Symmetry, Generic Bifurcations, and Mode Interaction in Nonlinear Railway Dynamics

IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics - Solid Mechanics and its Applications ◽

10.1007/978-94-011-5320-1_39 ◽

1999 ◽

pp. 387-396

Author(s):

Carsten Nordstrøm Jensen ◽

Martin Golubitsky ◽

Hans True

Keyword(s):

Mode Interaction ◽

Railway Dynamics

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SYMMETRY, GENERIC BIFURCATIONS, AND MODE INTERACTION IN NONLINEAR RAILWAY DYNAMICS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127499000924 ◽

1999 ◽

Vol 09 (07) ◽

pp. 1321-1331 ◽

Cited By ~ 15

Author(s):

CARSTEN NORDSTRØM JENSEN ◽

MARTIN GOLUBITSKY ◽

HANS TRUE

Keyword(s):

Mathematical Model ◽

Control Parameter ◽

Mode Interaction ◽

Hopf Bifurcations ◽

Additional Parameter ◽

Railway Dynamics ◽

Mode Interactions ◽

Symmetric Periodic Solution ◽

Pitchfork Bifurcations ◽

Degenerate Bifurcation

We investigate Cooperrider's complex bogie, a mathematical model of a railway bogie running on an ideal straight track. The speed of the bogie v is the control parameter. Taking symmetry into account, we find that the generic bifurcations from a symmetric periodic solution of the model are Hopf bifurcations for maps (or Neimark bifurcations), saddle-node bifurcations, and pitchfork bifurcations. The last ones are symmetry-breaking bifurcations. By variation of an additional parameter, bifurcations of higher degeneracy are possible. In particular, we consider mode interactions near a degenerate bifurcation. The bifurcation analysis and path-finding are done numerically.

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Azimuthal mode interaction in an unforced, high Reynolds-number axisymmetric shear layer

10.2514/6.1997-1810 ◽

1997 ◽

Cited By ~ 1

Author(s):

J. Citriniti ◽

J. Citriniti

Keyword(s):

Reynolds Number ◽

Shear Layer ◽

High Reynolds Number ◽

Mode Interaction ◽

Azimuthal Mode ◽

Axisymmetric Shear ◽

High Reynolds

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Amphiphilic Graft Copolymers Capable of Mixed-Mode Interaction as Alternative Nonviral Transfection Agents

ACS Applied Bio Materials ◽

10.1021/acsabm.0c01123 ◽

2021 ◽

Vol 4 (2) ◽

pp. 1268-1282

Author(s):

Ivonne L. Diaz Ariza ◽

Valérie Jérôme ◽

León D. Pérez Pérez ◽

Ruth Freitag

Keyword(s):

Mixed Mode ◽

Graft Copolymers ◽

Mode Interaction ◽

Amphiphilic Graft Copolymers ◽

Nonviral Transfection

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Acoustic mode equations with resonant mode interaction

Proceedings of the International Conference Days on Diffraction 2014 ◽

10.1109/dd.2014.7036456 ◽

2014 ◽

Author(s):

Mikhail Yu. Troflmov ◽

Sergey B. Kozitskiy ◽

Alena D. Zakharenko

Keyword(s):

Resonant Mode ◽

Acoustic Mode ◽

Mode Interaction

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The Desulfite Mechanism Exploration in a Mode: Interaction between Casein and Sulfite by Multi-Spectrometry

LWT ◽

10.1016/j.lwt.2021.111225 ◽

2021 ◽

pp. 111225

Author(s):

Kai Yang ◽

Cheng Zhou ◽

Caiping Liao ◽

Juan Sun ◽

Yan Wang ◽

...

Keyword(s):

Mode Interaction

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Transition to phase chaos in directional solidification: A two-mode interaction picture

Physical Review Letters ◽

10.1103/physrevlett.69.1544 ◽

1992 ◽

Vol 69 (10) ◽

pp. 1544-1547 ◽

Cited By ~ 12

Author(s):

Alexandre Valance ◽

Klaus Kassner ◽

Chaouqi Misbah

Keyword(s):

Directional Solidification ◽

Mode Interaction ◽

Interaction Picture

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Detecting the motion of a microresonator via mode-mode interaction

2010 IEEE Sensors ◽

10.1109/icsens.2010.5690734 ◽

2010 ◽

Author(s):

H J R Westra ◽

M Poot ◽

H S J van der Zant ◽

W J Venstra

Keyword(s):

Mode Interaction

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Buckling Mode Interaction in Composite Plate Assemblies

Applied Mechanics Reviews ◽

10.1115/1.3005083 ◽

1995 ◽

Vol 48 (11S) ◽

pp. S52-S60 ◽

Cited By ~ 7

Author(s):

Ioannis G. Raftoyiannis ◽

Luis A. Godoy ◽

Ever J. Barbero

Keyword(s):

Linear Elasticity ◽

Composite Plate ◽

Mode Interaction ◽

Equilibrium Path ◽

Buckling Mode ◽

Fiber Reinforced Composite ◽

Composite Columns ◽

Reinforced Composite ◽

Coupled Solution ◽

Coordinate Basis

The analysis of buckling mode interaction of fiber-reinforced composite columns, modeled as plate assemblies, is presented. The main assumptions are linear elasticity; a linear fundamental equilibrium path; the existence of critical states that are coincident or near coincident; and a coupled path rising from a quadratic combination of modal displacements due to interaction. The formulation adopted is known as the W-formulation, in which the energy is written in terms of a sliding set of incremental coordinates, measured with respect to the fundamental path. The energy is then expressed with respect to a reduced modal coordinate basis, and the coupled solution arising from interaction is computed. An example of a pultruded composite I-column subjected to axial compression illustrates the procedure.

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