General Homogenised Formulation for Thick Viscoelastic Layered Structures for Finite Element Applications

Abstract

Viscoelastic layered surface treatments are widely used for passive control of vibration and noise, especially in passenger vehicles and buildings. When the viscoelastic layer is thick, the structural models must account for shear effects. In this work, a homogenised formulation for thick N-layered viscoelastic structures for finite element applications is presented, which allows for avoiding computationally expensive models based on solids. This is achieved by substituting the flexural stiffness in the governing thin beam or plate equation by a frequency dependent equivalent flexural stiffness that takes shear and the properties of the different layers into account. The formulation is applied to Free Layer Damping (FLD) and Constrained Layer Damping (CLD) beams and plates and its ability to accurately compute the eigenpairs and dynamic response is tested by implementing it in a finite element model and comparing the obtained results to those given by the standard for the application—Oberst for the FLD case and RKU for the CLD one—and to a solid model, which is used as reference. For the cases studied, the homogenised formulation is nearly as precise as the model based on solids, but requires less computational effort, and provides better results than the standard model.

Dynamics of Structures, Frames, and Plates with Viscoelastic Dampers or Layers: A Literature Review

“…The results of free and forced vibrations analyses were obtained using the symbolic algebra program MATLAB. This approach was then extended to the cases of constrained VE layers in [145].…”

Transient Dynamic Analysis of Unconstrained Layer Damping Beams Characterized by a Fractional Derivative Model

“…[28] a validation of the model with that number of finite elements was carried out. The elementary matrices used to assemble the system are the ones provided by Equations (19) and (20). The simulation time is not fixed because different times are required for each parameter.…”

“…Similar methodology is used in [19] in order to compare the dynamic behavior between a viscoelastic beam and a viscous one. The application of a general homogenized formulation has been presented in [20] for thick viscoelastic layered structures with the aim to reduce computation time.…”