Abstract

Jointed interfaces, damage, wear, or non-idealized boundary conditions often introduce nonlinear characteristics to assembled structures. Consequently, extensive research has been carried out regarding nonlinear system identification. The development of nonlinear system identification is also enabling the intentional application of nonlinearities towards practical fields such as vibration control and energy harvesting. This research proposes a nonlinear identification procedure that consists of two steps: first, the raw data is filtered by the Double Reverse Multimodal Decomposition method that involves system reconstruction, expansion, and filtering twice. Second, the Peak Finding and Fitting method is applied to the filtered signal to extract the instantaneous amplitude and frequency. The identification procedure is applied to the measured responses from a jointed structure to assess its efficacy. The results are compared with those obtained from other well-known methods—the Hilbert transform and zero-crossing methods. The comparison results indicate that the Peaking Finding and Fitting method extracts the amplitude of the response signal more accurately. Consequently, this yields a higher signal-to-noise ratio in the extracted damping values. As a recommended last step, uncertainty assessment is conducted to calculate the 95% confidence intervals of the nonlinear properties of the system.

References

References
1.
Brake
,
M. R. W.
, eds.,
2017
,
The Mechanics of Jointed Structures: Recent Research and Open Challenges for Developing Predictive Models for Structural Dynamics
,
Springer
,
Cham, Switzerland
.
2.
Chen
,
W.
,
Jin
,
M.
,
Brake
,
M. R. W.
, and
Song
,
H.
,
2019
, “
Measurement of Slip and Separation in Jointed Structures With Non-flat Interfaces
,”
Mech. Syst. Signal Process.
,
134
, p.
106325
. 10.1016/j.ymssp.2019.106325
3.
Peeters
,
M.
,
Kerschen
,
G.
, and
Golinval
,
J. C.
,
2011
, “
Modal Testing of Nonlinear Vibrating Structures Based on Nonlinear Normal Modes: Experimental Demonstration
,”
Mech. Syst. Signal Process.
,
25
(
4
), pp.
1227
1247
. 10.1016/j.ymssp.2010.11.006
4.
Noel
,
J. P.
, and
Kerschen
,
G.
,
2017
, “
Nonlinear System Identification in Structural Dynamics: 10 More Years of Progress
,”
Mech. Syst. Signal Process.
,
83
, pp.
2
35
. 10.1016/j.ymssp.2016.07.020
5.
Haller
,
G.
, and
Ponsioen
,
S.
,
2016
, “
Nonlinear Normal Modes and Spectral Submanifolds: Existence, Uniqueness and Use in Model Reduction
,”
Nonlinear Dyn.
,
86
(
3
), pp.
1493
1534
. 10.1007/s11071-016-2974-z
6.
Feldman
,
M.
,
2014
, “
Hilbert Transform Methods for Nonparametric Identification of Nonlinear Time Varying Vibration Systems
,”
Mech. Syst. Signal Process.
,
47
(
1–2
), pp.
66
77
. 10.1016/j.ymssp.2012.09.003
7.
Dossogne
,
T.
,
Jerome
,
T. W.
,
Lancereau
,
D. P. T.
,
Smith
,
S. A.
,
Brake
,
M. R. W.
,
Pacini
,
B. R.
,
Reuß
,
P.
, and
Schwingshackl
,
C. W.
,
2017
,
Experimental Assessment of the Influence of Interface Geometries on Structural Dynamic Response
.
Garden Grove, CA
,
January
.
8.
Roettgen
,
D. R.
, and
Allen
,
M. S.
,
2017
, “
Nonlinear Characterization of a Bolted, Industrial Structure Using a Modal Framework
,”
Mech. Syst. Signal Process.
,
84
, pp.
152
170
. 10.1016/j.ymssp.2015.11.010
9.
Jin
,
M.
,
Brake
,
M. R. W.
, and
Song
,
H.
,
2019
, “
Comparison of Nonlinear System Identification Methods for Free Decay Measurements with Application to Jointed Structures
,”
J. Sound. Vib.
,
453
, pp.
268
293
. 10.1016/j.jsv.2019.04.021
10.
Brake
,
M. R. W.
,
Schwingshackl
,
C. W.
, and
Reuß
,
P.
,
2019
, “
Observations of Variability and Repeatability in Jointed Structures
,”
Mech. Syst. Signal Process.
,
129
, pp.
282
307
. 10.1016/j.ymssp.2019.04.020
11.
Singh
,
A.
,
Chen
,
W.
,
Jana
,
D.
,
Jin
,
M.
,
Cendese
,
M.
,
Brake
,
M. R. W.
,
Schwingshackl
,
C. W.
,
Moore
,
K. J
, and
Noel.
,
J.-P.
