Sandwich structures with viscoelastic core and metal face sheets are increasingly used in automotive industry to significantly reduce the amplitude of vibration and noise radiation. Several experimental methods such as dynamic mechanical analysis (DMA) and vibrating beam technique (VBT) are used to characterize the dynamic properties of viscoelastic materials as a function of frequency and temperature. This paper investigates the use of a free-free beam setup, as an alternative solution to the classical clamped-free VBT, for a better control of the effect of boundary conditions on the laminated steel specimen. The new setup is developed in combination with a frequency response function based optimization method, to automatically derive the dynamic properties of viscoelastic core materials and generate their master curves. A solver based on the normal mode superposition method, considering the added mass effect of the impedance head, is used in the cost function of the optimization approach. The sandwich model is based on the Ross–Kerwin–Ungar equation, and the four-parameter fractional derivative model is used in conjunction with the Williams–Landel–Ferry equation to describe the frequency and temperature dependent behavior of the viscoelastic material. The master curves are a direct result of the optimization process. Several applications are described to assess the performance of the present method. In particular, a systematic comparison with both the classical VBT and DMA (when available) is presented.

1.
Menard
,
K. P.
, 1999,
DMA: Introduction to the Technique, Its Applications and Theory
,
CRC
,
Boca Raton, FL
.
2.
Menard
,
K. P.
, 2008,
Dynamic Mechanical Analysis: A Practical Introduction
,
2nd ed.
,
CRC
,
Boca Raton, FL
.
3.
2005, Standard Test Method for Measuring Vibration-Damping Properties of Materials, ASTM E756-04.
4.
Kerwin
,
E. M.
, 1959, “
Damping of Flexural Waves by a Constrained Viscoelastic Layer
,”
J. Acoust. Soc. Am.
0001-4966,
31
, pp.
952
962
.
5.
Ross
,
D.
,
Kerwin
,
E. M.
, and
Ungar
,
E. E.
, 1959, “
Damping of Plate Flexural Vibration by Means of Viscoelastic Laminae
,”
Structural Damping
,
ASME
,
New York
.
6.
Friswell
,
M. I.
, and
Mottershead
,
J. E.
, 1995,
Finite Element Model Updating in Structural Dynamics
,
Kluwer Academic
,
Dordrecht
.
7.
Maia
,
N. M. M.
, and
Silva
,
J. M. M.
, 1997,
Theoretical and Experimental Modal Analysis
,
Wiley
,
New York
.
8.
DiTaranto
,
R. A.
, 1965, “
Theory of Vibratory Bending for Elastic and Viscoelastic Layered Finite-Length Beams
,”
ASME J. Appl. Mech.
0021-8936,
32
, pp.
881
886
.
9.
Mead
,
D. J.
, and
Markus
,
S.
, 1969, “
The Forced Vibration of a Three-Layer, Damped Sandwich Beam With Arbitrary Boundary Conditions
,”
J. Sound Vib.
0022-460X,
10
, pp.
163
175
.
10.
Yan
,
M. J.
, and
Dowell
,
E. H.
, 1972, “
Governing Equations for Vibrating Constrained-Layer Damping Sandwich Plates and Beams
,”
ASME J. Appl. Mech.
0021-8936,
39
, pp.
1041
1046
.
11.
Yu
,
Y. Y.
, 1962, “
Damping of Flexural Vibrations of Sandwich Plates
,”
J. Aerosp. Sci.
0095-9820,
29
, pp.
790
803
.
12.
Ghinet
,
S.
, 2005, “
Statistical Energy Analysis of the Transmission Loss of Sandwich and Laminate Composite Structures
,” Ph.D. thesis, Université de Sherbrooke, Sherbrooke, QC, Canada.
13.
Golla
,
D. F.
, and
Hughes
,
P. C.
, 1985, “
Dynamics of Viscoelastic Structures—A Time-Domain Finite Element Formulation
,”
ASME J. Appl. Mech.
