Shabana,
A. A.
, 1997, “
Flexible Multibody Dynamics: Review of Past and Recent Developments,” Multibody Syst. Dyn.,
1(2), pp. 189–222.

[CrossRef]
Gerstmayr,
J.
,
Sugiyama,
H.
, and
Mikkola,
A.
, 2013, “
Review on the Absolute Nodal Coordinate Formulation for Large Deformation Analysis of Multibody Systems,” ASME J. Comput. Nonlinear Dyn.,
8(3), p. 031016.

[CrossRef]
Kalker,
J.
, 1982, “
A Fast Algorithm for the Simplified Theory of Rolling Contact,” Veh. Syst. Dyn.,
11(1), pp. 1–13.

[CrossRef]
Grassie,
S.
,
Gregory,
R.
,
Harrison,
D.
, and
Johnson,
K.
, 1982, “
The Dynamic Response of Railway Track to High Frequency Vertical Excitation,” J. Mech. Eng. Sci.,
24(2), pp. 77–90.

[CrossRef]
Galvín,
P.
, and
Romero,
A.
, 2013, “
A 3D Time Domain Numerical Model Based on Half-Space Green's Function for Soil–Structure Interaction Analysis,” Comput. Mech.,
53(5), pp. 1073–1085.

[CrossRef]
Clouteau,
D.
,
Cottereau,
R.
, and
Lombaert,
G.
, 2013, “
Dynamics of Structures Coupled With Elastic Media—A Review of Numerical Models and Methods,” J. Sound Vib.,
332(10), pp. 2415–2436.

[CrossRef]
François,
S.
,
Schevenels,
M.
,
Galvín,
P.
,
Lombaert,
G.
, and
Degrande,
G.
, 2010, “
A 2.5D Coupled FE–BE Methodology for the Dynamic Interaction Between Longitudinally Invariant Structures and a Layered Halfspace,” Comput. Methods Appl. Mech. Eng.,
199, pp. 1536–1548.

[CrossRef]
Chamorro,
R.
,
Escalona,
J. L.
, and
González,
M.
, 2011, “
An Approach for Modeling Long Flexible Bodies With Application to Railroad Dynamics,” Multibody Syst. Dyn.,
26(2), pp. 135–152.

[CrossRef]
Pechstein,
A.
, and
Gerstmayr,
J.
, 2013, “
A Lagrange–Eulerian Formulation for an Axially Moving Beam Based on the Absolute Nodal Coordinate Formulation,” Multibody Syst. Dyn.,
30(3), pp. 343–358.

[CrossRef]
Lehner,
M.
, and
Eberhard,
P.
, 2006, “
On the Use of Moment-Matching to Build Reduced Order Models in Flexible Multibody Dynamics,” Multibody Syst. Dyn.,
16(2), pp. 191–211.

[CrossRef]
Fehr,
J.
, and
Eberhard,
P.
, 2011, “
Simulation Process of Flexible Multibody Systems With Non-Modal Model Order Reduction Techniques,” Multibody Syst. Dyn.,
25(3), pp. 313–334.

[CrossRef]
Sherif,
K.
,
Irschik,
H.
, and
Witteveen,
W.
, 2012, “
Transformation of Arbitrary Elastic Mode Shapes Into Pseudo-Free-Surface and Rigid Body Modes for Multibody Dynamic Systems,” ASME J. Comput. Nonlinear Dyn.,
7(2), p. 021008.

[CrossRef]
Rieker,
J. R.
,
Lin,
Y.-H.
, and
Trethewey,
M. W.
, 1996, “
Discretization Considerations in Moving Load Finite Element Beam Models,” Finite Elem. Anal. Des.,
21(3), pp. 129–144.

[CrossRef]
Koh,
C.
,
Ong,
J.
,
Chua,
D.
, and
Feng,
J.
, 2003, “
Moving Element Method for Train-Track Dynamics,” Int. J. Numer. Methods Eng.,
56(11), pp. 1549–1567.

[CrossRef]
Recuero,
A. M.
, and
Escalona,
J. L.
, 2013, “
Application of the Trajectory Coordinate System and the Moving Modes Method Approach to Railroad Dynamics Using Krylov Subspaces,” J. Sound Vib.,
332(20), pp. 5177–5191.

[CrossRef]
Recuero,
A. M.
, and
Escalona,
J. L.
, 2014, “
Dynamics of the Coupled Railway Vehicle–Flexible Track System With Irregularities Using a Multibody Approach With Moving Modes,” Veh. Syst. Dyn.,
52(1), pp. 45–67.

[CrossRef]
Tamarozzi,
T.
,
Ziegler,
P.
,
Eberhard,
P.
, and
Desmet,
W.
, 2013, “
On the Applicability of Static Modes Switching in Gear Contact Applications,” Multibody Syst. Dyn.,
30(2), pp. 209–219.

[CrossRef]
Tamarozzi,
T.
,
Heirman,
G.
, and
Desmet,
W.
, 2014, “
An On-Line Time Dependent Parametric Model Order Reduction Scheme With Focus on Dynamic Stress Recovery,” Comput. Methods Appl. Mech. Eng.,
268, pp. 336–358.

[CrossRef]
Recuero,
A. M.
, 2012, “
Simulation of Coupled Railroad Vehicle–Flexible Track Dynamics Using Moving Modes and Krylov Subspace Techniques,” Ph.D. thesis, University of Seville, Seville, Spain.

