In this work, two model identification methods are used to estimate the nonlinear large deformation behavior of a nonlinear resonator in the time and frequency domains. A doubly clamped beam with a slender geometry carrying a central intraspan mass when subject to a transverse excitation is used as the highly nonlinear resonator. A nonlinear Duffing equation has been used to represent the system for which the main source of nonlinearity arises from large midplane stretching. The first model identification technique uses the free vibration of the system and the Hilbert transform (HT) to identify a nonlinear force–displacement relationship in the large deformation region. The second method uses the frequency response of the system at various base accelerations to relate the maximum resonance frequency to the nonlinear parameter arising from the centerline extensibility. Experiments were conducted using the doubly clamped slender beam and an electrodynamic shaker to identify the model parameters of the system using both of the identification techniques. It was found that both methods produced near identical model parameters; an excellent agreement between theory and experiments was obtained using either of the identification techniques. This follows that two different model identification techniques in the time and frequency domains can be employed to accurately predict the nonlinear response of a highly nonlinear resonator.

References

References
1.
Soltani
,
P.
, and
Kerschen
,
G.
,
2015
, “
The Nonlinear Piezoelectric Tuned Vibration Absorber
,”
Smart Mater. Struct.
,
24
(
7
), p.
075015
.
2.
Febbo
,
M.
, and
Machado
,
S. P.
,
2013
, “
Nonlinear Dynamic Vibration Absorbers With a Saturation
,”
J. Sound Vib.
,
332
(
6
), pp.
1465
1483
.
3.
Chen
,
L.-Q.
, and
Jiang
,
W.-A.
,
2015
, “
Internal Resonance Energy Harvesting
,”
ASME J. Appl. Mech.
,
82
(
3
), p.
031004
.
4.
Masana
,
R.
, and
Daqaq
,
M. F.
,
2011
, “
Electromechanical Modeling and Nonlinear Analysis of Axially Loaded Energy Harvesters
,”
ASME J. Vib. Acoust.
,
133
(
1
), p.
011007
.
5.
Laura
,
R.
,
Ahmad
,
M. B.
,
Mohammad
,
I. Y.
,
Weili
,
C.
, and
Stefano
,
L.
,
2013
, “
Nonlinear Dynamics of an Electrically Actuated Imperfect Microbeam Resonator: Experimental Investigation and Reduced-Order Modeling
,”
J. Micromech. Microeng.
,
23
(
7
), p.
075012
.
6.
Ouakad
,
H. M.
, and
Younis
,
M. I.
,
2011
, “
Natural Frequencies and Mode Shapes of Initially Curved Carbon Nanotube Resonators Under Electric Excitation
,”
J. Sound Vib.
,
330
(
13
), pp.
3182
3195
.
7.
Nayfeh
,
A. H.
,
Mook
,
D. T.
, and
Marshall
,
L. R.
,
1973
, “
Nonlinear Coupling of Pitch and Roll Modes in Ship Motions
,”
J. Hydronautics
,
7
(
4
), pp.
145
152
.
8.
Spyrou
,
K. J.
, and
Thompson
,
J. M. T.
,
2000
, “
The Nonlinear Dynamics of Ship Motions: A Field Overview and Some Recent Developments
,”
Philos. Trans. R. Soc. London. Ser. A
,
358
(
1771
), pp.
1735
1760
.
9.
Lilien
,
J. L.
, and
da Costa
,
A. P.
,
1994
, “
Vibration Amplitudes Caused by Parametric Excitation of Cable Stayed Structures
,”
J. Sound Vib.
,
174
(
1
), pp.
69
90
.
10.
El Ouni
,
M. H.
,
Ben Kahla
,
N.
, and
Preumont
,
A.
,
2012
, “
Numerical and Experimental Dynamic Analysis and Control of a Cable Stayed Bridge Under Parametric Excitation
,”
Eng. Struct.
,
45
, pp.
244
256
.
11.
Shi
,
P.-M.
,
Li
,
J.-Z.
,
Jiang
,
J.-S.
,
Liu
,
B.
, and
Han
,
D.-Y.
,
2013
, “
Nonlinear Dynamics of Torsional Vibration for Rolling Mill's Main Drive System Under Parametric Excitation
,”
J. Iron Steel Res., Int.
,
20
(
1
), pp.
7
12
.
12.
Omidi
,
E.
, and
Mahmoodi
,
N.
,
2015
, “
Hybrid Positive Feedback Control for Active Vibration Attenuation of Flexible Structures
,”
IEEE/ASME Trans. Mechatronics
,
20
(
4
), pp.
1790
1797
.
13.
Omidi
,
E.
, and
Mahmoodi
,
S. N.
,
2015
, “
Sensitivity Analysis of the Nonlinear Integral Positive Position Feedback and Integral Resonant Controllers on Vibration Suppression of Nonlinear Oscillatory Systems
,”
Commun. Nonlinear Sci. Numer. Simul.
,
22
(
1–3
), pp.
149
166
.
14.
Peng
,
Z. K.
,
Lang
,
Z. Q.
, and
Billings
,
S. A.
,
2008
, “
Nonlinear Parameter Estimation for Multi-Degree-of-Freedom Nonlinear Systems Using Nonlinear Output Frequency-Response Functions
,”
Mech. Syst. Signal Process.
,
22
(
7
), pp.
1582
1594
.
15.
Doughty
,
T. A.
,
Davies
,
P.
, and
Bajaj
,
A. K.
,
2002
, “
A Comparison of Three Techniques Using Steady State Data to Identify Non-Linear Modal Behaviour of an Externally Excited Cantilever Beam
,”
J. Sound Vib.
,
249
(
4
), pp.
785
813
.
16.
Feldman
,
M.
,
1997
, “
Non-Linear Free Vibration Identification Via the Hilbert Transform
,”
J. Sound Vib.
,
208
(
3
), pp.
475
489
.
17.
Pai
,
P. F.
, and
Palazotto
,
A. N.
,
2008
, “
Detection and Identification of Nonlinearities by Amplitude and Frequency Modulation Analysis
,”
Mech. Syst. Signal Process.
,
22
(
5
), pp.
1107
1132
.
18.
Heidelberg
,
A.
,
Ngo
,
L. T.
,
Wu
,
B.
,
Phillips
,
M. A.
,
Sharma
,
S.
,
Kamins
,
T. I.
,
Sader
,
J. E.
, and
Boland
,
J. J.
,
2006
, “
A Generalized Description of the Elastic Properties of Nanowires
,”
Nano Lett.
,
6
(
6
), pp.
1101
1106
.
19.
Lulla
,
K. J.
,
Cousins
,
R. B.
,
Venkatesan
,
A.
,
Patton
,
M. J.
,
Armour
,
A. D.
,
Mellor
,
C. J.
, and
Owers-Bradley
,
J. R.
,
2012
, “
Nonlinear Modal Coupling in a High-Stress Doubly-Clamped Nanomechanical Resonator
,”
New J. Phys.
,
14
(
11
), p.
113040
.
You do not currently have access to this content.