A rigorous theoretical foundation for solving elastodynamic inverse problem of multilayered media under an impulse load is established in this paper. The inversion is built upon the forward dynamic analysis of multilayered elastic media using transfer matrix approach, with which displacement continuity is assumed at the interfaces of upper and lower adjacent layers. Formulations for inverse analysis are derived in both the time domain and the complex frequency domain. Least square estimates and nonlinear optimization algorithms are used to implement parameter identification. The proposed theory and formulae can be utilized to develop a computer software for nondestructive evaluation of laminated civil and aerospace structure (highway and airport pavements, bridge decks, soil foundations, aircraft wing, etc.), exploration and dynamic source detection and identification, and petroleum exploration in geophysics.

Issue Section:
Research Papers
Keywords:
multilayered medium, elasticity, surface wave, inverse problem, nonlinear optimization, elasticity, elastodynamics, frequency-domain analysis, least squares approximations, multilayers, shapes (structures), time-domain analysis, Young's modulus
Topics:
Displacement, Dynamic response, Elasticity, Impulse (Physics), Inverse problems, Nondestructive evaluation, Optimization, Optimization algorithms, Pavement, Stress, Surface waves (Fluid), Young's modulus, Dynamic analysis, Laplace transforms, Highways, Petroleum
1.
Sun
,
L.
, and
Luo
,
F.
, 2008, “
Transient Wave Propagation in Multilayered Viscoelastic Media: Theory, Numerical Computation and Validation
,”
ASME J. Appl. Mech.
JAMCAV 0021-8936,
75
(
3
), p. 031007.
2.
Foinquinos
,
R.
,
Roesset
,
J. M.
, and
Stokoe
,
K. H.
, II, 1996, “Response of Pavement Systems to Dynamic Loads Imposed by Nondestructive Tests,” Transportation Research Record No. 1504, National Research Council, Washington, DC, pp. 57–67.
3.
Lytton
,
R. L.
, 1989, “
Back-Calculation of Pavement Layer Properties
,”
Nondestructive Testing of Pavements and Back-Calculation of Moduli
,
A. J.
Bush
III and
G. Y.
Baladi
, eds.,
ASTM
,
Philadelphia
.
4.
Stolle
,
D. F. E.
, 1996, “Comparison of Simplified Elastostatic and Elastodynamic Models for Falling Weight Deflectometer Data Interpretation,” Transportation Research Record No. 1540, National Research Council, Washington, DC, pp. 72–76.
5.
Stolle
,
D. F. E.
, and
Sedram
,
G.
, 1995, “
Influence of Inertia on Falling Weight Deflectometer Test Response
,”
Can. Geotech. J.
CGJOAH 0008-3674,
32
(
6
), pp. 1044–1048.
6.
Chang
,
D. W.
,
Kang
,
Y. V.
,
Roesset
,
J. M.
, and
Stokoe
,
K. H.
, II, 1992, “Effect of Depth to Bedrock on Deflection Basins Obtained With Dynaflect and FWD Test,” Transportation Research Record No. 1355, National Research Council, Washington, DC, pp. 233–246.
7.
Roesset
,
J. M.
, and
Shao
,
X. Y.
, 1985, “Dynamic Interpretation of Dynaflect and Falling Weight Deflectometer Test,” Transportation Research Record No. 1022, National Research Council, Washington, DC, pp. 7–16.
8.
Stokoe
,
K. H.
, II,
Rix
,
G. J.
, and
Nazarian
,
S.
, 1989, “
In Situ Testing With Surface Waves
,”
Proceedings of the 12th International Conference on Soil Mechanics and Foundation Engineering
, pp. 331–334.
9.
Sun
,
L.
, 2001, “
A Closed-Form Solution of Bernoulli–Euler Beam on Viscoelastic Foundation Under Harmonic Line Loads
,”
J. Sound Vib.
JSVIAG 0022-460X,
242
(
4
), pp. 619–627.
10.
Sun
,
L.
, 2003, “
Dynamic Response of Kirchhoff Plate on a Viscoelastic Foundation to Harmonic Circular Loads
,”
ASME J. Appl. Mech.
JAMCAV 0021-8936,
70
(
4
), pp. 595–600.
11.
Chatti
,
K.
, 2004, “
Use of Dynamic Analysis for Interpreting Pavement Response in Falling Weight Deflectometer Testing
,”
Mater. Eval.
MAEVAD 0025-5327,
62
(
7
), pp. 764–774.
12.
Roesset
,
J. M.
,
Stokoe
,
K. H.
, II, and
Seng
,
C. R.
, 1995, “Determination of Depth to Bedrock From Falling Weight Deflectometer Test Data,” Transportation Research Record No. 1504, National Research Council, Washington, DC, pp. 68–78.
13.
Livneh
,
M.
, 1999, “
The Influence of Some Initial Assumptions on Back-Calculated Moduli
,”
Road & Transport Research
TRTREK 1037-5783,
8
(
4
), pp. 12–26.
14.
Erigen
,
A. C.
, and
Suhubi
,
E. S.
, 1975,
Elastodynamics, I and II
,
Academic
,
New York
.
15.
Watson
,
G. N.
, 1966,
A Treatise on the Theory of Bessel Functions
,
Cambridge University Press
,
Cambridge, United Kingdom
.
16.
Poularikas
,
A. D.
, 1996,
The Transforms and Applications Handbook
,
CRC Press
,
Boca Raton, FL
.
17.
Sun
,
L.
, 1996, “
Theoretical and Experimental Studies of Random Vehicle Loads and Dynamic Response of Pavements Under Moving Arbitrary Loads
,” Ph.D. thesis, Southeast University, Nanjing, China.
18.
Sun
,
L.
, and
Greenberg
,
B. S.
, 2000, “
Dynamic Response of Linear Systems to Moving Stochastic Sources
,”
J. Sound Vib.
JSVIAG 0022-460X,
229
(
4
), pp. 957–972.
19.
Brancik
,
L.
, 1999, “
Programs for Fast Numerical Inversion of Laplace Transforms in Matlab Language Environment
,”
Konference MATLAB ‘99-Praha. MATLAB ‘99, Praha: Konference MATLAB ‘99
, Praha, pp. 27–39.
20.
Jones
,
D. R.
,
Perttunen
,
C. D.
, and
Stuckman
,
B. E.
, 1993, “
Lipschitzian Optimization Without the Lipschitz Constant
,”
J. Optim. Theory Appl.
JOTABN 0022-3239,
79
(
1
), pp. 157–181.
21.
Bjorkman
,
M.
, and
Holmstrom
,
K.
, 1999, “
Global Optimization Using the DIRECT Algorithm in Matlab
,”
Advanced Modeling and Optimization
,
1
(
2
), pp. 17–37.
22.
Nelder
,
J. A.
, and
Mead
,
R.
, 1965, “
A Simplex Method for Function Minimization
,”
Comput. J.
CMPJA6 0010-4620,
7
, pp. 308–313.
23.
Meier
,
R. W.
, and
Rix
,
G. J.
, 1994, “Back-Calculation of Flexible Moduli Using Artificial Neural Networks,” Transportation Research Record No. 1448, National Research Council, Washington, DC, pp. 75–82.
Copyright © 2011
 by American Society of Mechanical Engineers
You do not currently have access to this content.