In this paper we consider a sinusoidal arch with one end pinned in space while the other end attached to a mass and supported by a spring. The supporting wall of the spring is moved a distance quasi-statically to initiate preload in the arch and the spring. The assembly is then set in motion by an impact at the attached mass. The condition under which the arch may snap to the other side dynamically depends on the initial speed of the attached mass due to impact. Sufficient condition on the initial speed against dynamic snap-through is formulated based on the concept of minimum energy barrier. The effects of damping on the transient response of the assembly are also discussed. An experimental setup is designed to measure the transient response of the arch following the impact and the critical initial speed of the attached mass. The experimental results are in good agreement with theoretical predictions.

1.
Timoshenko
,
S. P.
,
1935
, “
Buckling of Flat Curved Bars and Slightly Curved Plates
,”
ASME J. Appl. Mech.
,
2
, pp.
17
20
.
2.
Fung, Y. C., and Kaplan, A., 1952, “Buckling of Low Arches or Curved Beams of Small Curvature,” NACA Technical Note 2840.
3.
Gjelsvik
,
A.
, and
Bonder
,
S. R.
,
1962
, “
The Energy Criterion and Snap Buckling of Arches
,”
J. Eng. Mech. Div.
,
88
, pp.
87
134
.
4.
Franciosi
,
V.
,
Augusti
,
G.
, and
Sparacio
,
R.
,
1964
, “
Collapse of Arches Under Repeated Loading
,”
ASCE J. Struct. Div.
,
90
, pp.
165
201
.
5.
Schreyer
,
H. L.
, and
Masur
,
E. F.
,
1966
, “
Buckling of Shallow Arches
,”
J. Eng. Mech. Div.
,
92
, pp.
1
19
.
6.
Lee
,
H. N.
, and
Murphy
,
L. M.
,
1968
, “
Inelastic Buckling of Shallow Arches
,”
J. Eng. Mech. Div.
,
94
, pp.
225
239
.
7.
Simitses
,
G. J.
,
1973
, “
Snapping of Low Pinned Arches on an Elastic Foundation
,”
ASME J. Appl. Mech.
,
40
, pp.
741
744
.
8.
Roorda
,
J.
,
1965
, “
Stability of Structures With Small Imperfections
,”
J. Eng. Mech. Div.
,
91
, pp.
87
106
.
9.
Simitses, G. J., 1990, Dynamic Stability of Suddenly Loaded Structures, Springer, New York.
10.
Hoff
,
N. J.
, and
Bruce
,
V. G.
,
1954
, “
Dynamic Analysis of the Buckling of Laterally Loaded Flat Arches
,”
J. Math. Phys.
,
32
, pp.
276
288
.
11.
Hsu
,
C. S.
,
1967
, “
The Effects of Various Parameters on the Dynamic Stability of a Shallow Arch
,”
ASME J. Appl. Mech.
,
34
, pp.
349
358
.
12.
Hsu
,
C. S.
,
1968
, “
Stability of Shallow Arches Against Snap-Through Under Timewise Step Loads
,”
ASME J. Appl. Mech.
,
35
, pp.
31
39
.
13.
Hsu
,
C. S.
,
Kuo
,
C. T.
, and
Lee
,
S. S.
,
1968
, “
On the Final States of Shallow Arches on Elastic Foundations Subjected to Dynamical Loads
,”
ASME J. Appl. Mech.
,
35
, pp.
713
723
.
14.
Xu
,
J.-X.
,
Huang
,
H.
,
Zhang
,
P.-Z.
, and
Zhou
,
J.-Q.
,
2002
, “
Dynamic Stability of Shallow Arch With Elastic Supports—Application in the Dynamic Stability Analysis of Inner Winding of Transformer During Short Circuit
,”
Int. J. Non-Linear Mech.
,
37
, pp.
909
920
.
15.
Humphreys
,
J. S.
,
1966
, “
On Dynamic Snap Buckling of Shallow Arches
,”
AIAA J.
,
4
, pp.
878
886
.
16.
Lock
,
M. H.
,
1966
, “
The Snapping of a Shallow Sinusoidal Arch Under a Step Pressure Load
,”
AIAA J.
,
4
, pp.
1249
1256
.
17.
Huang
,
N. N.
, and
Nachbar
,
W.
,
1968
, “
Dynamic Snap-Through of Imperfect Viscoelastic Shallow Arches
,”
ASME J. Appl. Mech.
,
35
, pp.
289
296
.
18.
Ariaratnam
,
S. T.
, and
Sankar
,
T. S.
,
1968
, “
Dynamic Snap-Through of Shallow Arches Under Stochastic Loads
,”
AIAA J.
,
6
, pp.
798
802
.
19.
Fulton
,
R. E.
, and
Barton
,
F. W.
,
1971
, “
Dynamic Buckling of Shallow Arches
,”
J. Eng. Mech. Div.
,
97
, pp.
865
877
.
20.
Sundararajan
,
V.
, and
Kumani
,
D. S.
,
1972
, “
Dynamic Snap-Buckling of Shallow Arches Under Inclined Loads
,”
AIAA J.
,
10
, pp.
1090
1091
.
21.
Lo
,
D. L. C.
, and
Masur
,
E. F.
,
1976
, “
Dynamic Buckling of Shallow Arches
,”
J. Eng. Mech. Div.
,
102
, pp.
901
917
.
22.
Johnson
,
E. R.
, and
Mclvor
,
I. K.
,
1978
, “
The Effect of Spatial Distribution on Dynamic Snap-Through
,”
ASME J. Appl. Mech.
,
45
, pp.
612
618
.
23.
Johnson
,
E. R.
,
1980
, “
The Effect of Damping on Dynamic Snap-Through
,”
ASME J. Appl. Mech.
,
47
, pp.
601
606
.
24.
Huang, K. Y., and Plaut, R. H., 1982, “Snap-Through of a Shallow Arch Under Pulsating Load,” Stability in the Mechanics of Continua, F. H. Schroeder, ed., Springer, Berlin, pp. 215–223.
25.
Gregory
, Jr.,
W. E.
, and
Plaut
,
R. H.
,
1982
, “
Dynamic Stability Boundaries for Shallow Arches
,”
J. Eng. Mech. Div.
,
108
, pp.
1036
1050
.
26.
Donaldson
,
M. T.
, and
Plaut
,
R. H.
,
1983
, “
Dynamic Stability Boundaries for a Sinusoidal Arch Under Pulse Loads
,”
AIAA J.
,
21
, pp.
469
471
.
27.
Liao, C.-Y., 2003, “Experiment and Analysis of a Flexibly Supported Arch Under Impact at the End,” Master thesis, Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan.
28.
Rao, S. S., 1995, Mechanical Vibrations, 3rd ed., Addision-Wesley, Reading, MA.
You do not currently have access to this content.