0
TECHNICAL PAPERS

Reduced-Order Finite Element Models of Viscoelastically Damped Beams Through Internal Variables Projection

[+] Author and Article Information
Marcelo A. Trindade

Department of Mechanical Engineering, São Carlos School of Engineering, University of São Paulo, Av. Trabalhador São-Carlense, 400, São Carlos-SP, 13566-590, Braziltrindade@sc.usp.br

J. Vib. Acoust 128(4), 501-508 (Jan 24, 2006) (8 pages) doi:10.1115/1.2202155 History: Received September 15, 2004; Revised January 24, 2006

For a growing number of applications, the well-known passive viscoelastic constrained layer damping treatments need to be augmented by some active control technique. However, active controllers generally require time-domain modeling and are very sensitive to system changes while viscoelastic materials properties are highly frequency dependent. Hence, effective methods for time-domain modeling of viscoelastic damping are needed. This can be achieved through internal variables methods, such as the anelastic displacements fields and the Golla-Hughes-McTavish. Unfortunately, they increase considerably the order of the model as they add dissipative degrees of freedom to the system. Therefore, the dimension of the resulting augmented model must be reduced. Several researchers have presented successful methods to reduce the state space coupled system, resulting from a finite element structural model combined with an internal variables viscoelastic model. The present work presents an alternative two-step reduction method for such problems. The first reduction is applied to the second-order model, through a projection of the dissipative modes onto the structural modes. It is then followed by a second reduction applied to the resulting coupled state space model. The reduced-order models are compared in terms of performance and computational efficiency for a cantilever beam with a passive constrained layer damping treatment. Results show a reduction of up to 67% of added dissipative degrees of freedom at the first reduction step leading to much faster computations at the second reduction step.

FIGURES IN THIS ARTICLE
<>
Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Cantilever beam partially covered with a passive constrained layer damping treatment

Grahic Jump Location
Figure 2

Frequency dependence of 3M ISD112 viscoelastic material properties at 20°C (solid line) and curve fit using three (dashed line) and five (dashed-dotted line) ADF series terms

Grahic Jump Location
Figure 3

Eigenfrequency error when using different numbers of dissipative modes in second-order system compared to using all but rigid body modes

Grahic Jump Location
Figure 4

Damping factor error when using different numbers of dissipative modes in second-order system compared to using all but rigid body modes

Grahic Jump Location
Figure 5

Normalized residual and cumulative sum of residuals for the viscoelastic dissipative modes

Grahic Jump Location
Figure 6

Frequency response function using different numbers of dissipative modes in second-order system. –: all but rigid body modes (89), – –: 9 modes, - - -: 19 modes, –.–: 29 modes

Grahic Jump Location
Figure 7

Eigenfrequency error when using different numbers of dissipative modes in second-order system compared to using all but rigid body modes

Grahic Jump Location
Figure 8

Damping factor error when using different numbers of dissipative modes in second-order system compared to using all but rigid body modes

Grahic Jump Location
Figure 9

Frequency response function using different numbers of dissipative modes in second-order system. –: all but rigid body modes (52), – –: 5 modes, - - -: 9 modes, –.–: 18 modes

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In