0021-8936,
52
, pp.
897
906
.
14.
McTavish
,
D. J.
, and
Hughes
,
P. C.
, 1993, “
Modeling of Linear Viscoelastic Space Structures
,”
ASME J. Vibr. Acoust.
0739-3717,
115
, pp.
103
110
.
15.
McTavish
,
D. J.
,
Hughes
,
P. C.
,
Soucy
,
Y.
, and
Graham
,
W. B.
, 1992, “
Prediction and Measurement of Modal Damping Factors for Viscoelastic Space Structures
,”
AIAA J.
0001-1452,
30
, pp.
1392
1399
.
16.
Lesieutre
,
G. A.
, and
Bianchini
,
E.
, 1995, “
Time Domain Modeling of Linear Viscoelasticity Using Anelastic Displacement Fields
,”
ASME J. Vibr. Acoust.
0739-3717,
117
, pp.
424
430
.
17.
Lesieutre
,
G. A.
, and
Mingori
,
D. L.
, 1990, “
Finite Element Modeling of Frequency-Dependent Material Damping Using Augmenting Thermodynamic Fields
,”
J. Guid. Control Dyn.
0731-5090,
13
, pp.
1040
1050
.
18.
Dovstam
,
K.
, 1995, “
Augmented Hooke’s Law in Frequency Domain: A Three Dimensional Material Damping Formulation
,”
Int. J. Solids Struct.
0020-7683,
32
, pp.
2835
2852
.
19.
Bagley
,
R. L.
, and
Torvik
,
P. J.
, 1983, “
Fractional Calculus—A Different Approach to the Analysis of Viscoelastically Damped Structures
,”
AIAA J.
0001-1452,
21
, pp.
741
748
.
20.
Bagley
,
R. L.
, and
Torvik
,
P. J.
, 1983, “
A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
,”
J. Rheol.
0148-6055,
27
, pp.
201
210
.
21.
Pritz
,
T.
, 1996, “
Analysis of Four-parameter Fractional Derivative Model of Real Solid Materials
,”
J. Sound Vib.
0022-460X,
195
, pp.
103
115
.
22.
Pritz
,
T.
, 2003, “
Five-Parameter Fractional Derivative Model for Polymeric Damping Materials
,”
J. Sound Vib.
0022-460X,
265
, pp.
935
952
.
23.
Sun
,
C. T.
, and
Lu
,
Y. P.
, 1995,
Vibration Damping of Structural Elements
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
24.
Plouin
,
A. P.
, and
Balmes
,
E.
, 2000, “
Steel/viscoelastic/steel Sandwich Shells Computational Methods and Experimental Validations
,”
International Modal Analysis Conference
, pp.
384
390
.
25.
Balmes
,
E.
, and
Bobillot
,
A.
, 2002, “
Analysis and Design Tools for Structures Damped by Viscoelastic Materials
,”
International Modal Analysis Conference
, pp.
210
216
.
26.
Balmes
,
E.
, and
Germes
,
S.
, 2002, “
Tools for Viscoelastic Damping Treatment Design: Application to an Automotive Floor Panel
,”
International Seminar on Modal Analysis
, Leuven, Belgium.
27.
Balmes
,
E.
, and
Germes
,
S.
, 2004, “
Design Strategies for Viscoelastic Damping Treatment Applied to Automotive Components
,”
International Modal Analysis Conference
.
28.
Moreira
,
R.
, and
Rodrigues
,
J. D.
, 2004, “
Constrained Damping Layer Treatments: Finite Element Modeling
,”
J. Vib. Control
1077-5463,
10
, pp.
575
595
.
29.
Amichi
,
K.
, and
Atalla
,
N.
, 2009, “
A New 3D Finite Element for Sandwich Beams With a Viscoelastic Core
,”
ASME J. Vibr. Acoust.
0739-3717,
131
, p.
021010
.
30.
