We perform an investigation on the vibration response of a simply supported plate buried in glass particles, focusing on the nonlinear dynamic behaviors of the plate. Various excitation strategies, including constant-amplitude variable-frequency sweep and constant-frequency variable-amplitude sweep are used during the testing process. We employ the analysis methods of power spectroscopy, phase diagramming, and Poincare mapping, which reveal many complicated nonlinear behaviors in the dynamic strain responses of an elastic plate in granular media, such as the jump phenomena, period-doubling bifurcation, and chaos. The results indicate that the added mass, damping, and stiffness effects of the granular medium on the plate are the source of the nonlinear dynamic behaviors in the oscillating plate. These nonlinear behaviors are related to the burial depth of the plate (the thickness of the granular layer above plate), force amplitude, and particle size. Smaller particles and a suitable burial depth cause more obvious jump and period-doubling bifurcation phenomena to occur. Jump phenomena show both soft and hard properties near various resonant frequencies. With an increase in the excitation frequency, the nonlinear added stiffness effect of the granular layer makes a transition from strong negative stiffness to weak positive stiffness.

References

References
1.
Aranson
,
I. S.
, and
Tsimring
,
L. S.
,
2005
, “
Patterns and Collective Behavior in Granular Media: Theoretical Concepts
,”
Rev. Mod. Phys.
,
78
(
2
), pp.
641
692
.
2.
Gandhi
,
P.
,
Knobloch
,
E.
, and
Beaume
,
C.
,
2015
, “
Localized States in Periodically Forced Systems
,”
Phys. Rev. Lett.
,
114
(
3
), p.
034102
.
3.
Aoki
,
K. M.
,
Akiyama
,
T.
,
Yamamoto
,
K.
, and
Yoshikawa
,
T.
,
1997
, “
Experimental Study on the Mechanism of Convection Modes in Vibrated Granular Beds
,”
Europhys. Lett.
,
40
(
2
), pp.
159
164
.
4.
Lee
,
J.
,
1998
, “
Subharmonic Motion of Particles in a Vibrating Tube
,”
Phys. Rev. E
,
58
(
2
), pp.
1218
1221
.
5.
Jiang
,
Z. H.
,
Wang
,
Y. Y.
, and
Wu
,
J.
,
2007
, “
Subharmonic Motion of Granular Particles Under Vertical Vibrations
,”
Europhys. Lett.
,
74
(
3
), pp.
417
423
.
6.
Ji
,
S. Y.
, and
Shen
,
H. H.
,
2008
, “
Internal Parameters and Regime Map for Soft Poly-Dispersed Granular Materials
,”
J. Rheol.
,
52
(
1
), pp.
87
103
.
7.
Ji
,
S. Y.
,
2013
, “
Probability Analysis of Contact Forces in Quasi-Solid-Liquid Phase Transition of Granular Shear Flow
,”
Sci. China Phys. Mech. Astron.
,
56
(
2
), pp.
395
403
.
8.
Wang
,
Y. Q.
, and
Zu
,
J. W.
,
2017
, “
Analytical Analysis for Vibration of Longitudinally Moving Plate Submerged in Infinite Liquid Domain
,”
Appl. Math. Mech.
,
38
(
5
), pp.
625
646
.
9.
Wang
,
Y. Q.
,
Xue
,
S. W.
,
Huang
,
X. B.
, and
Du
,
W.
,
2016
, “
Vibrations of Axially Vertical Rectangular Plates in Contact With Fluid
,”
Int. J. Struct. Stability Dyn.
,
16
(
2
), p.
1450092
.
10.
Liao
,
C. Y.
,
Wu
,
Y. C.
,
Chang
,
C. Y.
, and
Ma
,
C. C.
,
2017
, “
Theoretical Analysis Based on Fundamental Functions of Thin Plate and Experimental Measurement for Vibration Characteristics of a Plate Coupled With Liquid
,”
J. Sound Vib.
,
394
, pp.
545
574
.
11.
Wang
,
Y. Q.
, and
Zu
,
J. W.
,
2017
, “
Nonlinear Steady-State Responses of Longitudinally Traveling Functionally Graded Material Plates in Contact With Liquid
,”
Compos. Struct.
,
164
, pp.
130
144
.
12.
Soni
,
S.
,
Jain
,
N. K.
, and
Joshi
,
P. V.
,
2018
, “
Vibration Analysis of Partially Cracked Plate Submerged in Fluid
,”
J. Sound Vib.
,
412
, pp.
28
57
.
13.
