Abstract
The effective design of viscoelastic dampers as applied to real-world complex engineering structures can be conveniently carried out by using modern numerical optimization and/or model updating techniques. However, the large number of exact evaluations of the cost functions, combined with the typically high dimensions of large finite element models of industrial structures incorporating viscoelastic materials, makes the numerical processes very costly, sometimes unfeasible. Those difficulties motivate the study reported herein, in which a general strategy to improve the standard condensation methods by taking into account a priori information of the modifications into the viscoelastic zones is introduced. The proposed method can be used with any condensation procedure, including direct reductions and component mode synthesis.
Highlights
The use of viscoelastic materials has been regarded as a convenient strategy in many types of industrial applications, where these materials can be applied either as discrete devices or surface treatments at a relatively low cost [1,2,3]
For finite element (FE) models of engineering structures incorporating viscoelastic materials composed by many thousands of degrees-of-freedom (DOFs) the time to compute the exact evaluations during the iterative processes, performed on the full FE matrices, can become prohibitive [5,6]
In an attempt to compute the modified matrices involved in the further condensation, it becomes interesting to perform a parameterization of the FE model, which is understood as a means of making them to appear explicitly in the finite element mass and stiffness matrices
Summary
The use of viscoelastic materials has been regarded as a convenient strategy in many types of industrial applications, where these materials can be applied either as discrete devices or surface treatments at a relatively low cost [1,2,3]. For finite element (FE) models of engineering structures incorporating viscoelastic materials composed by many thousands of degrees-of-freedom (DOFs) (for example an aerospace structure can be composed by more than 106 DOFs) the time to compute the exact evaluations during the iterative processes, performed on the full FE matrices, can become prohibitive [5,6] Those difficulties motivate the study reported with the intent to propose a general strategy to reduce the size of the viscoelastic structures for mainly several reasons: the cost of computation when one wants to extract the eigensolutions or to predict the behavior of the full structure, the optimization or model updating procedures and reliability-based optimization which require fast iterative techniques. Bouazzouni et al [7] developed an optimal method to construct additional vectors by using the dynamic behavior of the structure before modification The disadvantage of such approaches lies in the fact that a basis of reduction composed by a great number of residual static vectors is obtained, augmenting the computation effort involved in the condensation. After the various aspects related to the theoretical foundations, the description of a numerical application composed by a stiffened panel treated by a passive constraining damping layer demonstrates the effectiveness of the robust condensation strategy of viscoelastic systems
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