A reduction procedure for joint models that was developed in earlier work is extended to allow for relative motion between surfaces, and the effect of this procedure on timestep issues is considered. A general one-dimensional structure containing a frictional interface is considered. Coulomb friction is approximated with nonlinear springs of large but finite stiffness. The system of equations describing this structure is reduced in a procedure similar to Guyan reduction by assuming that the system deforms only in the shapes that it takes when the interface is massless. The result of this procedure is that the dynamics associated with the interface region are removed from the analysis. Following the development of the reduction procedure, the reduced formulation is specialized to the case of a simple lap joint. A numerical example problem is considered in which both the full and reduced equations of motion are integrated over time. It is seen that, for the example problem considered, the reduction procedure results in tremendous computational savings with little loss of accuracy. Based on the results of the simple example problem, it appears that the proposed reduction procedure has potential to be an accurate and effective method of alleviating the timestep difficulties associated with direct finite element analysis of joints in structural dynamics applications.

1.
Beards
,
C. F.
, 1992, “
Damping in Structural Joints
,”
Shock Vib. Dig.
0583-1024,
24
, pp.
3
7
.
2.
Gregory
,
D. L.
, and
Martinez
,
D. R.
, 2001, “
On the Development of Methodologies for Constructing Predictive Models of Structures With Joints and Interfaces
,” Sandia National Laboratories, Technical Report No. SAND2001-0003P.
3.
Dohner
,
J. L.
, 2000, “
A Reduced Order, One Dimensional Model of Joint Response
,” Sandia National Laboratories, Technical Report No. SAND2000-2753C.
4.
Gaul
,
L.
, and
Nitsche
,
R.
, 2001, “
The Role of Friction in Mechanical Joints
,”
Appl. Mech. Rev.
0003-6900,
54
(
2
), pp.
93
105
.
5.
Liu
,
W.
, and
Ewins
,
D. J.
, 2000, “
Substructure Synthesis via Elastic Media Part I: Joint Identification
,”
Proceedings of the International Modal Analysis Conference
, San Antonio, TX.
6.
Ren
,
Y.
, 1992, “
The Analysis and Identification of Friction Joint Parameters in the Dynamic Response of Structures
,” Ph.D. thesis, Imperial College of Science, Technology, and Medicine, University of London, London, UK.
7.
Crawley
,
E. F.
, and
Aubert
,
A. A.
, 1986, “
Identification of Nonlinear Structural Elements by Force-State Mapping
,”
AIAA J.
0001-1452,
24
(
1
), pp.
155
162
.
8.
Ren
,
Y.
,
Lim
,
T. M.
, and
Lim
,
M. K.
, 1998, “
Identification of Properties of Nonlinear Joints Using Dynamic Test Data
,”
ASME J. Vibr. Acoust.
0739-3717,
120
, pp.
324
330
.
9.
Iwan
,
W. D.
, 1966, “
A Distributed-Element Model for Hysteresis and Its Steady-State Dynamic Response
,”
ASME J. Appl. Mech.
0021-8936,
33
, pp.
893
900
.
10.
Iwan
,
W. D.
, 1967, “
On a Class of Models for the Yielding Behavior of Continuous and Composite Systems
,”
ASME J. Appl. Mech.
0021-8936,
34
, pp.
612
617
.
11.
Segalman
,
D. J.
, 2001, “
An Initial Overview of Iwan Modeling for Mechanical Joints
,” Sandia National Laboratories, Technical Report No. SAND2001-0811.
12.
Segalman
,
D. J.
, 2002, “
A Four-Parameter Iwan Model for Lap-Type Joints
,” Sandia National Laboratories, Technical Report No. SAND2002-3828.
13.
Segalman
,
D. J.
,
Paez
,
T.
,
Smallwood
,
D.
,
Sumali
,
A.
, and
Urbina
,
A.
, 2003, “
Status and Integrated Road-Map for Joints Modeling Research
,” Sandia National Laboratories, Technical Report No. SAND2003-0897.
14.
Gregory
,
D.
,
Smallwood
,
D.
, and
Coleman
,
R. G.
, 2000, “
Damping Investigations of a Simplified Frictional Shear Joint
,”
Proceedings of the 71st Shock and Vibration Symposium
.
15.
