Viscoelastic Damping Technologies-Part I: Modeling and Finite Element Implementation ⋆

Abstract

This is the first of two companion articles addressing an integrated study on the mathematical modeling and assessment of the efficiency of surface mounted or embedded viscoelastic damping treatments, typically used to reduce structural vibration and/or noise radi- ation from structures, incorporating the adequate use and development of viscoelastic (arbitrary frequency dependent) damping models, along with their finite element (FE) implementation, and the experimental identification of the constitutive behavior of viscoelastic materials. This first article (Part I) is devoted to the development of mathematical descriptions of material damping to represent the linear viscoelastic constitutive behavior, their implementation into FE formulations and the use of the underlying different solution methods. To this end, internal variables models, such as the Golla-Hughes-McTavish (GHM) and anelastic displacement fields (ADF) models, and other methods such as the direct frequency response (DFR), based on the complex modulus approach (CMA), iterative modal strain energy (IMSE) and an approach based on an iterative complex eigensolution (ICE) are described and implemented at the global FE model level. The experimental identification of viscoelastic materials properties and the aforementioned viscoelastically damped FE modeling approaches are assessed and validated in the companion article (Vasques, C.M.A. et al., Viscoelastic damping technologies-Part II: Experimental identification procedure and validation, Journal of Advanced Research in Mechanical Engineering 1(2): 96-110 (2010)).