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time, one must integrate over the entire strain history beginning from time zero. Thus, stress
calculations become more and more expensive as the solution progresses. On the other hand,
generalized Maxwell (or Prony series) models possess a separable relaxation modulus that greatly
reduces the computational burden. Additionally, the generalized Maxwell model can provide a very
reasonable representation of the frequency dependent response of viscoelastic solids, and consequently
is adopted in the present work. Although details cannot be provided here, Fig. 4 illustrates the
behavior of the model in the frequency range of primary interest. Furthermore, we assume that the
material is thermorheologically simple, leading to the definition of an intrinsic time scale that may
vary throughout the damper, depending on current temperature.
VE CONSTITUTIVE MODEL
Generalised Maxwell Model
Comple< Moduli
Figure 4: Generalized Maxwell Model - Frequency Domain Response
VE Damper Analysis
The thermally sensitive generalized Maxwell constitutive model described in the previous section is
readily available in the commercial finite element code ABAQUS (1998) within the context of a
quasistatic coupled thermomechanical analysis. In order to incorporate dynamic effects within the
damper, user-defined subroutines must be developed (Radhakrishnan, 2000). However, results
reported here utilize only the quasistatic formulation.
As an illustrative example, consider a constant amplitude cyclic strain-controlled analysis of a single
layer VE damper. For this analysis, the width of the damper is 3.5in, while the thickness of the
viscoelastic layer is 0.5in. The adjoining 0.5in thick steel plates are also included in this plane strain
thermomechanical analysis. The damper is assumed to begin at rest in an unstressed state at a uniform
temperature of 21.7°C. Then constant shear strain range sinusoidal cycling begins with 50%
amplitude at an excitation frequency of 1 Hz for a duration of 10s.
Some results are shown in Figs. 5-7. Figure 5 presents the temperature response as a function of time
for points in the center of the viscoelastic layer and at the VE-steei interface. The most significant rise
occurs at the center, where an increase of approximately 6°C during the ten seconds of excitation. On
the other hand, very little temperature increase occurs at the interface because heat is conducted into
the steel plates. The overall wavy nature of these curves is a consequence of the sinusoidal excitation.