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Triangular Plate Metallic Damper Analysis
Next the two-surface plasticity model is applied to study the cyclic response of metallic triangular
plate dampers. For the finite element analysis, a solid element model for one-half of one plate is used.
The particular triangular-shaped damper plate studied here has an overall length of 0.304m, a base
width of 0.1333m and a 0.0361m thickness. This damper is designated 2B2 by Tsai et al. (1993). The
wide end of the plate is clamped, symmetry is enforced about the centerline and a constant amplitude
displacement-controlled loading history is applied normal to the plate at the tip. The plate is subjected
to five complete loading cycles at low frequency. Quasistatic response is assumed.
In the finite element analysis, the amplitude of the enforced displacement at the tip of the plate is set at
0.0912m. This corresponds to a nominal angle x 0 =0.30 as defined in Tsai et al. (1993) and Dargush
and Soong (1995). The longitudinal plastic strains are presented in Fig. 3a at maximum displacement
with the deformation shown at actual scale. Meanwhile, the damper force-displacement response,
using the present two-surface model is displayed in Fig. 3b. Not only does the response stabilize, the
shape is quite similar to that obtained hi experiments (Tsai et al., 1993). Furthermore, the stiffening
that occurs at large strain amplitudes can be attributed to the effects of large deformation. One often
must account for these effects in passive devices due to the intentional high concentration of energy
dissipation. Although these trends are well predicted, the magnitude of the forces obtained from the
present analysis is approximately 20% higher than those measured in the experiments. Further
investigation is needed to properly account for this difference.
Figure 3: Triangular Plate Damper (a) Longitudinal Plastic Strains, (b) Cyclic Response
VISCOELASTIC DAMPERS
Constitutive Model
A number of models for viscoelastic solids and fluids have appeared in the literature. For example,
Shen and Soong (1995) used a Williams four-parameter model, while Makris et al. (1993, 1995) and
Kasai et al. (1993) employed a fractional derivative model. Both models have attractive features that
permit material characterization over a rather broad frequency range with a limited number of
parameters. Under certain circumstances, one can also establish a theoretical basis for these models
from the underlying micromechamcs. However, neither of these models is particularly effective for
transient nonlinear analysis, which is necessary for proper description of response under significant
seismic excitation. The difficulty pertains to the fact that the time-dependent relaxation moduli
associated with these models are not separable. This means that to compute the stress at any instant of