Von Karman,
T.
, 1940, “
The Engineer Grapples With Nonlinear Problem,” Bull. Am. Math. Soc.,
46(8), pp. 615–683.
[CrossRef]
Amabili,
M.
, and
Paidoussis,
M.
, 2003, “
Review of Studies on Geometrically Nonlinear Vibrations and Dynamics of Circular Cylindrical Shells and Panels, With and Without Fluid-Structure Interaction,” ASME Appl. Mech. Rev.,
56(4), pp. 349–381.
[CrossRef]
Schmidt,
G.
, and
Tondl,
A.
, 1986, Non-Linear Vibration,
Cambridge University Press,
Cambridge, UK.
Nayfeh,
A. H.
, and
Mook,
D. T.
, 1979, Nonlinear Oscillations,
Wiley-Interscience,
New York.
Verhulst,
F.
, 1999, Nonlinear Differential Equations and Dynamical Systems, 2nd, ed.,
Springer,
Berlin.
Nayfeh,
A. H.
, and
Pai,
P. F.
, 2004, Linear and Nonlinear Structural Mechanics,
Wiley-Interscience,
New York.
Babitsky,
V. I.
, and
Krupenin,
V. L.
, 2001, Vibrations of Strongly Nonlinear Discontinuous Systems,
Springer,
Berlin.
Worden,
K.
, and
Tomlinson,
G. R.
, 2002, Nonlinearity in Structural Dynamics: Detection, Identification and Modeling,
CRC Press,
Boca Raton, FL.
Doebling,
S. W.
,
Farrar,
C. R.
,
Prime,
M. B.
, and
Shevitz,
D. W.
, 1996, “
Damage Identification and Health Monitoring of Structural and Mechanical Systems From Changes in Their Vibration Characteristics: A Literature Review,” Los Alamos National Laboratory, Report No. LA-13070-MS.
Cabrera,
D.
,
Sancho,
F.
,
Sanchez,
R. V.
,
Zurita,
G.
,
Cerrada,
M.
,
Li,
C.
, and
Vasquez,
R. E.
, 2015, “
Fault Diagnosis of Spur Gearbox Based on Random Forest and Wavelet Packet Decomposition,” Front. Mech. Eng.,
10(3), pp. 277–286.
[CrossRef]
Falco,
M.
,
Liu,
M.
,
Nguyen,
S. H.
, and
Chelidze,
D.
, 2014, “
Nonlinear System Identification and Modeling of a New Fatigue Testing Rig Based on Inertial Forces,” ASME J. Vib. Acoust.,
136(4), p. 041001.
Kerschen,
G.
,
Worden,
K.
, and
Vakakis,
A. F.
, 2006, “
Past, Present and Future of Nonlinear System Identification in Structural Dynamics,” Mech. Syst. Signal Process.,
20(3), pp. 505–592.
[CrossRef]
Socha,
L.
, and
Pawleta,
M.
, 2001, “
Are Statistical Linearization and Standard Equivalent Linearization the Same Methods in the Analysis of Stochastic Dynamic Systems?,” J. Sound Vib.,
248(2), pp. 387–394.
[CrossRef]
Iwan,
W. D.
, and
Mason,
A. B.
, 1980, “
Equivalent Linearization for Systems Subjected to Non-Stationary Random Excitation,” Int. J. Non-Linear Mech.,
15(2), pp. 71–82.
[CrossRef]
Miles,
H. J.
, 1995, “
Identification of Weakly Non-Linear Systems Using Equivalent Linearization,” J. Sound Vib.,
185(3), pp. 473–481.
[CrossRef]
Soize,
C.
, 1994, “
Stochastic Linearization Method With Random Parameters and Power Spectral Density Calculation,” 6th International Conference on Structural Safety and Reliability, Innsbruck, Austria, Aug. 9–13, pp. 217–222.
Billings,
S. A.
, and
Tsang,
K. M.
, 1989, “
Spectral Analysis for Nonlinear Systems, Part I: Parametric Non-Linear Spectral Analysis,” Mech. Syst. Signal Process.,
3(4), pp. 319–339.
[CrossRef]
Billings,
S. A.
, and
Tsang,
K. M.
, 1989, “
Spectral Analysis for Nonlinear Systems, Part II: Interpretation of Nonlinear Frequency Response Functions,” Mech. Syst. Signal Process.,
3(4), pp. 341–359.
