This paper presents four alternate models of varying complexity to examine mechanical snubbing in elastomeric isolators. Although the modeling, analysis, and experimentation presented is limited to snubbing of elastomeric isolators, the models are generic and can be adapted to other snubbing mechanisms as well, such as friction snubbing. Two of the four models presented in this paper use the Bouc–Wen model in order to capture hysteresis and gradual stiffening behavior, which is generally exhibited by elastomeric snubbing systems. The other two models are relatively simplistic and do not account for a time-varying parameter to model significant hysteresis. However, these two models can still be useful for applications with a small range of excitation frequencies and for applications where the snubbing design needs to incorporate an abrupt transition in stiffness. A parameter identification technique is used to determine the variables associated with each model. The parameter identification technique is based on the use of an optimization algorithm associated with the force–displacement characterization. All four models presented in this paper capture the coupled dynamics of the isolation system and the snubbing system and are, therefore, a significant improvement upon the currently used models. The models presented are expected to facilitate the design and analysis of a passive isolation system in conjunction with the design of the snubbing system and the base frame supporting the snubbing system.

References

References
1.
Ni
,
Y. Q.
Ko
,
J. M.
, and
Wong
,
C. W.
, 1998,
“Identification of Non-Linear Hysteretic Isolators From Periodic Vibration Tests,”
J. Sound Vib.
,
217
(
4
), pp.
737
756
.
2.
Wen
,
Y.
, 1976,
“Method for Random Vibration of Hysteretic Systems,”
J. Eng. Mech.
,
102
(
2
), pp.
249
263
.
3.
Ikhouane
,
F.
Manosa
,
V.
, and
Rodellar
,
J.
, 2007,
“Dynamic Properties of the Hysteretic Bouc–Wen Model,”
Syst. Contr. Lett.
,
56
, pp.
197
205
.
4.
Ikhouane
,
F.
, and
Rodellar
,
J.
, 2007,
Systems With Hysteresis: Analysis, Identification and Control Using the Bouc–Wen Model
,
1st ed.
,
John Wiley & Sons
,
New York.
5.
Ye
,
M.
, and
Wang
,
X.
, 2007,
“Parameter Estimation of the Bouc–Wen Hysteresis Model Using Particle Swarm Optimization,”
Smart Mater. Struct.
,
16
, pp.
2341
2349
.
6.
Mallik
,
A. K.
Kher
,
V.
Puri
,
M.
, and
Hatwal
,
H.
, 1999,
“On the Modeling of Non-Linear Elastomeric Vibration Isolators,”
J. Sound Vib.
,
219
(
2
), pp.
239
253
.
7.
Richards
,
C. M.
, and
Singh
,
R.
, 2001,
“Characterization of Rubber Isolator Nonlinearities in the Context of Single- and Multi-Degree-of-Freedom Experimental Systems,”
J. Sound Vib.
,
247
(
5
), pp.
807
834
.
8.
Ibrahim
,
R. A.
, 2008,
“Recent Advances in Nonlinear Passive Vibration Isolators,”
J. Sound Vib.
,
314
, pp.
371
452
.
9.
Aidanpaa
,
J. O.
, and
Gupta
,
R. B.
, 1993,
“Periodic and Chaotic Behavior of a Threshold-Limited Two-Degree-of-Freedom System,”
J. Sound Vib.
,
165
(
2
), pp.
305
327
.
10.
Kulakowski
,
B. T.
,
Gardner
,
J. L.
, and
Shearer
,
J. L.
, 2007,
Dynamic Modeling and Control of Engineering Systems
,
3rd ed.
,
Cambridge University Press
,
New York.
11.
Chiba
,
T.
, and
Kobayashi
,
H.
, 1985,
“A Study of Modeling the Mechanical Snubber for Dynamic Analysis,”
Transactions of the International Conference on Structural Mechanics in Reactor Technology
, Vol.
K
, North-Holland, Amsterdam, pp.
189
194
.
12.
Kachadourian
,
G.
Orth
,
C. L.
, and
Inskeep
,
D. W.
, 1984,
“Stiffness and Friction Force Measurements on a Freight Car Truck From Quasi-Static Tests,”
ASME J. Eng. Ind.
,
106
, pp.
16
20
.
13.
Wiercigroch
,
M.
, 2006,
“Applied Nonlinear Dynamics of Non-Smooth Mechanical Systems
,”
J. Braz. Soc. Mech. Sci. Eng.
,
XXVIII
(
4
), pp.
519
526
.
14.
Narimani
,
A.
Golnaraghi
,
M. F.
, and
Jazar
,
G. N.
, 2004,
“Frequency Response of a Piecewise Linear Vibration Isolator,”
J. Vib. Contr.
,
10
, pp.
1775
1794
.
15.
Awrejcewicz
,
J.
Dzyubak
,
L.
, and
Lamarque
,
C.
, 2008,
“Modelling of Hysteresis Using Masing-Bouc Wen’s Framework and Search of Conditions for the Chaotic Responses,”
Commun. Nonlin. Sci. Numer. Simul.
,
13
, pp.
939
958
.
16.
Zhang
,
J.
, and
Richards
,
C. M.
, 2006,
“Dynamic Analysis and Parameter Identification of a Single Mass Elastomeric Isolation System Using a Maxwell-Voigt Model,”
ASME J. Vib. Acoust.
,
128
, pp.
713
721
.
17.
MathWorks, 2007, MATLAB User Guide, MathWorks, Natick, MA.
You do not currently have access to this content.