Abstract

A series of coaxial magnetic pendulums is studied as a simple physical surrogate for more general nonlinearly coupled almost-identical resonators that arise in quantum communications and the dynamics of social networks. The equations of motion for a series of coaxial magnetic pendulums are derived, and the solution is compared to experimental results. The equilibrium points and their stability are also determined.

Issue Section:
Research Papers
Keywords:
algebraic/geometric methods, MEMS, model validation, modeling, multibody systems, nonlinear systems, vibrations
Topics:
Equations of motion, Pendulums, Stability, Equilibrium (Physics)

References

1.
Russell
,
F. M.
,
Zolotaryuk
,
Y.
,
Eilbeck
,
J. C.
, and
Dauxois
,
T.
,
1997
, “
Moving Breathers in a Chain of Magnetic Pendulums
,”
Phys. Rev. B
,
55
(
10
), pp.
6304
–
6308
.
Google Scholar
Crossref
Search ADS
 
2.
Mehrem
,
A.
,
Jimenez
,
N.
,
Salmerón-Contreras
,
L. J.
,
García-Andrés
,
X.
,
Garcãndia Raffi
,
L. M.
,
Picó
,
R.
, and
Sánchez-Morcillo
,
V. J.
,
2017
, “
Nonlinear Dispersive Waves in Repulsive Lattices
,”
Phys. Rev. E
,
96
(
1
), p.
012208
.
Google Scholar
Crossref
Search ADS
PubMed
 
3.
Molerón
,
M.
,
Leonard
,
A.
, and
Daraio
,
C.
,
2014
, “
Solitary Waves in a Chain of Repelling Magnets
,”
J. Appl. Phys.
,
115
(
18
), p.
184901
.
Google Scholar
Crossref
Search ADS
 
4.
Wang
,
W.
,
Cao
,
J.
,
Mallick
,
D.
,
Roy
,
S.
, and
Lin
,
J.
,
2018
, “
Comparison of Harmonic Balance, Multi-Scale Method in Characterizing the Response of Monostable Energy Harvesters
,”
Mech. Syst., Signal Process.
,
108
, pp.
252
–
261
.
Google Scholar
Crossref
Search ADS
 
5.
Litak
,
G.
,
Friswell
,
M. I.
,
Kitio Kwuimy
,
C. A.
,
Adhikari
,
S.
, and
Borowiec
,
M.
,
2012
, “
Energy Harvesting by Two Magnetopiezoelastic Oscillators With Mistuning
,”
Theor. Appl. Mech. Lett.
,
2
(
4
), p.
043009
.
Google Scholar
Crossref
Search ADS
 
6.
Tang
,
L.
, and
Yang
,
Y.
,
2012
, “
A Nonlinear Piezoelectric Energy Harvester With Magnetic Oscillator
,”
Appl. Phys. Lett.
,
10
(
9
), p.
094102
.
Google Scholar
Crossref
Search ADS
 
7.
Cho
,
J. Y.
,
Jeong
,
S.
,
Jabbar
,
H.
,
Song
,
Y.
,
Ahn
,
J. H.
,
Kim
,
J. H.
,
Jung
,
H. J.
,
Yoo
,
H. H.
, and
Sung
,
T. H.
,
2016
, “
Piezoelectric Energy Harvesting System With Magnetic Pendulum Movement for Self-Powered Safety Sensor of Trains
,”
Sensors, Actuators A: Phys.
,
250
, pp.
210
–
218
.
Google Scholar
Crossref
Search ADS
 
8.
Malaji
,
P. V.
, and
Ali
,
S. F.
,
2017
, “
Magneto-Mechanically Coupled Electromagnetic Harvesters for Broadband Energy Harvesting
,”
Appl. Phys. Lett.
,
111
(
8
), p.
083901
.
Google Scholar
Crossref
Search ADS
 
9.
Wiesenfeld
,
K.
,
Colet
,
P.
, and
Strogatz
,
S. H.
,
1996
, “
Synchronization Transitions in a Disordered Josephson Series Array
,”
Phys. Rev. Lett.
,
76
(
3
), pp.
404
–
407
.
Google Scholar
Crossref
Search ADS
PubMed
 
10.
Yung
,
K. W.
,
Landecker
,
P. B.
, and
Villani
,
D. D.
,
1998
, “
An Analytic Solution for the Force Between Two Magnetic Dipoles
,”
Magnetic, Electrical Separation
,
9
(
1
), pp.
39
–
52
.
Google Scholar
Crossref
Search ADS
 
11.
Saeidi Hosseini
,
R. S.
,
2019
, “
Interactions of Magnetic Pendulums
,”
Master's thesis
,
University of Waterloo
,
Waterloo, Canada
.
Copyright © 2021 by ASME
You do not currently have access to this content.