Measurements are presented from a two-beam structure with several bolted interfaces in order to characterize the nonlinear damping introduced by the joints. The measurements (all at force levels below macroslip) reveal that each underlying mode of the structure is well approximated by a single degree-of-freedom (SDOF) system with a nonlinear mechanical joint. At low enough force levels, the measurements show dissipation that scales as the second power of the applied force, agreeing with theory for a linear viscously damped system. This is attributed to linear viscous behavior of the material and/or damping provided by the support structure. At larger force levels, the damping is observed to behave nonlinearly, suggesting that damping from the mechanical joints is dominant. A model is presented that captures these effects, consisting of a spring and viscous damping element in parallel with a four-parameter Iwan model. The parameters of this model are identified for each mode of the structure and comparisons suggest that the model captures the stiffness and damping accurately over a range of forcing levels.

References

References
1.
Segalman
,
D. J.
,
2001
, “
An Initial Overview of Iwan Modelling for Mechanical Joints
,” Sandia National Laboritories, Albuquerque, NM, Report No. SAND2001-0811.
2.
Segalman
,
D. J.
,
2005
, “
A Four-Parameter Iwan Model for Lap-Type Joints
,”
ASME J. Appl. Mech.
,
72
(
5
), pp.
752
760
.10.1115/1.1989354
3.
Segalman
,
D. J.
, and
Starr
,
M. J.
,
2012
, “
Iwan Models and Their Provenance
,”
ASME
Paper No. DETC2012-71534.10.1115/DETC2012-71534
4.
Allen
,
M. S.
, and
Mayes
,
R. L.
,
2010
, “
Estimating the Degree of Nonlinearity in Transient Responses With Zeroed Early-Time Fast Fourier Transforms
,”
Mech. Syst. Sig. Process.
,
24
(
7
), pp.
2049
2064
.10.1016/j.ymssp.2010.02.012
5.
Segalman
,
D. J.
, and
Holzmann
,
W.
,
2005
, “
Nonlinear Response of a Lap-Type Joint Using a Whole-Interface Model
,”
23rd International Modal Analysis Conference (IMAC-XXIII)
, Orlando, FL, Jan. 31–Feb. 3.
6.
Segalman
,
D. J.
,
2010
, “
A Modal Approach to Modeling Spatially Distributed Vibration Energy Dissipation
,” Sandia National Laboratories, Albuquerque, NM, Livermore, CA, Report No. SAND2010-4763.
7.
Deaner
,
B. J.
,
Allen
,
M. S.
,
Starr
,
M. J.
, and
Segalman
,
D. J.
,
2014
, “
Investigation of Modal Iwan Models for Structures With Bolted Joints
,”
Topics in Experimental Dynamic Substructuring
(Conference Proceedings of the Society for Experimental Mechanics Series, Vol.
2
), Springer, New York, pp.
9
25
.10.1007/978-1-4614-6540-9_2
8.
Eriten
,
M.
,
Kurt
,
M.
,
Luo
,
G.
,
Michael
,
D.
,
McFarland
,
Bergman
,
L. A.
, and
Vakakis
,
A. F.
,
2013
, “
Nonlinear System Identification of Frictional Effects in a Beam With a Bolted Joint Connection
,”
Mech. Syst. Sig. Process.
,
39
(
1–2
), pp.
245
264
.10.1016/j.ymssp.2013.03.003
9.
Reuss
,
P.
,
Kruse
,
S.
,
Peter
,
S.
,
Morlock
,
F.
, and
Gaul
,
L.
,
2013
, “
Identification of Nonlinear Joint Characteristic in Dynamic Substructuring
,”
Topics in Experimental Dynamic Substructuring
(Conference Proceedings of the Society for Experimental Mechanics Series, Vol. 2), Springer, New York, pp.
27
36
.10.1007/978-1-4614-6540-9_3
10.
Reuss
,
P.
,
Zeumer
,
B.
,
Herrmann
,
J.
, and
Gaul
,
L.
,
2012
, “
Consideration of Interface Damping in Dynamic Substructuring
,” Topics in Experimental Dynamics Substructuring and Wind Turbine Dynamics (Conference Proceedings of the Society for Experimental Mechanics Series, Vol. 2), Springer, New York, pp.
81
88
.10.1007/978-1-4614-2422-2_10
11.
Bograd
,
S.
,
Reuss
,
P.
,
Schmidt
,
A.
,
Gaul
,
L.
, and
Mayer
,
M.
,
2011
, “
Modeling the Dynamics of Mechanical Joints
,”
Mech. Syst. Sig. Process.
,
25
(
8
), pp.
2801
2826
.10.1016/j.ymssp.2011.01.010
12.
Hammami
,
C.
, and
Balmes
,
E.
,
2014
, “
Meta-Models of Repeated Dissipative Joints for Damping Design Phase
,”
26th International Seminar on Modal Analysis (ISMA)
, Leuven, Belgium, Sept. 15–17, pp.