Doyle
,
J. F.
, 1997,
Wave Propagation in Structures: A FFT-Based Spectral Analysis Methodology
,
Springer
,
New York
.
31.
Grafe
,
H.
, 1999, “
Model Updating of Large Structural Dynamics Models Using Measured Response Functions
,” Ph.D. thesis, University of London, UK.
32.
Heylen
,
W.
, and
Lammens
,
S.
, 1996, “
FRAC: A Consistent Way of Comparing Frequency Response Functions
,”
Proceedings of the Conference on Identification in Engineering Systems
, Swansea, UK, pp.
48
57
.
33.
Zang
,
C.
,
Grafe
,
H.
, and
Imregun
,
M.
, 2001, “
Frequency-Domain Criteria for Correlating and Updating Dynamic Finite Element Models
,”
Mech. Syst. Signal Process.
0888-3270,
15
, pp.
139
155
.
34.
Balmes
,
E.
, 1993, “
A Finite Element Updating Procedure Using Frequency Response Functions. Applications to the MIT/SERC Interferometer Tested
,”
International Modal Analysis Conference
, Kissimmee, FL, pp.
176
182
.
35.
Balmes
,
E.
, 1993, “
Integration of Existing Methods and User Knowledge in a MIMO Identification Algorithm for Structures With High Modal Densities
,”
International Modal Analysis Conference
, Kissimmee, FL, pp.
613
619
.
36.
Moreira
,
R. A. S.
, and
De-Carvalho
,
R.
, 2009, “
Inverse Method for Dynamic Characterisation of Cork Compounds
,”
International Journal of Materials Engineering Innovation
,
1
, pp.
254
275
.
37.
Hambric
,
S. A.
,
Jarrett
,
A. W.
,
Lee
,
G. F.
, and
Fedderly
,
J. J.
, 2007, “
Inferring Viscoelastic Dynamic Material Properties From Finite Element and Experimental Studies of Beams With Constrained Layer Damping
,”
ASME J. Vibr. Acoust.
0739-3717,
129
, pp.
158
168
.
38.
Renault
,
A.
, 2008, “
Caractérisation Mécanique Dynamique de Matériaux Poro-visco- élastiques
,” Ph.D. thesis, Université de Sherbrooke, QC, Canada.
39.
McConnell
,
K. G.
, 1995,
Vibration Testing: Theory and Practice
,
Wiley
,
New York
.
40.
Nashif
,
A.
,
Jones
,
D. I. G.
, and
Henderson
,
J.
, 1985,
Vibration Damping
,
Wiley
,
New York
.
41.
Weaver
,
W.
,
Timoshenko
,
S.
, and
Young
,
D. H.
, 1990,
Vibration Problems in Engineering
,
Wiley
,
New York
.
42.
Jones
,
D. I. G.
, 2001,
Handbook of Viscoelastic Vibration Damping
,
Wiley
,
New York
.
43.
Williams
,
M. L.
,
Landel
,
R. F.
, and
Ferry
,
J. D.
, 1955, “
The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids
,”
J. Am. Chem. Soc.
0002-7863,
77
, pp.
3701
3707
.
44.
Ferry
,
J. D.
, 1980,
Viscoelastic Properties of Polymers
,
3rd ed.
,
Wiley
,
New York
.
45.
MathWorks
, 2008, MATLAB Genetic Algorithm and Direct Search Toolbox™ User’s Guide.
46.
Beda
,
T.
, and
Chevalier
,
Y.
, 2004, “
New Methods for Identifying Rheological Parameter for Fractional Derivative Modeling of Viscoelastic Behaviour
,”
Mech. Time-Depend. Mater.
1385-2000,
8
, pp.
105
118
.
47.
Ren
,
Z.
, 2010, “
Identification and Optimization of the Dynamic Properties of Viscoelastic Materials
,” Ph.D. thesis, Université de Sherbrooke, QC, Canada.
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