[CrossRef]
Storer,
D. M.
, and
Tomlinson,
G. R.
, 1993, “
Recent Developments in the Measurements and Interpretation of Higher Order Functions From Non-Linear Structures,” Mech. Syst. Signal Process.,
7(2), pp. 173–189.
[CrossRef]
Schetzen,
M.
, 1980, The Volterra and Wiener Theories of Nonlinear Systems,
Wiley,
New York.
Scussel,
O.
, and
da Silva,
S.
, 2016, “
Output-Only Identification of Nonlinear System Via Volterra Series,” ASME J. Vib. Acoust.,
138(4), p. 041012.
[CrossRef]
Riche,
R. L.
,
Gualandris,
D.
,
Thomas,
J. J.
, and
Hemez,
F.
, 2001, “
Neural Identification of Non-Linear Dynamic Structures,” J. Sound Vib.,
248(2), pp. 247–265.
[CrossRef]
Chassiakos,
A. G.
, and
Masri,
S. F.
, 1996, “
Modelling Unknown Structural Systems Through the Use of Neural Networks,” Earthquake Eng. Struct. Dyn.,
25(2), pp. 117–128.
[CrossRef]
Cinar,
A.
, 1995, “
Nonlinear Time Series Models for Multivariable Dynamic Processes,” Chemom. Intell. Lab. Syst.,
30(1), pp. 147–158.
[CrossRef]
Zou,
Y.
,
Tong,
L.
, and
Steven,
G. P.
, 2000, “
Vibration-Based Model-Dependent Damage (Delamination) Identification and Health Monitoring for Composite Structures-a Review,” J. Sound Vib.,
230(2), pp. 357–378.
[CrossRef]
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,” J. Vib. Control,
14(1–2), pp. 77–105.
[CrossRef]
Sun,
Y.
,
Zhuang,
C.
, and
Xiong,
Z.
, 2015, “
Transform Operator Pair Assisted Hilbert-Huang Transform for Signals With Instantaneous Frequency Intersections,” ASME J. Vib. Acoust.,
137(6), p. 061016.
[CrossRef]
Feldman,
M.
, and
Braun,
S.
, 1995, “
Identification of Non-Linear System Parameters Via the Instantaneous Frequency: Application of the Hilbert Transform and Wigner–Ville Technique,” 13th International Modal Analysis Conference, Nashville, TN, Feb. 13–16, pp. 637–642.
Franco,
H.
, and
Pauletti,
R. M. O.
, 1997, “
Analysis of Nonlinear Oscillations by Gabor Spectrograms,” Nonlinear Dyn.,
12(3), pp. 215–236.
[CrossRef]
Bellizzi,
S.
,
Guillemain,
P.
, and
Kronland-Martinet,
R.
, 2001, “
Identification of Coupled Non-Linear Modes From Free Vibration Using Time–Frequency Representations,” J. Sound Vib.,
243(2), pp. 191–213.
[CrossRef]
Argoul,
P.
, and
Le,
T. P.
, 2003, “
Instantaneous Indicators of Structural Behaviour Based on the Continuous Cauchy Wavelet Analysis,” Mech. Syst. Signal Process.,
17(1), pp. 243–250.
[CrossRef]
Staszewski,
W. J.
, 1998, “
Identification of Non-Linear Systems Using Multi-Scale Ridges and Skeletons of the Wavelet Transform,” J. Sound Vib.,
214(4), pp. 639–658.
[CrossRef]
Pailwal,
D.
,
Choudhur,
A.
, and
Govandhan,
T.
, 2014, “
Identification of Faults Through Wavelet Transform Vis-à-Vis Fast Fourier Transform of Noisy Vibration Signals Emanated From Defective Rolling Element Bearings,” Front. Mech. Eng.,
9(2), pp. 130–141.
[CrossRef]
Pai,
P. F.
, 2013, “
Time–Frequency Analysis for Parametric and Non-Parametric Identification of Nonlinear Dynamical Systems,” Mech. Syst. Signal Process.,
36(2), pp. 332–353.
[CrossRef]
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.
[CrossRef]
Feldman,
M.
, 1994, “
Non-Linear System Vibration Analysis Using Hilbert Transform—II. Forced Vibration Analysis Method ‘FORCEVIB’,” Mech. Syst. Signal Process.,
8(3), pp. 309–318.
