A thin plate resting on a Winkler elastic foundation subject to a moving harmonic load can be used as the model for highway and airport pavement under moving vehicle load and many other applications. The study of dynamic response of the plate thus becomes very important. In this paper we study the dynamic displacement of a plate caused by a moving harmonic line and point load. The solution is represented by the convolution of dynamic Green’s function of plate. An approximate relationship between critical load velocity and critical frequency is established analytically. It is found that the maximum displacement response occurs at the center of the moving load and travels at the same speed with the load.

1.
Sousa
,
J. B.
,
Lysmer
,
J.
,
Chen
,
S. S.
, and
Monismith
,
C. L.
, 1987, “
Response of Asphalt Concrete Pavements to Dynamic Truck Loads
,”
Report to Transportation Laboratory, University of California
, Berkeley.
2.
Monismith
,
C. L.
,
Sousa
,
J.
, and
Lysmer
,
J.
, 1988, “
Modern Pavement Design Technology Including Dynamic Load Conditions
,”
Trans. ASAE
0001-2351, No. 881856.
3.
Sun
,
L.
, 1998, “
Theoretical Investigations on Vehicle-Ground Dynamic Interaction, Southeast University, Nanjing, China
,”
Final Report Prepared for National Science Foundation of China
.
4.
Sun
,
L.
, and
Deng
,
X.
, 1998, “
Predicting Vertical Dynamic Loads Caused by Vehicle-Pavement Interaction
,”
J. Transp. Eng.
0733-947X,
124
(
5
), pp.
470
478
.
5.
Sun
,
L.
, and
Kennedy
,
T. W.
, 2002, “
Spectral Analysis and Parametric Study of Stochastic Pavement Loads
,”
J. Eng. Mech.
0733-9399,
128
(
3
), pp.
318
327
.
6.
Deng
,
X.
, and
Sun
,
L.
, 2001,
Dynamics of Vehicle-Pavement Interaction
,
People’s Transport Publishing
, Beijing.
7.
Sun
,
L.
, 2002, “
Optimum Design of ‘Road-Friendly’ Vehicle Suspension Systems Subject to Rough Road Surface
,”
Appl. Math. Model.
0307-904X,
26
(
5
), pp.
635
652
.
8.
Bush
,
A. J.
, 1980, “
Nondestructive Testing for Light Aircraft Pavements, Phase II. Development of the Nondestructive Evaluation Methodology, Federal Aviation Administration
,” Final Report FAA RD-80-9.
9.
Scullion
,
T.
,
Uzan
,
J.
, and
Paredes
,
M.
, 1990, “
A Microcomputer-Based Backcalculation System
,”
Transp. Res. Rec.
0361-1981, No. 1260 MODULUS.
10.
Uzan
,
J.
, and
Lytton
,
R.
, 1990, “
Analysis of Pressure Distribution under Falling Weight Deflectometer Loading
,”
J. Transp. Eng.
0733-947X,
116
(
2
), pp.
246
250
.
11.
Salawu
,
O. S.
, and
Williams
,
C.
, 1995, “
Full-Scale Force-Vibration Test Conducted Before and After Structural Repairs on Bridge
,”
J. Struct. Eng.
0733-9445,
121
(
2
), pp.
161
173
.
12.
Sun
,
L.
, and
Greenberg
,
B.
, 2000, “
Dynamic Response of Linear Systems to Moving Stochastic Sources
,”
J. Sound Vib.
0022-460X,
229
(
4
), pp.
957
972
.
13.
Taheri
,
M. R.
, 1986, “
Dynamic Response of Plates to Moving Loads
,” Ph.D. Thesis, Purdue University, West Lafayette, IN.
14.
Kukreti
,
A. R.
,
Taheri
,
M.
, and
Ledesma
,
R. H.
, 1992, “
Dynamic Analysis of Rigid Airport Pavements with Discontinuities
,”
J. Transp. Eng.
0733-947X,
118
(
3
), pp.
341
360
.
15.
Zaghloul
,
S. M.
,
White
,
T. D.
,
Dmevich
,
V. P.
, and
Coree
,
B.
, 1994, “
Dynamic Analysis of FWD Loading and Pavement Response using a Three Dimensional Dynamic Finite Element Program
,”
Transp. Res. Board
, Washington, D. C.
16.
Kenney
,
J. T.
, 1954, “
Steady-State Vibrations of Beam on Elastic Foundation for Moving Load
,”
ASME J. Appl. Mech.
0021-8936,
21
, pp.
359
364
.
17.
Deshun
,
Z.
, 1999, “
A Dynamic Model for Thick Elastic Plates
,”
J. Sound Vib.
0022-460X,
221
(
2
), pp.
187
203
.
18.
Bo
,
J.
, 1999, “
The Vertical Vibration of an Elastic Circular Plate on a Fluid-Saturated Porous Half Space
,”
Int. J. Eng. Sci.
0020-7225,
37
, pp.
379
393
.
19.
Fryba
,
L.
, 1999,
Vibration of Solids and Structures under Moving Loads
,
Thomas Telford
, London.
20.
Westergaard
,
H. M. S.
, 1926, “
Computation of Stresses in Concrete Roads
,”
Highw. Res. Board, Proc. Annu. Meet.
0096-1027
5
(
I
), pp.
90
112
.
21.
Yoder
,
E. J.
, and
Witczak
,
M. W.
, 1975,
Principles of Pavement Design
,
Wiley
, New York.
22.
Hass
,
R.
,
Hudson
,
W. R.
, and
Zniewski
,
J.
, 1994,
Modern Pavement Management
,
Krieger
, Malabar, FL.
23.
Zhu
,
Z.
,
Wang
,
B.
, and
Guo
,
D.
, 1984,
Pavement Mechanics
,
Renming Jiaotong
, Beijing, China.
24.
Eringen
,
A. C.
, and
Suhubi
,
E. S.
, 1975,
Elastodynamics
,
Academic Press
, New York, Vols.
I
and
II
.
25.
Watson
,
G. N.
, 1966,
A Treatise on the Theory of Bessel Functions
,
2nd ed.
,
Cambridge University Press
, London.
26.
Press
,
W. H.
,
Flannery
,
B. P.
,
Teukolsky
,
S. A.
, and
Vetterling
,
W. T.
, 1993,
Numerical Recipes in C: The Art of Scientific Computing
,
Cambridge University Press
, Cambridge.
27.
Kim
,
S. M.
, and
Roesser
,
J. M.
, 1996, “
Dynamic Response of Pavement Systems to Moving Loads
,” Research Report, 1422-2,
Center for Transportation Research, University of Texas at Austin
.
28.
Pesterev
,
A. V.
,
Yang
,
B.
,
Bergman
,
L. A.
, and
Tan
,
C. A.
, 2001, “
Response of Elastic Continum Carrying Multiple Moving Oscillators
,”
J. Eng. Mech.
0733-9399,
127
(
3
), pp.
260
265
.
29.
Pesterev
,
A. V.
,
Tan
,
C. A.
, and
Bergman
,
L. A.
, 2001, “
A New Method for Calculating Bending Moment and Shear Force in Moving Load Problems
,”
ASME J. Appl. Mech.
0021-8936,
68
(
1
), pp.
252
259
.
30.
Sun
,
L.
, 2001, “
Closed-Form Representation of Beam Response to Moving Line Loads
,”
ASME J. Appl. Mech.
0021-8936,
68
(
2
), pp.
348
350
.
You do not currently have access to this content.