Quinn
,
D. D.
, and
Segalman
,
D. J.
, 2005, “
Using Series-Series Iwan-Type Models for Understanding Joint Dynamics
,”
ASME J. Appl. Mech.
0021-8936,
72
, pp.
666
673
.
16.
Menq
,
C. -H.
, and
Griffin
,
J. H.
, 1985, “
A Comparison of Transient and Steady State Finite Element Analyses of the Forced Response of a Frictionally Damped Beam
,”
ASME J. Vib., Acoust., Stress, Reliab. Des.
0739-3717,
107
, pp.
19
25
.
17.
Menq
,
C. -H.
,
Griffin
,
J. H.
, and
Bielak
,
J.
, 1986, “
The Influence of Microslip on Vibratory Response, Part I: A New Microslip Model
,”
J. Sound Vib.
0022-460X,
107
(
2
), pp.
279
293
.
18.
Menq
,
C. -H.
,
Griffin
,
J. H.
, and
Bielak
,
J.
, 1986, “
The Influence of Microslip on Vibratory Response, Part II: A Comparison With Experimental Results
,”
J. Sound Vib.
0022-460X,
107
(
2
), pp.
295
307
.
19.
Canudas de Wit
,
C.
,
Olsson
,
H.
,
Astrom
,
K. J.
, and
Lischinsky
,
P.
, 1995, “
A New Model for Control of Systems With Friction
,”
IEEE Trans. Autom. Control
0018-9286,
40
(
3
), pp.
419
425
.
20.
Gaul
,
L.
, and
Lenz
,
J.
, 1997, “
Nonlinear Dynamics of Structures Assembled by Bolted Joints
,”
Acta Mech.
0001-5970,
125
, pp.
169
181
.
21.
Bauchau
,
O. A.
, and
Ju
,
C.
, 2006, “
Modeling Friction Phenomena in Flexible Multibody Dynamics
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
195
, pp.
6909
6924
.
22.
Willner
,
K.
, and
Gaul
,
L.
, 1995, “
A Penalty Approach for Contact Description by FEM Based on Interface Physics
,”
Proceedings of the Contact Mechanics II
, Ferrara, Italy.
23.
Guthrie
,
M. A.
, and
Kammer
,
D. C.
, 2008, “
A General Reduced Representation of One-Dimensional Frictional Interfaces
,”
ASME J. Appl. Mech.
0021-8936,
75
(
1
), p.
011019
.
24.
Guyan
,
R. J.
, 1965, “
Reduction of Stiffness and Mass Matrices
,”
AIAA J.
0001-1452,
3
(
2
), p.
380
.
25.
Miller
,
J. D.
, and
Quinn
,
D. D.
, 2009, “
A Two-Sided Interface Model for Dissipation in Structural Systems With Frictional Joints
,”
J. Sound Vib.
0022-460X,
321
(
1-2
), pp.
201
219
.
26.
Bampton
,
M. C. C.
, and
Craig
,
R. R.
, Jr.
, 1968, “
Coupling of Substructures for Dynamic Analysis
,”
AIAA J.
0001-1452,
6
(
7
), pp.
1313
1319
.
27.
Antunes
,
J.
,
Axisa
,
F.
,
Beaufils
,
B.
, and
Guilbaud
,
D.
, 1990, “
Coulomb Friction Modeling in Numerical Simulations of Vibration and Wear Work Rate of Multispan Tube Bundles
,”
J. Fluids Struct.
0889-9746,
4
, pp.
287
304
.
28.
Dahl
,
P.
, 1976, “
Solid Friction Damping of Mechanical Vibrations
,”
AIAA J.
0001-1452,
14
(
12
), pp.
1675
1682
.
29.
Haessig
,
D. A.
, and
Friedland
,
B.
, 1991, “
On the Modeling and Simulation of Friction
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
113
, pp.
354
362
.
30.
Guthrie
,
M. A.
, 2009, “
Reduced Order Modeling of Frictional Interfaces in Structural Dynamics
,” Ph.D. thesis, University of Wisconsin, Madison, WI.
31.
Cook
,
R. D.
,
Malkus
,
D. S.
,
Plesha
,
M. E.
, and
Witt
,
R. J.
, 2001,
Concepts and Applications of Finite Element Analysis
,
4th Ed.
,
Wiley
,
New York
.
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