In this paper, a new series expansion for calculating the bending moment and the shear force in a proportionally damped, one-dimensional distributed parameter system due to moving loads is suggested. The number of moving forces, which may be functions of time and spatial coordinate, and their velocities are arbitrary. The derivation of the series expansion is not limited to moving forces that are a priori known, making this method also applicable to problems in which the moving forces depend on the interactions between the continuous system and the subsystems it carries, e.g., the moving oscillator problem. A main advantage of the proposed method is in the accurate and efficient evaluation of the bending moment and shear force, and in particular, the shear jumps at the locations where the moving forces are applied. Numerical results are presented to demonstrate the rapid convergence of the new series representation.

1.
Diana
,
G.
, and
Cheli
,
F.
,
1989
, “
Dynamic Interaction of Railway Systems With Large Bridges
,”
Veh. Syst. Dyn.
,
18
, pp.
71
106
.
2.
Taheri
,
M. R.
,
Ting
,
E. C.
, and
Kukreti
,
A. R.
,
1990
, “
Vehicle-Guideway Interactions: A Literature Review
,”
Shock Vib. Dig.
,
22
, pp.
3
9
.
3.
Chen
,
C. H.
, and
Wang
,
K. W.
,
1994
, “
An Integrated Approach Toward the Modeling and Dynamic Analysis of High-Speed Spindles, Part II: Dynamics Under Moving End Load
,”
ASME J. Vibr. Acoust.
,
116
, pp.
514
522
.
4.
Mote
,
C. D.
, Jr.
,
1970
, “
Stability of Circular Plates Subjected to Moving Loads
,”
J. Franklin Inst.
,
290
, No.
4
, pp.
329
344
.
5.
Weisenel
,
G. N.
, and
Schlack
,
A. L.
,
1993
, “
Response of Annular Plates to Circumferentially and Radially Moving Loads
,”
ASME J. Appl. Mech.
,
60
, pp.
649
661
.
6.
Zhu
,
W. D.
, and
Mote
,
C. D.
, Jr.
,
1994
, “
Free and Forced Response of an Axially Moving String Transporting a Damped Linear Oscillator
,”
J. Sound Vib.
,
177
, No.
5
, pp.
591
610
.
7.
C-J Online News, 1997, http://www.cjonline.com/stories/110397/new_usbridges.html.
8.
Pesterev
,
A. V.
, and
Bergman
,
L. A.
,
1997
, “
Vibration of Elastic Continuum Carrying Moving Linear Oscillator
,”
J. Eng. Mech.
,
123
, pp.
878
884
.
9.
Pesterev
,
A. V.
, and
Bergman
,
L. A.
,
1997
, “
Vibration of Elastic Continuum Carrying Accelerating Oscillator
,”
J. Eng. Mech.
,
123
, pp.
886
889
.
10.
Pesterev
,
A. V.
, and
Bergman
,
L. A.
,
1998
, “
Response of a Nonconservative Continuous System to a Moving Concentrated Load
,”
ASME J. Appl. Mech.
,
65
, pp.
436
444
.
11.
Bisplinghoff, R. L., Ashley, H., and Halfman, R. L., 1955, Aeroelasticity, Addison-Wesley, Boston (reprinted 1996, Dover, New York).
12.
Dowell
,
E. H.
,
1996
, “
Comment on Energy Flow Predictions in a Structure of Rigidly Joined Beams Using Receptance Theory
,”
J. Sound Vib.
,
194
, pp.
445
447
.
13.
Palazzolo
,
A. B.
,
Wang
,
B. P.
, and
Pilkey
,
W. D.
,
1982
, “
A Receptance Formula for General Second-Degree Square Lambda Matrices
,”
Int. J. Numer. Methods Eng.
,
18
, pp.
829
843
.
14.
Pesterev
,
A. V.
, and
Tavrizov
,
G. A.
,
1994
, “
Vibrations of Beams With Oscillators, I: Structural Analysis Method for Solving the Spectral Problem
,”
J. Sound Vib.
,
170
, pp.
521
536
.
15.
Yang
,
B.
,
1996
, “
Closed-Form Transient Response of Distributed Damped Systems, Part I: Modal Analysis and Green’s Function Formula
,”
ASME J. Appl. Mech.
,
63
, pp.
997
1003
.
16.
Pesterev
,
A. V.
, and
Bergman
,
L. A.
,
2000
, “
An Improved Series Expansion of the Solution to the Moving Oscillator Problem
,”
ASME J. Vibr. Acoust.
,
122
, pp.
54
61
.
17.
Caughey
,
T. K.
, and
O’Kelly
,
M. E. J.
,
1965
, “
Classical Normal Modes in Damped Linear Dynamic Systems
,”
ASME J. Appl. Mech.
,
32
, pp.
583
588
.
18.
Yang
,
B.
,
1996
, “
Integral Formulas for Non-Self-Adjoint Distributed Dynamic Systems
,”
AIAA J.
,
34
, pp.
2132
2139
.
19.
Pesterev, A. V., Yang, B., Bergman, L. A., and Tan, C. A., 2001, “Response of an Elastic Continuum Carrying Multiple Moving Oscillators,” J. Eng. Mech., in press.
20.
Sadiku
,
S.
, and
Leipholz
,
H. H. E.
,
1987
, “
On the Dynamics of Elastic Systems With Moving Concentrated Masses
,”
Ing.-Arch.
,
57
, pp.
223
242
.
You do not currently have access to this content.