The method of substructure synthesis, originally conceived for undamped and viscously damped systems, has been extended to systems with viscoelastic damping in the hereditary integral form. Based on a new variational principle, the substructure synthesis method is formulated in the time domain. The displacement in each substructure is represented by a set of real admissible trial vectors. The traditional state space formulation is avoided by the proposed method so that the approach is independent of the form of viscoelastic models. Effectiveness of the method is illustrated through numerical examples.

Issue Section:
Technical Papers
Topics:
Damping, Displacement, Variational principles
1.
Beˆliveau
J.-G.
, and
Soucy
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,
1985
, “
Damping Synthesis Using Complex Substructure Modes and a Hermitian System Representation
,”
AIAA Journal
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23
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1956
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2.
Biot
M. A.
,
1954
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The Theory of Stress-Strain Relations in Anisotropic Viscoelasticity and Relaxation Phenomena
,”
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3.
Christensen, R. M., 1982, Theory of Viscoelasticity, Academic Press, New York.
4.
Craig
R. R.
, and
Ni
Z.
,
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Component Mode Synthesis for Model Order Reduction of Nonclassically Damped Systems
,”
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5.
Dowell
E. H.
,
1972
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Free Vibration of an Arbitrary Structure in Term of Component Modes
,”
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6.
Hale
A. L.
, and
Bergman
L. A.
,
1985
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The Dynamic Synthesis of General Nonconservative Structures from Separately Identified Substructure Models
,”
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431
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446
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7.
Hasselman
T. K.
, and
Kaplan
A.
,
1974
, “
Dynamic Analysis of Large Systems by Complex Mode Synthesis
,”
ASME Journal of Dynamic Systems, Measurement and Control
, Vol.
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327
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333
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8.
Hurty
W. C.
,
1965
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Dynamic Analysis of Structural Systems Using Component Modes
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AIAA Journal
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9.
Kubomura
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,
1982
, “
A Theory of Substructure Modal Synthesis
,”
ASME JOURNAL OF APPLIED MECHANICS
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10.
Meirovitch
L.
, and
Hale
A. L.
,
1981
, “
On the Substructure Synthesis Method
,”
AIAA Journal
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11.
Oden, J. T., and Reddy, J. N., 1976, Variational Methods in Theoretical Mechanics, Springer-Verlag, New York.
12.
Qian, D., 1993, “Substructure Synthesis Methods for Viscoelastic Structures,” Ph.D. thesis, University of Toronto.
13.
Qian, D., and Hansen, J. S., 1995, “A Substructure Synthesis Method for Non-Symmetric Viscoelastic Systems,” Journal of Sound and Vibration, accepted for publication.
14.
Staverman
A. J.
, and
Schwarzl
F.
,
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Non-Equilibrium Thermodynamics of Viscoelastic Behavior
,”
Koninklijke Nederlandse Akademic Van Wetenschappen, Proceeding of the Section of Sciences, Series B
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492
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15.
Suarez
L. E.
, and
Singh
M. P.
,
1991
, “
Successive Synthesis of Substructure Modes
,”
ASME JOURNAL OF APPLIED MECHANICS
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759
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765
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16.
Wilson
E. L.
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Bayo
E. P.
,
1986
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Use of Special Ritz Vectors in Dynamic Substructure Analysis
,”
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1956
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17.
Yee
E. K. L.
, and
Tsuei
Y. G.
,
1990
, “
Transient Responses by Component Mode Synthesis Method
,”
ASME Journal of Vibration and Acoustics
, Vol.
112
, pp.
21
–
25
.
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