,
2020
, “
Nonlinear System Identification of a Jointed Structure Using Full-Field Data: Part 1 Experimental Investigation
,”
IMAC XXXVIII A Conference and Exposition on Structural Dynamics
,
Houston, TX
.
12.
Kosova
,
G.
,
Jin
,
M.
,
Cendese
,
M.
,
Chen
,
W.
,
Singh
,
A.
,
Jana
,
D.
,
Brake
,
M. R. W.
,
Schwingshackl
,
C. W.
,
Moore
,
K. J
, and
Noel
,
J.-P.
,
2020
, “
Nonlinear System Identification of a Jointed Structure Using Full-Field Data: Part II Analysis
,”
IMAC XXXVIII A Conference and Exposition on Structural Dynamics
,
Houston, TX
.
13.
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
.
Technical Report SAND2009-4164
.
Sandia National Laboratories
,
Albuquerque, NM
.
14.
Deaner
,
B. J.
,
Allen
,
M. S.
,
Starr
,
M. J.
,
Segalman
,
D. J.
, and
Sumali
,
H.
,
2015
, “
Application of Viscous and Iwan Modal Damping Models to Experimental Measurements From Bolted Structures
,”
ASME J. Vib. Acoust.
,
137
(
2
), p.
021012
. 10.1115/1.4029074
15.
Smith
,
S. A.
,
Bilbao-Ludena
,
J. C.
,
Catalfamo
,
S.
,
Brake
,
M. R. W.
,
Reuss
,
P.
, and
Schwingshackl
,
C. W.
,
2015
, “
The Effects of Boundary Conditions, Measurement Techniques, and Excitation Type on Measurements of the Properties of Mechanical Joints
,”
IMAC XXXIII A Conference and Exposition on Structural Dynamics
,
Orlando, FL
,
February
.
16.
Schwingshackl
,
C. W.
,
Joannin
,
C.
,
Pesaresi
,
L.
,
Green
,
J. S.
, and
Hoffmann
,
N.
, Test Method Development for Nonlinear Damping Extraction of Dovetail Joints.
Dynamics of Coupled Structures
, Vol.
1
, pp.
229
237
.
Springer International Publishing
.
17.
Nol
,
J. P.
,
Renson
,
L.
,
Grappasonni
,
C.
, and
Kerschen
,
G.
,
2016
, “
Identification of Nonlinear Normal Modes of Engineering Structures Under Broadband Forcing
,”
Mech. Syst. Signal Process.
,
74
, pp.
95
110
. 10.1016/j.ymssp.2015.04.016
18.
Szalai
,
R.
,
Ehrhardt
,
D.
, and
Haller
,
G.
,
2017
, “
Nonlinear Model Identification and Spectral Submanifolds for Multi-degree-of-freedom Mechanical Vibrations
,”
Proc. R. Soc. A
,
473
(
2202
), p.
20160759
. 10.1098/rspa.2016.0759
19.
Cenedese
,
M.
, and
Haller
,
G.
,
2019
, “
Constructing Backbone Curves From Free-Decay Vibrations Data in Multi-Degrees of Freedom Oscillatory Systems
,”
IMAC XXXVII A Conference and Exposition on Structural Dynamics
,
Orlando, FL
. 10.1007/978-3-030-12391-8_30
20.
Kerschen
,
G.
,
Worden
,
K.
,
Vakakis
,
A. F.
, and
Golinval
,
J. C.
,
2006
, “
Past, Present and Future of Nonlinear System Identification in Structural Dynamics
,”
Mech. Syst. Signal Process.
,
20
(
3
), pp.
505
592
. 10.1016/j.ymssp.2005.04.008
21.
Feldman
,
M.
,
2011
, “
Hilbert Transform in Vibration Analysis
,”
Mech. Syst. Signal Process.
,
25
(
3
), pp.
735
802
. 10.1016/j.ymssp.2010.07.018
22.
Lee
,
Y. S.
,
Tsakirtzis
,
S.
,
Vakakis
,
A. F.
,
Bergman
,
L. A.
, and
McFarland
,
D. M.
,
2009
, “
Physics-based Foundation for Empirical Mode Decomposition
,”
AIAA J.
,
47
(
12
), pp.
2938
2963
. 10.2514/1.43207
23.
Londono
,
J. M.
,
Neild
,
S. A.
, and
Cooper
,
J. E.
,
2015
, “
Identification of Backbone Curves of Nonlinear Systems From Resonance Decay Responses
,”
J. Sound. Vib.
,
348
, pp.
224
238
. 10.1016/j.jsv.2015.03.015
24.
Huang
,
N. E.
,
Shen
,
Z.