2573
2584
.
13.
Petrov
,
E. P.
, and
Ewins
,
D. J.
,
2003
, “
Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Disks
,”
ASME J. Turbomach.
,
125
(
2
), pp.
364
371
.10.1115/1.1539868
14.
Segalman
,
D. J.
,
Gregory
,
D. L.
,
Starr
,
M. J.
,
Resor
,
B. R.
,
Jew
,
M. D.
,
Lauffer
,
J. P.
, and
Ames
,
N. M.
,
2009
, “
Handbook on Dynamics of Jointed Structures
,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND2009-4164.
15.
Gregory
,
D. L.
,
Resor
,
B. R.
, and
Coleman
,
R. G.
,
2003
, “
Experimental Investigations of an Inclined Lap-Type Bolted Joint
,” Sandia National Laboritories, Albuquerque, NM, Report No. SAND2003-1193.
16.
Sracic
,
M. W.
,
Allen
,
M. S.
, and
Sumali
,
H.
,
2012
, “
Identifying the Modal Properties of Nonlinear Structures Using Measured Free Response Time Histories From a Scanning Laser Doppler Vibrometer
,”
30th International Modal Analysis Conference
, Jacksonville, FL, Jan. 30–Feb. 2.
17.
Zhang
,
Q.
,
Allemang
,
R. J.
, and
Brown
,
D. L.
,
1990
, “
Modal Filter: Concept and Application
,”
8th International Modal Analysis Conference (IMAC VIII)
, Kissimmee, FL, Jan. 29–Feb. 1.
18.
Stearns
,
S. D.
,
2003
,
Digital Signal Processing With Examples in matlab
,
CRC Press
,
Boca Raton, FL
.
19.
Braun
,
S.
, and
Feldman
,
M.
,
2011
, “
Decomposition of Non-Stationary Signals Into Varying Time Scales: Some Aspects of the EMD and HVD Methods
,”
Mech. Syst. Sig. Process.
,
25
(
7
), pp.
2608
2630
.10.1016/j.ymssp.2011.04.005
20.
Sumali
,
H.
, and
Kellogg
,
R. A.
,
2011
, “
Calculating Damping From Ring-Down Using Hilbert Transform and Curve Fitting
,”
4th International Operational Modal Analysis Conference (IOMAC)
, Istanbul, Turkey, May 9–11.
21.
Feldman
,
M.
,
2011
, “
Hilbert Transform in Vibration Analysis
,”
Mech. Syst. Sig. Process.
,
25
(
3
), pp.
735
802
.10.1016/j.ymssp.2010.07.018
22.
Kerschen
,
G.
,
Vakakis
,
A. F.
,
Lee
,
Y. S.
,
McFarland
,
D. M.
, and
Bergman
,
L. A.
,
2008
, “
Toward a Fundamental Understanding of the Hilbert-Huang Transform in Nonlinear Structural Dynamics
,”
JVC/J. Vib. Control
,
14
(
1–2
), pp.
77
105
.10.1177/1077546307079381
23.
Jones
,
D. R.
,
Perttunen
,
C. D.
, and
Stuckman
,
B. E.
,
1993
, “
Lipschitzian Optimization Without the Lipschitz Constant
,”
J. Optim. Theory Appl.
,
79
(
1
), pp.
157
181
.10.1007/BF00941892
24.
Coleman
,
T.
,
Branch
,
M. A.
, and
Grace
,
A.
,
2003
,
Optimization Toolbox for Use With matlab
,
The MathWorks
,
Natick, MA
.
25.
Dickinson
,
S. M.
,
1978
, “
On the Use of Simply Supported Plate Functions in Raleigh's Method Applied to the Flexural Vibration of Rectangular Plates
,”
J. Sound Vib.
,
59
(
1
), pp.
143
146
.10.1016/0022-460X(78)90493-5
26.
Carne
,
T. G.
,
Griffith
,
D. T.
, and
Casias
,
M. E.
,
2007
, “
Support Conditions for Experimental Modal Analysis
,”
Sound Vib.
,
41
, pp.
10
16
.
27.
Allen
,
M. S.
, and
Ginsberg
,
J. H.
,
2006
, “
A Global, Single-Input-Multi-Output (SIMO) Implementation of the Algorithm of Mode Isolation and Applications to Analytical and Experimental Data
,”
Mech. Syst. Sig. Process.
20
(
5
), pp.
1090
1111
.10.1016/j.ymssp.2005.09.007
28.
Allen
,
M. S.
, and
Ginsberg
,
J. H.
,
2005
, “
Global, Hybrid, MIMO Implementation of the Algorithm of Mode Isolation
,”
23rd International Modal Analysis Conference (IMAC XXIII)
, Orlando, FL, Jan. 31–Feb. 3.
You do not currently have access to this content.