
1989
, “Periodic Response and Stability of Oscillators with Symmetric Trilinear Restoring Force
,” Journal of Sound and Vibration
, Vol. 134
, pp. 315
–331
.21.
Natsiavas
S.
Gonzalez
H.
1992
, “Vibration of Harmonically Excited Oscillators with Asymmetric Constraints
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 59
, pp. S284–S290
S284–S290
.22.
Padmanabhan
C.
Singh
R.
1995
, “Dynamics of a Piecewise Nonlinear System Subject to Dual Harmonic Excitation Using Parametric Continuation
,” Journal of Sound and Vibration
, Vol. 184
, pp. 767
–799
.23.
Padmanabhan
C.
Singh
R.
1996
, “Analysis of Periodically Forced Hill’s Oscillator with Application to a Geared System
,” Journal of Acoustical Society of America
, Vol. 99
, pp. 324
–334
.24.
Richards, J. A., 1983, Analysis of Periodically Time-Varying Systems, Springer-Verlag, New York.
25.
Sato
K.
Yamamoto
S.
Kawakami
T.
1991
, “Bifurcation Sets and Chaotic States of a Gear System Subjected to Harmonic Excitation
,” Computational Mechanics
, Vol. 7
, pp. 173
–182
.26.
Shaw
S. W.
Holmes
P. J.
1983
, “A Periodically Forced Piecewise Linear Oscillator
,” Journal of Sound and Vibration
, Vol. 90
, pp. 129
–155
.27.
Shaw
S. W.
1985
, “Forced Vibrations of a Beam with One-Sided Amplitude Constraint: Theory and Experiment
,” Journal of Sound and Vibration
, Vol. 99
, pp. 199
–212
.28.
Thompson
J. M. T.
Elvey
J. S. N.
1984
, “Elimination of Sub-harmonic Resonances of Compliant Marine Structures
,” Int. J. Mech. Sci.
, Vol. 26
, pp. 419
–426
.29.
Tomlinson
G. R.
Lain
J.
1984
, “Frequency Response Characteristics of Structures with Single and Multiple Clearance-Type Non-linearity
,” Journal of Sound and Vibration
, Vol. 96
, pp. 111
–125
.
This content is only available via PDF.
Copyright © 1997
by The American Society of Mechanical Engineers
You do not currently have access to this content.