A bed of granular material which is subjected to vertical vibration will exhibit at least one sudden expansion at a critical acceleration amplitude. This sudden expansion corresponds to a bifurcation similar to that exhibited by a single ball bouncing on a vibrating plate. Theoretical analysis based on this model yields results which are in accord with the experimental observations. Other bifurcations may occur at higher vibration levels.

1.
Bachmann, D., 1940, Verfahrenstechnik Z.V.D.I. Beiheft, No. 2, p. 43 (cited by Gutman, 1976a).
2.
Chlenov
V. A.
, and
Mikhailov
N. V.
,
1965
, “
Some Properties of Vibrating Fluidized Bed
,”
Inzh.-Fiz. Zh.
, Vol.
9
, No.
2
, pp.
196
200
.
3.
Chlenov, V. A., and Mikhailov, N. V., 1972, Vibrofluidized beds, Izdatel’stvo Nauka, Moscow.
4.
Cle´ment
E. M.
,
Luding
S.
,
Blumen
A.
,
Rajchenbach
J.
, and
Duran
J.
,
1993
, “
Fluidization, Condensation, and Clusterization of a Vibrating Column of Beads
,”
International J. of Mod. Phys. B
, Vol.
7
, Nos.
9 and 10
, pp.
1807
1827
.
5.
Douady
S.
,
Fauve
S.
, and
Laroche
C.
,
1989
, “
Subharmonic Instabilities and Defects in a Granular Layer Under Vertical Vibrations
,”
Europhys. Lett.
, Vol.
8
, No.
7
, pp.
621
627
.
6.
Evesque
P.
, and
Rajchenbach
J.
,
1989
, “
Instability in a Sand Heap
,”
Phys. Rev. Lett
, Vol.
62
, No.
1
, pp.
44
46
.
7.
Gutman
R. G.
,
1976
a, “
Vibrated Beds of Powders Part I: A Theoretical Model for the Vibrated Ved
,”
Trans. Instn. Chem. Engrs.
, Vol.
54
, pp.
174
183
.
8.
Gutman
R. G.
,
1976
b, “
Vibrated Beds of Powders Part II: Heat Transfer in and Energy Dissipation of a Vibrated Bed
,”
Trans. lnstn. Chem. Engrs.
, Vol.
54
, pp.
251
257
.
9.
Holmes
P. J.
,
1982
, “
The Dynamics of Repeated Impacts with a Sinusoidally Vibrating Table
,”
J. of Sound and Vibration
, Vol.
84
, No.
2
, pp.
173
189
.
10.
Jaeger
H. M.
, and
Nagel
S. R.
,
1992
, “
Physics of the Granular State
,”
Science
, Vol.
255
, No.
5051
, pp.
1523
1531
.
11.
Laroche
C.
,
Douady
S.
, and
Fauve
S.
,
1989
, “
Convective Flow of Granular Masses Under Vertical Vibrations
,”
J. Phys. France
, Vol.
50
, No.
7
, pp.
699
706
.
12.
Rajchenbach
J.
, and
Evesque
P.
,
1988
, “
Instabilite´ Convective Dans un tas de Sable
,”
C.R. Acad. Sci. Ser. II (Paris)
, Vol.
307
, pp.
1
4
.
13.
Thomas
B.
,
Mason
M. O.
,
Liu
Y. A.
, and
Squires
A. M.
,
1989
, “
Identifying States in Shallow Vibrated Beds
,”
Powder Tech.
, Vol.
57
, pp.
267
280
.
14.
Wood
L. A.
, and
Byrne
K. P.
,
1981
, “
Analysis of a Random Repeated Impact Process
,”
J. of Sound and Vibration
, Vol.
78
, No.
3
, pp.
329
345
.
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