,
Long
,
S. R.
,
Wu
,
M. L. C.
,
Shih
,
H. H.
,
Zheng
,
Q. N.
,
Yen
,
N. C.
,
Tung
,
C. C.
, and
Liu
,
H. H.
,
1998
, “
The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis
,”
Proc. R. Soc. A-Math. Phys. Eng. Sci.
,
454
(
1971
), pp.
903
995
. 10.1098/rspa.1998.0193
25.
Moore
,
K. J.
,
Kurt
,
M.
,
Eriten
,
M.
,
McFarland
,
D. M.
,
Bergman
,
L. A.
, and
Vakakis
,
A. F.
,
2018
, “
Wavelet-bounded Empirical Mode Decomposition for Measured Time Series Analysis
,”
Mech. Syst. Signal Process.
,
99
, pp.
14
29
. 10.1016/j.ymssp.2017.06.005
26.
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. Signal Process.
,
25
(
7
), pp.
2608
2630
. 10.1016/j.ymssp.2011.04.005
27.
Roettgen
,
D.
,
Allen
,
M. S.
,
Kammer
,
D.
, and
Mayes
,
R. L.
,
2017
, “
Substructuring of a Nonlinear Beam Using a Modal Iwan Framework, Part I: Nonlinear Modal Model Identification
,”
IMAC XXXV A Conference and Exposition on Structural Dynamics
,
Garden Grove, CA
.
28.
Deraemaeker
,
A.
, and
Preumont
,
A.
,
2006
, “
Vibration Based Damage Detection Using Large Array Sensors and Spatial Filters
,”
Mech. Syst. Signal Process.
,
20
(
7
), pp.
1615
1630
. 10.1016/j.ymssp.2005.02.010
29.
Gustafsson
,
F.
,
1996
, “
Determining the Initial States in Forward-backward Filtering
,”
IEEE Trans. Signal Process.
,
44
(
4
), pp.
988
992
. 10.1109/78.492552
30.
Goyder
,
H. G. D.
, and
Lancereau
,
D. P. T.
,
2017
, “
Methods for the Measurement of Non-linear Damping and Frequency in Built-up Structures
,”
Proceedings of the ASME 2017 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
,
IDETC 2017
.
31.
H. G. D.
Goyder
, and
D. P. T.
Lancereau
,
Extracting Natural Frequencies and Damping from Time Histories. Better than the Frequency Domain?
ISMA International Conference on Noise and Vibration Engineering
.
32.
Juang
,
J. N.
, and
Pappa
,
R. S.
,
1985
, “
An Eigensystem Realization Algorithm for Modal Parameter Identification and Model Reduction
,”
J. Guid., Contr. Dyn.
,
8
(
5
), pp.
620
627
. 10.2514/3.20031
33.
Paarmann
,
L. D.
,
2003
,
Design and Analysis of Analog Filters: A Signal Processing Perspective with MATLAB Example
,
New York, Boston
,
Dordrecht, London, Moscow
.
34.
Feldman
,
M.
,
1994
, “
Non-linear System Vibration Analysis Using Hilbert Transform-I. Free Vibration Analysis Method ‘Freevib’
,”
Mech. Syst. Signal Process.
,
8
(
2
), pp.
119
127
. 10.1006/mssp.1994.1011
35.
Ondra
,
V.
,
Riethmueller
,
R.
,
Brake
,
M. R. W.
,
Schwingshackl
,
C. W.
,
Polunin
,
Pavel M.
, and
Shaw
,
S. W.
,
2017
, “
Comparison of Nonlinear System Identification Methods for Free Decay Measurements with Application to MEMS Devices
,”
IMAC XXXV A Conference and Exposition on Structural Dynamics
,
Garden Grove, CA
.
36.
Krack
,
M.
,
2015
, “
Nonlinear Modal Analysis of Nonconservative Systems: Extension of the Periodic Motion Concept
,”
Comput. Struct.
,
154
, pp.
59
71
. 10.1016/j.compstruc.2015.03.008
37.
Rosatello
,
M.
,
Cooper
,
S.
,
Johnson
,
K.
,
Mathis
,
A.
,
Brake
,
M. R. W.
,
Allen
,
M. S.
,
Ferri
,
A. A.
,
Roettgen
,
D.
,
Pacini
,
B. R.
, and
Mayes
,
R. L.
,
2017
, “
Effect of Far-Field Structure on Joint Properties
,”
IMAC XXXV A Conference and Exposition on Structural Dynamics
,
Garden Grove, CA
.
38.
Pai
,
P. F.
, and
Palazotto
,
A. N.
,
2008
, “
HHT-based Nonlinear Signal Processing Method for Parametric and Non-parametric Identification of Dynamical Systems
,”
Int. J. Mech. Sci.
,
50
(
12
), pp.
1619
1635
. 10.1016/j.ijmecsci.2008.10.001
You do not currently have access to this content.