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

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.