There are internal-variable techniques that account for the frequency-dependent behavior of viscoelastic materials, but the temperature dependence of these materials has received much less attention. Two methods for designing controllers robust to temperature disturbances are given: (1) Modal reference adaptive control and (2) time-varying pole placement control. Examples that demonstrate the strengths and weaknesses of each are given. The results show that it is possible to achieve vibration reduction while simultaneously rejecting the effects of a temperature disturbance. This work shows that both the frequency and temperature dependence of viscoelastic materials can be modeled with internal variables.

1.
Ferry
J.D.
,
1980
, Viscoelastic Properties of Polymers, Wiley, New York.
2.
Schapery
R. A.
,
1964
, “
Application of Thermodynamics to Thermomechanical, Fracture, and Birefringent Phenomena in Viscoelastic Media
,”
J. Appl. Phys.
,
35
(
5
), pp.
1451
1465
.
3.
Lesieutre
G. A.
, and
Govindswamy
K.
,
1996
, “
Finite Element Modeling of Frequency-Dependent and Temperature-Dependent Dynamic Behavior of Viscoelastic Materials in Simple Shear
,”
Int. J. Solids Struct.
,
33
(
3
), pp.
419
432
.
4.
Lukasiewicz
S.
, and
Xia
Z.Q.
,
1993
, “Nonlinear, Damped Vibrations of Sandwich Plates with Time-Dependent Temperature,” in Proceedings of the 14th ASME Biennial Conference on Mechanical Vibration and Noise,” Albuquerque NM, pp.
427
436
.
5.
Nashif
A.D.
,
Jones
D.I.G.
, and
Henderson
J.P.
,
1985
, Vibration Damping, Wiley, New York.
6.
Banks
H. T.
, and
Inman
D. J.
,
1992
, “
Significance of Modeling Internal Damping in the Control of Structures
,”
J. Guid. Control
,
15
(
6
), pp.
1509
1512
.
7.
Trindade
M. A.
,
Benjeddou
A.
, and
Ohayon
R.
,
2000
, “
Finite Element Analysis of Frequency- and Temperature-Dependent Hybrid Active-Passive Vibration Damping
,”
Revue Europe´enne des Ele´ments Finis
,
9
(
1–3
), pp.
89
111
.
8.
Linz
P.
,
1985
, Analytical and Numerical Methods for Volterra Equations, SIAM Studies in Applied Mathematics, SIAM, Philadelphia.
9.
Johnson
A. R.
,
1999
, “
Modeling viscoelastic materials using internal variables
,”
Shock Vib. Dig.
,
31
(
2
), pp.
91
100
.
10.
da Silva
L.A.
,
2003
, “
Internal Variable and Temperature Modeling Behavior of Viscoelastic Structures—A Control Analysis
,” Ph.D. thesis, Virginia Tech, URL http://scholar.lib.vt.edu/theses/available/etd-08252003-065520/.
11.
Drake
M.L.
, and
Soovere
J.
,
1984
, “A Design Guide for Damping of Aerospace Structures,” in AFWAL Vibration Damping Workshop Proceedings,
3
.
12.
Slotine
J.J.E.
, and
Li
W.
,
1991
, Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, NJ.
13.
Silva
L.A.
, and
Inman
D.J.
,
2002
, “
On The Application of Independent Modal-Space Control to Internal Variable Based Viscoelastic Bar
,” XX IMAC.
14.
Meirovitch
L.
, and
Oz
H.
,
1980
, “
Modal-Space Control of Distributed Gyroscopic Systems
,”
J. Guid. Control
,
3
(
2
), pp.
140
150
.
15.
Tsakalis
K.S.
, and
Ioannou
P.A.
,
1993
, Linear Time-Varying Systems: Control and Adaptation, Prentice Hall, Englewood Cliffs, NJ.
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