Negative, nonlinear stiffness elements have been recently designed as configurations of pairs or groups of linear springs. We propose a new design of such a system by using a single linear spring with its moving end rolling on a path described by an equation of varying complexity. We examine the effect that the selection of the path has on the size of the deflection regime where negative stiffness is achieved. The stability properties of the equilibrium positions of the system are also investigated, highlighting the influence that the complexity of the path equation brings. The latter naturally affects the characteristics of the forcing functions around these positions. It is demonstrated that the properties of the system can be tailored according to the nature of the equation used and we show how essentially nonlinear negative stiffness elements, (i.e., with no linear parts) can be designed. These results provide a useful standpoint for designers of such systems, who wish to achieve the desired properties in reduced space, which is a common requirement in modern applications.

References

References
1.
Platus
,
D. L.
,
1999
, “
Negative-Stiffness-Mechanism Vibration Isolation Systems
,”
Proc. SPIE
,
3786
, Optomechanical Engineering and Vibration Control, 98 (September 28, 1999), pp.
98
105
.10.1117/12.363841
2.
Trimboli
,
M. S.
,
Wimmel
,
R.
, and
Breitbach
,
E.
,
1994
, “
A Quasi-Active Approach to Vibration Isolation Using Magnetic Springs
,”
Proc. SPIE
,
2193
, Smart Structures and Materials 1994: Passive Damping, 73 (May 1, 1994), pp.
73
83
.10.1117/12.174116
3.
Mizuno
,
T.
,
Toumiya
,
T.
, and
Takasaki
,
M.
,
2003
, “
Vibration Isolation System Using Negative Stiffness
,”
JSME Int. J., Ser. C
,
46
, pp.
807
812
.10.1299/jsmec.46.807
4.
Kashdan
,
L.
,
Seepersad
,
C.
,
Haberman
,
M.
, and
Wilson
,
P. S.
,
2012
, “
Design, Fabrication and Evaluation of Negative Stiffness Elements Using SLS
,”
Rapid Prototyping J.
,
18
, pp.
194
200
.10.1108/13552541211218108
5.
Lee
,
C. M.
,
Goverdovskiy
,
V. N.
, and
Temnikov
,
A. I.
,
2007
, “
Design of Springs With ‘‘Negative’’ Stiffness to Improve Vehicle Driver Vibration Isolation
,”
J. Sound Vib.
,
302
, pp.
865
874
.10.1016/j.jsv.2006.12.024
6.
Lee
,
C. M.
, and
Goverdovskiy
,
V. N.
,
2002
, “
Alternative Vibration Protecting Systems for Men-Operators of Transport Machines: Modern Level and Prospects
,”
J. Sound Vib.
,
249
, pp.
635
647
.10.1006/jsvi.2001.3839
7.
Virginia
,
L. N.
,
Santillan
,
S. T.
, and
Plaut
,
R. H.
,
2008
, “
Vibration Isolation Using Extreme Geometric Nonlinearity
,”
J. Sound Vib.
,
315
, pp.
721
731
.10.1016/j.jsv.2007.12.025
8.
Wang
,
Y. C.
, and
Lakes
,
R. S.
,
2004
, “
Extreme Stiffness Systems Due to Negative Stiffness Elements
,”
Am. J. Phys.
,
72
, pp.
40
50
.10.1119/1.1619140
10.
Carrella
,
A.
,
Brennan
,
M. J.
, and
Waters
,
T. P.
,
2007
, “
Static Analysis of a Passive Vibration Isolator With Quasi-Zero-Stiffness Characteristic
,”
J. Sound Vib.
,
301
, pp.
678
689
.10.1016/j.jsv.2006.10.011
11.
Ramlan
,
R.
,
Brennan
,
M. J.
,
Mace
,
B. R.
, and
Kovacic
,
I.
,
2010
, “
Potential Benefits of a Non-Linear Stiffness in an Energy Harvesting Device
,”
Nonlinear Dyn.
,
59
, pp.
545
558
.10.1007/s11071-009-9561-5
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