Oscillatory behavior in a chain of masses connected by springs with continuous but nonmonotonic spring forces can be induced under quasistatic loading. An insight into the birth of this behavior is obtained from a single mass system. A bifurcation study shows the potential for equilibrium jumps between multiple equilibria. As such, the transients occurring under quasistatic loading do not converge to the static loading case. Transients during dynamic loading show sensitivity to the loading parameters.
Issue Section:
Research Papers
1.
Balk
, A. M.
, Cherkaev
, A. V.
, and Slepyan
, L. I.
, 2001, “Dynamics of Chains With Non-Monotone Stress-Strain Relations. I. Model and Numerical Experiments
,” J. Mech. Phys. Solids
0022-5096, 49
(1
), pp. 131
–148
.2.
Balk
, A. M.
, Cherkaev
, A. V.
, and Slepyan
, L. I.
, 2001, “Dynamics of Chains With Non-Monotone Stress-Strain Relations. II. Nonlinear Waves and Waves of Phase Transition
,” J. Mech. Phys. Solids
0022-5096, 49
(1
), pp. 149
–171
.3.
Cherkaev
, A.
, Cherkaev
, E.
, and Slepyan
, L.
, 2005, “Transition Waves in Bistable Structures. I. Delocalization of Damage
,” J. Mech. Phys. Solids
0022-5096, 53
(2
), pp. 383
–405
.4.
Slepyan
, L.
, Cherkaev
, A.
, and Cherkaev
, E.
, 2005, “Transition Waves in Bistable Structures. II. Analytical Solution: Wave Speed and Energy Dissipation
,” J. Mech. Phys. Solids
0022-5096, 53
(2
), pp. 407
–436
.5.
Cherkaev
, A.
, and Zhornitskaya
, L.
, 2005, “Protective Structures With Waiting Links and Their Damage Evolution
,” Multibody Syst. Dyn.
1384-5640, 13
(1
), pp. 53
–67
.6.
Cherkaev
, A.
, Vinogradov
, V.
, and Leelavanichkul
, S.
, 2006, “The Waves of Damage in Elastic-Plastic Lattices With Waiting Links: Design and Simulation
,” Mech. Mater.
0167-6636, 38
(8–10
), pp. 748
–756
.7.
Gottwald
, J. A.
, Virgin
, L. N.
, and Dowell
, E. H.
, 1995, “Routes to Escape From an Energy Well
,” J. Sound Vib.
0022-460X, 187
(1
), pp. 133
–144
.8.
Johnson
, E. R.
, 1980, “The Effect of Damping on Dynamic Snap-Through
,” ASME J. Appl. Mech.
0021-8936, 47
(3
), pp. 601
–606
.9.
Kounadis
, A. N.
, and Raftoyiannis
, J.
, 1990, “Dynamic Stability-Criteria of Nonlinear Elastic Damped Undamped Systems Under Step Loading
,” AIAA J.
0001-1452, 28
(7
), pp. 1217
–1223
.10.
Lock
, M. H.
, 1966, “Snapping of a Shallow Sinusoidal Arch Under a Step Pressure Load
,” AIAA J.
0001-1452, 4
(7
), pp. 1249
–1256
.11.
Moon
, F. C.
, and Holmes
, P. J.
, 1979, “Magnetoelastic Strange Attractor
,” J. Sound Vib.
0022-460X, 65
(2
), pp. 275
–296
.12.
Holmes
, P. J.
, and Moon
, F. C.
, 1983, “Strange Attractors and Chaos in Non-Linear Mechanics
,” ASME J. Appl. Mech.
0021-8936, 50
(4B
), pp. 1021
–1032
.13.
Moon
, F. C.
, and Li
, G. X.
, 1985, “Fractal Basin Boundaries and Homoclinic Orbits for Periodic Motion in a 2-Well Potential
,” Phys. Rev. Lett.
0031-9007, 55
(14
), pp. 1439
–1442
.14.
Guckenheimer
, J.
, and Holmes
, P. J.
, 1983, “Nonlinear Oscillations Dynamical Systems and Bifurcation Fields
” Springer-Verlag
, New York
.15.
Haberman
, R.
, 1979, “Slowly Varying Jump and Transition Phenomena Associated With Algebraic Bifurcation Problems
,” SIAM J. Appl. Math.
0036-1399, 37
, pp. 69
–106
.16.
Lebovitz
, N. R.
, and Schaar
, R. J.
, 1975, “Exchange of Stabilities in Autonomous Systems
,” Stud. Appl. Math.
0022-2526, 54
, pp. 229
–260
.17.
Lebovitz
, N. R.
, and Schaar
, R. J.
, 1975, “Exchange of Stabilities in Autonomous Systems II: Vertical Bifurcation
,” Stud. Appl. Math.
0022-2526, 56
, pp. 1
–50
.18.
Davies
, H.
, and Krishna
, R.
, 1996, “Nonstationary Response Near Generic Bifurcations
,” Nonlinear Dyn.
0924-090X, 10
(3
), pp. 235
–250
.19.
Raman
, A.
, Bajaj
, A. K.
, and Davies
, P.
, 1996, “On the Slow Transition Across Instabilities in Nonlinear Dissipative Systems
,” J. Sound Vib.
0022-460X, 192
(4
), pp. 835
–865
.20.
Raman
, A.
, and Bajaj
, A. K.
, 1998, “On the Nonstationary Passage Through Bifurcations in Resonantly Forced Hamiltonian Oscillators
,” Int. J. Non-Linear Mech.
0020-7462, 33
(5
), pp. 907
–933
.21.
Marée
, G. J. M.
, 1996, “Slow Passage Through a Pitchfork Bifurcation
,” SIAM J. Appl. Math.
0036-1399, 56
(3
), pp. 889
–918
.22.
Puglisi
, G.
, and Truskinovsky
, L.
, 2000, “Mechanics of a Discrete Chain With Bi-Stable Elements
,” J. Mech. Phys. Solids
0022-5096, 48
(1
), pp. 1
–27
.23.
Puglisi
, G.
, and Truskinovsky
, L.
, 2002, “A Mechanism of Transformational Plasticity
,” Continuum Mech. Thermodyn.
0935-1175, 14
(5
), pp. 437
–457
.24.
Puglisi
, G.
, and Truskinovsky
, L.
, 2002, “Rate Independent Hysteresis in a Bi-Stable Chain
,” J. Mech. Phys. Solids
0022-5096, 50
(2
), pp. 165
–187
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by American Society of Mechanical Engineers
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