Shabana,
A. A.
, 2005, Dynamics of Multibody Systems,
Cambridge University Press,
Cambridge, UK.

Kawamoto,
A.
,
Krenk,
S.
,
Suzuki,
A.
, and
Inagaki,
M.
, 2010, “
Flexible Body Dynamics in a Local Frame With Explicitly Predicted Motion,” Int. J. Numer. Methods Eng.,
81(2), pp. 246–268.

Chamorro,
R.
,
Escalona,
J. L.
, and
Recuero,
A. M.
, 2014, “
Stability Analysis of Multibody Systems With Long Flexible Bodies Using the Moving Modes Method and Its Application to Railroad Dynamics,” ASME J. Comput. Nonlinear Dyn.,
9(1), p. 011005.

Recuero,
A. M.
,
Aceituno,
J.
,
Escalona,
J.
, and
Shabana,
A.
, “
A Nonlinear Approach for Modeling Rail Flexibility Using the Absolute Nodal Coordinate Formulation,” Nonlinear Dyn.
83(1), pp. 463–481.

Hong,
D.
, and
Ren,
G.
, 2011, “
A Modeling of Sliding Joint on One-Dimensional Flexible Medium,” Multibody Syst. Dyn.,
26(1), pp. 91–110.

[CrossRef]
Hyldahl,
P.
,
Mikkola,
A.
, and
Balling,
O.
, 2013, “
A Thin Plate Element Based on the Combined Arbitrary Lagrange–Euler and Absolute Nodal Coordinate Formulations,” Proc. Inst. Mech. Eng., Part K,
227(3), pp. 211–219.

[CrossRef]
Escalona,
J. L.
, 2012, “
Modeling Hoisting Machines With the Arbitrary Lagrangian–Eulerian Absolute Nodal Coordinate Formulation,” 2nd International Conference on Multibody System Dynamics, Stuttgart, Germany, May 29–June 1.

Irschik,
H.
, and
Holl,
H.
, 2002, “
The Equations of Lagrange Written for a Non-Material Volume,” Acta Mech.,
153(3), pp. 231–248.

[CrossRef]
Shabana,
A. A.
,
Zaazaa,
K. E.
, and
Sugiyama,
H.
, 2008, Railroad Vehicle Dynamics. A Computational Approach,
CRC Press,
Boca Raton, FL.

Popp,
K.
, and
Schiehlen,
W.
, 2010, Ground Vehicle Dynamics,
Springer-Verlag,
Berlin.

Recuero,
A. M.
,
Escalona,
J. L.
, and
Chamorro,
R.
, 2012, “
A Trajectory Frame-Based Dynamic Formulation for Railroad Vehicles Simulation,” Int. J. Railw. Technol.,
1(2), pp. 21–44.

[CrossRef]
Donea,
J.
,
Huerta,
A.
,
Ponthot,
J.-P.
,
Rodríguez-Ferran,
A.
, 2004, “
Arbitrary Lagrangian–Eulerian Methods,” Encyclopedia of Computational Mechanics, Volume 1: Fundamentals,
Wiley, Chichester, UK, pp. 1–25.

Schilders,
W. H.
,
van der Vorst,
H. A.
, and
Rommes,
J.
, eds., 2008, Model Order Reduction: Theory, Research Aspects and Applications,
Springer-Verlag,
Berlin.

Feldmann,
P.
, and
Freund,
R.
, 1995, “
Efficient Linear Circuit Analysis by Padé Approximation Via the Lanczos Process,” IEEE Trans. Comput. Aided Des. Integr. Circuits Syst.,
14(5), pp. 639–649.

[CrossRef]
Koutsovasilis,
P.
, and
Beitelschmidt,
M.
, 2008, “
Comparison of Model Reduction Techniques for Large Mechanical Systems,” Multibody Syst. Dyn.,
20(2), pp. 111–128.

[CrossRef]
Liang,
Y.
,
Lee,
H.
,
Lim,
S.
,
Lin,
W.
,
Lee,
K.
, and
Wu,
C.
, 2002, “
Proper Orthogonal Decomposition and Its Applications—Part I: Theory,” J. Sound Vib.,
252(3), pp. 527–544.

[CrossRef]
Goldstein,
H.
,
Poole,
C.
, and
Safko,
J.
, 2001, Classical Mechanics, 3rd ed.,
Addison-Wesley, New York.

Giménez,
G.
, 1978, “
Cálculo y Optimización del Comportamiento Dinámico de Vehículos Ferroviarios,” Ph.D. thesis, Universidad de Navarra, Navarra, Spain.

Mallik,
C. S.
, and
Singh,
A. K.
, 2006, “
Steady-State Response of an Elastically Supported Infinite Beam to a Moving Load,” J. Sound Vib.,
291, pp. 1148–1169.

[CrossRef]
Shabana,
A.
, 1997, Vibration of Discrete and Continuous Systems,
Springer,
New York.

Frýba,
L.
, 1999, Vibration of Solids and Structures Under Moving Loads, 3rd ed.,
Thomas Telford Ltd.,
Prague, Czech Republic.

Vostroukhov,
A.
, and
Metrikine,
A.
, 2003, “
Periodically Supported Beam on a Visco-Elastic Layer as a Model for Dynamic Analysis of a High-Speed Railway Track,” Int. J. Solids Struct.,
40(21), pp. 5723–5752.

[CrossRef]