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.
Highlights
When a structure is subjected to vibration and the emitted sound must be reduced, surface treatments are a handy solution
Surface treatments are layered slender structures that can be divided into two groups: free layer damping (FLD) and constrained layer damping (CLD)
First, the formulation for a general one- or two-dimensional surface treatment with any number of layers is presented; the method is implemented in a finite element model and applied to FLD and CLD beams and plates for which the eigenpairs, i.e., eigenvalues and eigenvectors, and the dynamic response to an external force are computed; the obtained results are compared to the ones provided by a three-dimensional finite element model and to the standard model in the field: the Oberst model for FLD structures and the RKU for those with a CLD configuration
Summary
When a structure is subjected to vibration and the emitted sound must be reduced, surface treatments are a handy solution. The formulation uses conventional beam and plate finite elements and introduces the effect of shear by means of a frequency dependent equivalent flexural stiffness With this aim, first, the formulation for a general one- or two-dimensional surface treatment with any number of layers is presented; the method is implemented in a finite element model and applied to FLD and CLD beams and plates for which the eigenpairs, i.e., eigenvalues and eigenvectors, and the dynamic response to an external force are computed; the obtained results are compared to the ones provided by a three-dimensional finite element model and to the standard model in the field: the Oberst model for FLD structures and the RKU for those with a CLD configuration. The dynamic behaviour of the viscoelastic layer is represented by a four parameter fractional derivative model
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