[CrossRef]
Feldman,
M.
, 2007, “
Considering High Harmonics for Identification of Non-Linear Systems by Hilbert Transform,” Mech. Syst. Signal Process.,
21(2), pp. 943–958.
[CrossRef]
Feldman,
M.
, 2006, “
Time-Varying Vibration Decomposition and Analysis Based on the Hilbert Transform,” J. Sound Vib.,
295(3–5), pp. 518–530.
[CrossRef]
Feldman,
M.
, 1997, “
Non-Linear Free Vibration Identification Via the Hilbert Transform,” J. Sound Vib.,
208(3), pp. 475–489.
[CrossRef]
Feldman,
M.
, 2012, “
Nonparametric Identification of Asymmetric Nonlinear Vibration Systems With the Hilbert Transform,” J. Sound Vib.,
331(14), pp. 3386–3396.
[CrossRef]
Peng,
Z. K.
,
Meng,
G.
, and
Chu,
F. L.
, 2011, “
Polynomial Chirplet Transform With Application to Instantaneous Frequency Estimation,” IEEE Trans. Instrum. Meas.,
60(9), pp. 3222–3229.
[CrossRef]
Yang,
Y.
,
Zhang,
W.
,
Peng,
Z.
, and
Meng,
G.
, 2013, “
Multicomponent Signal Analysis Based on Polynomial Chirplet Transform,” IEEE Trans. Ind. Electron.,
60(9), pp. 3948–3956.
[CrossRef]
Wang,
L. L.
,
Zhang,
J. H.
,
Wang,
C.
, and
Hu,
S. Y.
, 2003, “
Time–Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves,” ASME J. Vib. Acoust.,
125(2), pp. 170–177.
[CrossRef]
Weaver,
W.
,
Timoshenko,
S. P.
, and
Young,
D. H.
, 1990, Vibration Problems in Engineering, 5th ed.,
Wiley,
New York.
Feldman,
M.
, 2011, Hilbert Transform Application in Mechanical Vibration,
Wiley,
Chichester, UK.
Deng,
Y.
,
Peng,
Z. K.
,
Yang,
Y.
,
Zhang,
W. M.
, and
Meng,
G.
, 2013, “
Identification of Nonlinear Vibration Systems Based on Parametric TFA,” Chin. J. Theor. Appl. Mech.,
45(6), pp. 992–996 (in Chinese).
Boashash,
B.
, 1992, “
Estimating and Interpreting the Instantaneous Frequency of a Signal. I. Fundamentals,” Proc. IEEE,
80(4), pp. 520–538.
[CrossRef]
Boashash,
B.
, 1992, “
Estimating and Interpreting the Instantaneous Frequency of a Signal. II. Algorithms and applications,” Proc. IEEE,
80(4), pp. 540–568.
[CrossRef]
Kwok,
H. K. C.
, and
Jones,
D. L.
, 1995, “
Instantaneous Frequency Estimation Using an Adaptive Short-Time Fourier Transform,” Twenty-Ninth Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, Oct. 30–Nov. 1, pp. 543–546.
Shui,
P. L.
,
Bao,
Z.
, and
Su,
H. T.
, 2008, “
Nonparametric Detection of FM Signals Using Time–Frequency Ridge Energy,” IEEE Trans. Signal Process.,
56(5), pp. 1749–1760.
[CrossRef]
Li,
Y. Y.
,
Huang,
X. Q.
, and
Mao,
W. X.
, 2005, “
Effect of the Cubic Nonlinear Factors for Displacement and Velocity on Amplitude Frequency Characteristics of Dry Friction System for Metal Rubber,” J. Mech. Strength,
27(4), pp. 436–439 (in Chinese).
Ling,
R. J.
,
Weng,
J. S.
, and
Jin,
Z. L.
, 2009, “
Non-Linear Finite Element Analysis on Stiffness and Hysteresis Characteristic of Leaf Spring,” J. Chongqing Inst. Technol. (Nat. Sci),
23(1), pp. 19–23 (in Chinese).
Li,
S. H.
, and
Yang,
S. P.
, 2006, “
Research Status of Hysteretic Nonlinear Models,” J. Dyn. Control,
4(2), pp. 8–15 (in Chinese).
