1. Date of download: 6/28/2016 Copyright © ASME. All rights reserved. From: Nonlinear Train-Bridge Lateral Interaction Using a Simplified Wheel-Rail Contact Method Within a Finite Element Framework J. Comput. Nonlinear Dynam. 2012;7(4):041014-041014-9. doi:10.1115/1.4006736 For description of the wheelset kinematics three reference frames are used: the inertial reference frame (I, ei); the body coordinate system (w, eiw); and an intermediate frame which does not consider the rotation of wheelset around its axis of revolution (w, eiv) Figure Legend:

2. Date of download: 6/28/2016 Copyright © ASME. All rights reserved. From: Nonlinear Train-Bridge Lateral Interaction Using a Simplified Wheel-Rail Contact Method Within a Finite Element Framework J. Comput. Nonlinear Dynam. 2012;7(4):041014-041014-9. doi:10.1115/1.4006736 For track kinematics; in addition to the inertial frame, two more frames are used: an intermediate frame attached to the deck section (b, eib) and the track coordinate system (t, eit) Figure Legend:

3. Date of download: 6/28/2016 Copyright © ASME. All rights reserved. From: Nonlinear Train-Bridge Lateral Interaction Using a Simplified Wheel-Rail Contact Method Within a Finite Element Framework J. Comput. Nonlinear Dynam. 2012;7(4):041014-041014-9. doi:10.1115/1.4006736 Geometric compatible relative vertical motion Δzw and rotation Δψw for S1002 wheel profile and UIC60 rail Figure Legend:

4. Date of download: 6/28/2016 Copyright © ASME. All rights reserved. From: Nonlinear Train-Bridge Lateral Interaction Using a Simplified Wheel-Rail Contact Method Within a Finite Element Framework J. Comput. Nonlinear Dynam. 2012;7(4):041014-041014-9. doi:10.1115/1.4006736 Contact angle γ and rolling radii r at contact points of both wheels as a function of Δyw for the wheel and rail profiles S1002 and UIC60, respectively (a) Contact angle; (b) Rolling radii Figure Legend:

5. Date of download: 6/28/2016 Copyright © ASME. All rights reserved. From: Nonlinear Train-Bridge Lateral Interaction Using a Simplified Wheel-Rail Contact Method Within a Finite Element Framework J. Comput. Nonlinear Dynam. 2012;7(4):041014-041014-9. doi:10.1115/1.4006736 Contact reference frame (C, eic) at contact point of one wheel Figure Legend:

6. Date of download: 6/28/2016 Copyright © ASME. All rights reserved. From: Nonlinear Train-Bridge Lateral Interaction Using a Simplified Wheel-Rail Contact Method Within a Finite Element Framework J. Comput. Nonlinear Dynam. 2012;7(4):041014-041014-9. doi:10.1115/1.4006736 Flow chart of the contact forces determination algorithm Figure Legend:

7. Date of download: 6/28/2016 Copyright © ASME. All rights reserved. From: Nonlinear Train-Bridge Lateral Interaction Using a Simplified Wheel-Rail Contact Method Within a Finite Element Framework J. Comput. Nonlinear Dynam. 2012;7(4):041014-041014-9. doi:10.1115/1.4006736 Elastic wheelset model and impact load definition Figure Legend:

8. Date of download: 6/28/2016 Copyright © ASME. All rights reserved. From: Nonlinear Train-Bridge Lateral Interaction Using a Simplified Wheel-Rail Contact Method Within a Finite Element Framework J. Comput. Nonlinear Dynam. 2012;7(4):041014-041014-9. doi:10.1115/1.4006736 Dynamic responses of the elastic single wheelset under an impact load action: (a) v=200 km/h; (b) v=320 km/h Figure Legend:

9. Date of download: 6/28/2016 Copyright © ASME. All rights reserved. From: Nonlinear Train-Bridge Lateral Interaction Using a Simplified Wheel-Rail Contact Method Within a Finite Element Framework J. Comput. Nonlinear Dynam. 2012;7(4):041014-041014-9. doi:10.1115/1.4006736 Bridge and vehicle main distances (a) Bridge sketch; (b) Vehicle-bridge system sketch Figure Legend:

10. Date of download: 6/28/2016 Copyright © ASME. All rights reserved. From: Nonlinear Train-Bridge Lateral Interaction Using a Simplified Wheel-Rail Contact Method Within a Finite Element Framework J. Comput. Nonlinear Dynam. 2012;7(4):041014-041014-9. doi:10.1115/1.4006736 Lateral force history on vehicle car-body Figure Legend:

11. Date of download: 6/28/2016 Copyright © ASME. All rights reserved. From: Nonlinear Train-Bridge Lateral Interaction Using a Simplified Wheel-Rail Contact Method Within a Finite Element Framework J. Comput. Nonlinear Dynam. 2012;7(4):041014-041014-9. doi:10.1115/1.4006736 Lateral response of last wheelset when a wind gust load, which corresponds to a theoretical chinese hat function, is applied on vehicle car-body; vertical dotted lines mean left wheel flange contact with the rail Figure Legend:

12. Date of download: 6/28/2016 Copyright © ASME. All rights reserved. From: Nonlinear Train-Bridge Lateral Interaction Using a Simplified Wheel-Rail Contact Method Within a Finite Element Framework J. Comput. Nonlinear Dynam. 2012;7(4):041014-041014-9. doi:10.1115/1.4006736 Lateral response of the car-body under a wind gust load applied on it Figure Legend:

13. Date of download: 6/28/2016 Copyright © ASME. All rights reserved. From: Nonlinear Train-Bridge Lateral Interaction Using a Simplified Wheel-Rail Contact Method Within a Finite Element Framework J. Comput. Nonlinear Dynam. 2012;7(4):041014-041014-9. doi:10.1115/1.4006736 Tangential contact forces at the left wheel of the last wheelset of the vehicle; vertical dotted lines mean left wheel flange contact with the rail Figure Legend: