Analytical, numerical, and experimental results of energy pumping in a strongly inhomogeneous two-degree-of-freedom system are to be presented in this study. The latter is based both on efficient analytical solution and comparative analysis for various types of energetic sinks. Considering the efficient pumping process as damped beating with strong energy transfer, it is shown that we can design the sinks with amplitude-phase variables which provide the most efficient result. In this study, the main types of energetic sinks are to be compared. Computer simulation has confirmed the analytical predictions which had been obtained. Experimental verification of the analytical prediction is considered for a particular type of sink.

Issue Section:
Technical Papers
Keywords:
nonlinear dynamical systems, damping, oscillators, inhomogeneous media, energy pumping, multiple scales, complex variables, building model
Topics:
Damping, Design, Resonance, Computer simulation, Energy transformation
1.
Gendelman
,
O.
, 2001, “
Transition of Energy to a Nonlinear Localized Mode in a Highly Asymmetric System of Two Oscillators
,”
Nonlinear Dyn.
0924-090X,
25
, pp.
237
–
253
.
Crossref
Search ADS
 
2.
Vakakis
,
A. F.
, 2001, “
Inducing Passive Nonlinear Energy Sinks in Linear Vibrating Systems
,”
ASME J. Vibr. Acoust.
0739-3717,
123
, pp.
324
–
332
.
Crossref
Search ADS
 
3.
Vakakis
,
A. F.
, and
Gendelman
,
O.
, 2001, “
Energy Pumping in Nonlinear Mechanical Oscillators II: Resonance Capture
,”
ASME J. Appl. Mech.
0021-8936,
68
, pp.
42
–
48
.
Crossref
Search ADS
 
4.
Gendelman
,
O.
,
Manevitch
,
L. I.
,
Vakakis
,
A. F.
, and
M’Closkey
,
R.
, 2001, “
Energy Pumping in Nonlinear Mechanical Oscillators I: Dynamics of the Underlying Hamiltonian Systems
,”
ASME J. Appl. Mech.
0021-8936,
68
, pp.
34
–
41
.
Crossref
Search ADS
 
5.
Manevitch
,
L. I.
,
Gendelman
,
O.
,
Musienko
,
A. I.
,
Vakakis
,
A. F.
, and
Bergman
,
L.
, 2003, “
Dynamic Interaction of a Semi-infinite Linear Chain of Coupled Oscillators with a Strongly Nonlinear End Attachment
,”
Physica D
0167-2789,
178
, pp.
1
–
18
.
Crossref
Search ADS
 
6.
Vakakis
,
A. F.
,
Manevitch
,
L. I.
,
Musienko
,
A. I.
,
Kerschen
,
G.
, and
Bergman
,
L. A.
, 2005, “
Transient Dynamics of a Dispersive Elastic Wave Guide Weakly Coupled to an Essentially Nonlinear End Attachment
,”
Wave Motion
0165-2125,
41
, pp.
109
–
132
.
Crossref
Search ADS
 
7.
Gendelman
,
O. V.
,
Gorlov
,
D. V.
,
Manevitch
,
L. I.
, and
Musienko
,
A. I.
, 2005, “
Dynamics of Coupled Linear and Essentially Nonlinear Oscillators with Substantially Different Masses
,”
J. Sound Vib.
0022-460X,
286
, pp.
1
–
19
.
Crossref
Search ADS
 
8.
Gourdon
,
E.
, and
Lamarque
,
C. H.
, 2005, “
Energy Pumping with Various Nonlinear Structures: Numerical Evidences
,”
Nonlinear Dyn.
0924-090X,
40
, pp.
281
–
307
.
Crossref
Search ADS
 
9.
Manevitch
,
L. I.
,
Musienko
,
A. I.
, and
Lamarque
,
C. H.
, 2006, “
A New Analytical Approach to Energy Pumping in Strongly Nonhomogeneous 2DOF Systems
,”
Meccanica
0025-6455,
41
(
5
).
10.
Manevitch
,
L. I.
, 1999, “
Complex Representation of Dynamics of Coupled Nonlinear Oscillators
,”
Mathematical Models of Nonlinear Excitations, Transfer, Dynamics, and Control in Condensed Systems and Other Media
,
Kluwer Academic
,
Plenum, New York
, pp.
269
–
300
.
11.
Manevitch
,
L. I.
, 2001, “
The Description of Localized Normal Modes in a Chain of Nonlinear Coupled Oscillators Using Complex Variables
,”
Nonlinear Dyn.
0924-090X,
25
, pp.
95
–
109
.
Crossref
Search ADS
 
12.
McFarland
,
D.
,
Bergman
,
L.
, and
Vakakis
,
A.
, 2005, “
Experimental Study of Non-Linear Energy Pumping Occurring at a Single Fast Frequency
,”
Int. J. Non-Linear Mech.
0020-7462,
40
, pp.
891
–
899
.
Crossref
Search ADS
 
13.
Gourdon
,
E.
,
Coutel
,
S.
,
Lamarque
,
C. H.
, and
Pernot
,
S.
, 2005, “
Nonlinear Energy Pumping with Strongly Nonlinear Coupling: Identification of Resonance Captures in Numerical and Experimental Results
,”
Proceedings of IDETC/CIE 2005
, September 24–28, Long Beach, CA, Paper No. DETC2005-84233.
14.
Manevitch
,
L. I.
,
Lamarque
,
C. H.
, and
Gourdon
,
E.
, 2007, “
Parameters Optimization for Energy Pumping in Strongly Nonhomogeneous 2DOF System
,”
Chaos, Solitons Fractals
0960-0779,
31
(
4
), pp.
900
–
911
.
Crossref
Search ADS
 
15.
Vakakis
,
A. F.
,
Manevitch
,
L. I.
,
Gendelman
,
O.
, and
Bergman
,
L.
, 2003, “
Dynamics of Linear Discrete Systems Connected to Local, Essentially Nonlinear Attachments
,”
J. Sound Vib.
0022-460X,
264
, pp.
559
–
577
.
Crossref
Search ADS
 
16.
Vakakis
,
A. F.
,
Manevitch
,
L. I.
,
Mikhlin
,
Yu. V.
,
Pilipchuk
,
V. N.
, and
Zevin
,
A. A.
, 1996,
Normal Modes and Localization in Nonlinear Systems
,
Wiley Interscience
,
New York
.
17.
Gendelman
,
O.
,
Manevitch
,
L. I.
,
Vakakis
,
A. F.
, and
Bergman
,
L.
, 2003, “
A Degenerate Bifurcation Structure in the Dynamics of Coupled Oscillators with Essential Stiffness Nonlinearities
,”
Nonlinear Dyn.
0924-090X,
33
, pp.
1
–
10
.
Crossref
Search ADS
 
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 by American Society of Mechanical Engineers
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