This work regards the use of cubic springs with intervals of negative stiffness, in other words, “snap-through” elements, in order to convert low-frequency ambient vibrations into high-frequency oscillations, referred to as “twinkling.” The focus of this paper is on the bifurcation of a two-mass chain that, in the symmetric system, involves infinitely many equilibria at the bifurcation point. The structure of this “eclipse bifurcation” is uncovered, and perturbations of the bifurcation are studied. The energies associated with the equilibria are examined.

References

References
1.
Feeny
,
B. F.
, and
Diaz
,
A. R.
,
2010
, “
Twinkling Phenomena in Snap-Through Oscillators
,”
ASME J. Vib. Acoust.
,
132
(
5
), p.
061013
.10.1115/1.4000764
2.
Balk
,
A. M.
,
Cherkaev
,
A. V.
, and
Slepyan
,
L. I.
,
2001
, “
Dynamics of Chains With Non-Monotone Stress-Strain Relations. I. Model and Numerical Experiments
,”
J. Mech. Phys. Solids
,
49
(
1
), pp.
131
148
.10.1016/S0022-5096(00)00025-9
3.
Wang
,
Y. C.
, and
Lakes
,
R. S.
,
2004
, “
Extreme Stiffness Systems Due to Negative Stiffness Elements
,”
Am. J. Phys.
,
72
(
1
), pp.
40
50
.10.1119/1.1619140
4.
Puglisi
,
G.
, and
Truskinovsky
,
L.
,
2000
, “
Mechanics of a Discrete Chain With Bi-Stable Elements
,”
J. Mech. Phys. Solids
,
48
(
1
), pp.
1
27
.10.1016/S0022-5096(99)00006-X
5.
Puglisi
,
G.
, and
Truskinovsky
,
L.
,
2002
, “
Rate Independent Hysteresis in a Bi-Stable Chain
,”
J. Mech. Phys. Solids
,
50
(
2
), pp.
165
187
.10.1016/S0022-5096(01)00055-2
6.
Panigrahi
,
S. R.
,
Feeny
,
B. F.
, and
Diaz
,
A. R.
,
2012
, “
Bifurcations in Twinkling Oscillators
,”
ASME International Design Engineering Technical Conferences, 24th Conference on Mechanical Vibration and Noise
, Chicago, IL, August 12–15,
ASME
Paper No. DETC2012-70943.10.1115/DETC2012-70943
7.
Panigrahi
,
S. R.
,
Feeny
,
B. F.
, and
Diaz
,
A. R.
,
2014
, “
Degenerate ‘Star’ Bifurcations in a Twinkling Oscillator
,”
ASME J. Vib. Acoust.
,
136
(
2
), p.
021004
.10.1115/1.4025442
8.
Storti
,
D. W.
, and
Rand
,
R. H.
,
1982
, “
Dynamics of Two Strongly Coupled van der Pol Oscillators
,”
Int. J. Non-Lin. Mech.
,
17
(
3
), pp.
143
152
.10.1016/0020-7462(82)90014-2
9.
Vakakis
,
A.
,
Gendelman
,
O.
,
Bergman
,
L.
,
McFarland
,
D.
,
Kerschen
,
G.
, and
Lee
,
Y. S.
,
2009
,
Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems: I and II
,
Springer
,
Berlin
.
10.
Anton
,
S. R.
, and
Sodano
,
H. A.
,
2007
, “
A Review of Power Harvesting Using Piezoelectric Materials (2003-2006)
,”
Smart Mater. Struct.
,
16
(
3
),
R1
.10.1088/0964-1726/16/3/R01
11.
Priya
,
S.
, and
Inman
,
D. J.
,
2008
,
Energy Harvesting Technologies
,
Springer
,
New York
.
12.
Nayfeh
,
A. H.
, and
Balachandran
,
B.
,
1995
,
Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods
,
Wiley
,
New York
.
13.
Wiggins
,
S.
,
2003
,
Introduction to Applied Nonlinear Dynamical Systems and Chaos
, Vol.
2
,
Springer
,
New York
.
14.
Yates
,
R. C.
,
1947
,
Conics. A Handbook on Curves and Their Properties
,
J. W. Edwards
,
Ann Arbor, MI
.
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