When a rigid body negotiates a curve, the centrifugal force takes a simple form which is function of the body mass, forward velocity, and the radius of curvature of the curve. In this simple case of rigid body dynamics, curve negotiation does not lead to Coriolis forces. In the case of a flexible body negotiating a curve, on the other hand, the inertia of the body becomes function of the deformation, curve negotiations lead to Coriolis forces, and the expression for the deformation-dependent centrifugal forces becomes more complex. In this paper, the nonlinear constrained dynamic equations of motion of a flexible body negotiating a circular curve are used to develop a systematic procedure for the calculation of the centrifugal forces during curve negotiations. The floating frame of reference (FFR) formulation is used to describe the body deformation and define the nonlinear centrifugal and Coriolis forces. The algebraic constraint equations which define the motion trajectory along the curve are formulated in terms of the body reference and elastic coordinates. It is shown in this paper how these algebraic motion trajectory constraint equations can be used to define the constraint forces that lead to a systematic definition of the resultant centrifugal force in the case of curve negotiations. The embedding technique is used to eliminate the dependent variables and define the equations of motion in terms of the system degrees of freedom. As demonstrated in this paper, the motion trajectory constraints lead to constant generalized forces associated with the elastic coordinates, and as a consequence, the elastic velocities and accelerations approach zero in the steady state. It is also shown that if the motion trajectory constraints are imposed on the coordinates of a flexible body reference that satisfies the mean-axis conditions, the centrifugal forces take the same form as in the case of rigid body dynamics. The resulting flexible body dynamic equations can be solved numerically in order to obtain the body coordinates and evaluate numerically the constraint and centrifugal forces. The results obtained for a flexible body negotiating a circular curve are compared with the results obtained for the rigid body in order to have a better understanding of the effect of the deformation on the centrifugal forces and the overall dynamics of the body.

References

References
1.
Bibel
,
G.
,
2013
, “
The Physics of Disaster: An Exploration of Train Derailments
,” http://www.scientificamerican.com/article/the-physics-of-disaster/#comments
2.
Toppo
,
G.
, and
Stanglin
,
G.
,
2015
, “
Amtrak Train Traveled Twice the Speed Limit on Track Curve Before Crash
,” http://www.usatoday.com/story/news/nation/2015/05/13/fatal-train-crash/27222401/
3.
Wang
,
L.
,
Shi
,
H.
, and
Shabana
,
A. A.
,
2015
, “
Analysis of Tank Car Deformations Using Multibody Systems and Finite Element Algorithms
,”
ASME
Paper No. DETC2015-46368.
4.
Abramowicz
,
M. A.
,
1990
, “
Centrifugal Force: A Few Surprises
,”
Mon. Not. R. Astron. Soc.
,
245
, pp.
733
746
.
5.
Theodorsen
,
T.
,
1935
, “
Propeller Vibrations and the Effect of the Centrifugal Force
,”
National Advisory Committee for Aeronautics
, Springfield, VA.
6.
Herivel
,
J. W.
,
1960
, “
Newton's Discovery of the Law of Centrifugal Force
,”
Isis
,
51
(
4
), pp.
546
553
.
7.
Behzad
,
M.
, and
Bastami
,
A. R.
,
2004
, “
Effect of Centrifugal Force on Natural Frequency of Lateral Vibration of Rotating Shafts
,”
J. Sound Vib.
,
274
(
3
), pp.
985
995
.
8.
Chen
,
J. S.
, and
Hwang
,
Y. W.
,
2006
, “
Centrifugal Force Induced Dynamics of a Motorized High-Speed Spindle
,”
Int. J. Adv. Manuf. Technol.
,
30
(
1–2
), pp.
10
19
.
9.
Maqueda
,
L. G.
,
Bauchau
,
O. A.
, and
Shabana
,
A. A.
,
2008
, “
Effect of the Centrifugal Forces on the Finite Element Eigenvalue Solution of a Rotating Blade: A Comparative Study
,”
Multibody Syst. Dyn.
,
19
(
3
), pp.
281
302
.
10.
Mondal
,
R. N.
,
Ray
,
S. C.
, and
Yanase
,
S.
,
2014
, “
Combined Effects of Centrifugal and Coriolis Instability of the Flow Through a Rotating Curved Duct With Rectangular Cross Section
,”
Open J. Fluid Dyn.
,
4
(1), pp.
1
14
.
11.
Diana
,
G.
,
Cheli
,
F.
,
Bruni
,
S.
, and
Collina
,
A.
,
1995
, “
Dynamic Interaction Between Rail Vehicles and Track for High Speed Train
,”
Veh. Syst, Dyn.
,
24
(
Sup1
), pp.
15
30
.
12.
Wang
,
L.
,
Octavio
,
J. R. J.
,
Wei
,
C.
, and
Shabana
,
A. A.
,
2015
, “
Low Order Continuum-Based Liquid Sloshing Formulation for Vehicle System Dynamics
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
2
), p.
021022
.
13.
Wei
,
C.
,
Wang
,
L.
, and
Shabana
,
A. A.
,
2015
, “
A Total Lagrangian ANCF Liquid Sloshing Approach for Multibody System Applications
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
5
), p.
051014
.
14.
Shi
,
H.
,
Luo
,
R.
,
Wu
,
P.
,
Zeng
,
J.
, and
Guo
,
J.
,
2014
, “
Application of DVA Theory in Vibration Reduction of Carbody With Suspended Equipment for High-Speed EMU
,”
Sci. China Technol. Sci.
,
57
(
7
), pp.
1425
1438
.
15.
Ashley
,
H.
,
1967
, “
Observations on the Dynamic Behavior of Large Flexible Bodies in Orbit
,”
AIAA J.
,
5
(
3
), pp.
460
469
.
16.
Agrawal
,
O. P.
, and
Shabana
,
A. A.
,
1986
, “
Application of Deformable-Body Mean Axis to Flexible Multibody System Dynamics
,”
Comput. Methods Appl. Mech. Eng.
,
56
(
2
), pp.
217
245
.
17.
Roberson
,
R. E.
, and
Schwertassek
,
R.
,
1988
,
Dynamics of Multibody Systems
,
Springer-Verlag
,
Berlin
.
18.
Shabana
,
A. A.
,
2013
,
Dynamics of Multibody Systems
,
4th ed.
,
Cambridge University
,
New York
.
19.
Aboubakr
,
A. K.
, and
Shabana
,
A. A.
,
2015
, “
Efficient and Robust Implementation of the TLISMNI Method
,”
J. Sound Vib.
,
353
, pp.
220
242
.
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