Wang
,
Y. Q.
, and
Zu
,
J. W.
,
2016
, “
Instability of Viscoelastic Plates With Longitudinally Variable Speed and Immersed in Ideal Liquid
,”
Int. J. Appl. Mech.
,
9
(
1
), p.
1750005
.
14.
Soni
,
S.
,
Jain
,
N. K.
, and
Joshi
,
P. V.
,
2017
, “
Analytical Modeling for Nonlinear Vibration Analysis of Partially Cracked Thin Magneto-Electro-Elastic Plate Coupled With Fluid
,”
Nonlinear Dyn.
,
90
(
1
), pp.
137
170
.
15.
Koch
,
S.
,
Duvigneau
,
F.
,
Orszulik
,
R.
,
Gabbert
,
U.
, and
Woschke
,
E.
,
2017
, “
Partial Filling of a Honeycomb Structure by Granular Materials for Vibration and Noise Reduction
,”
J. Sound Vib.
,
393
, pp.
30
40
.
16.
Xu
,
Z. W.
,
Wang
,
M. Y.
, and
Chen
,
T. N.
,
2004
, “
An Experimental Study of Particle Damping for Beams and Plates
,”
ASME J. Vib. Acoust.
,
126
(
1
), pp.
141
148
.
17.
Filipich
,
C. P.
, and
Rosales
,
M. B.
,
2002
, “
A Further Study about the Behavior of Foundation Piles and Beams in a Winkler–Pasternak Soil
,”
Int. J. Mech. Sci.
,
44
(
1
), pp.
21
36
.
18.
Morfidis
,
K.
,
2010
, “
Vibration of Timoshenko Beams on Three-Parameter Elastic Foundation
,”
Comput. Struct.
,
88
(
5–6
), pp.
294
308
.
19.
Donskoy
,
D.
,
Reznik
,
A.
,
Zagrai
,
A.
, and
Ekimov
,
A.
,
2005
, “
Nonlinear Vibrations of Buried Landmines
,”
J. Acoust. Soc. Am.
,
117
(
2
), pp.
690
700
.
20.
Zagrai
,
A.
,
Donskoy
,
D.
, and
Ekimov
,
A.
,
2005
, “
Structural Vibrations of Buried Land Mines
,”
J. Acoust. Soc. Am.
,
118
(
6
), pp.
3619
3628
.
21.
Kang
,
W.
,
Turner
,
J. A.
,
Bobaru
,
F.
,
Yang
,
L.
, and
Rattanadit
,
K.
,
2007
, “
Granular Layers on Vibrating Plates: Effective Bending Stiffness and Particle-Size Effects
,”
J. Acoust. Soc. Am.
,
121
(
2
), pp.
888
896
.
22.
Dorbolo
,
S.
,
Volfson
,
D.
,
Tsimring
,
L.
, and
Kudrolli
,
A.
,
2005
, “
Dynamics of a Bouncing Dimer
,”
Phys. Rev. Lett.
,
95
(
4
), p.
044101
.
23.
Dorbolo
,
S.
,
Ludewig
,
F.
, and
Vandewalle
,
N.
,
2008
, “
Bouncing Trimer: A Random Self-Propelled Particle, Chaos and Periodical Motions
,”
New J. Phys.
,
15
(
3
), p.
033016
.
24.
Pachecovázquez
,
F.
,
Ludewig
,
F.
, and
Dorbolo
,
S.
,
2014
, “
Dynamics of a Grain-Filled Ball on a Vibrating Plate
,”
Phys. Rev. Lett.
,
113
(
11
), p.
118001
.
25.
Wang
,
Y. Q.
, and
Yang
,
Z.
,
2017
, “
Nonlinear Vibrations of Moving Functionally Graded Plates Containing Porosities and Contacting With Liquid: Internal Resonance
,”
Nonlinear Dyn.
,
90
(
2
), pp.
1461
1480
.
26.
Ho
,
C.
,
Lang
,
Z. Q.
, and
Billings
,
S. A.
,
2014
, “
A Frequency Domain Analysis of the Effects of Nonlinear Damping on the Duffing Equation
,”
Mech. Syst. Signal Process.
,
45
(
1
), pp.
49
67
.
27.
Josserand
,
C.
,
Tkachenko
,
A. V.
,
Mueth
,
D. M.
, and
Jaeger
,
H. M.
,
2000
, “
Memory Effects in Granular Materials
,”
Phys. Rev. Lett.
,
85
(
17
), pp.
3632
3635
.
You do not currently have access to this content.