A finite element formulation for the transient response of free layer damping plates including fractional derivatives. (1st July 2023) - Cortés, Fernando; Brun, Mikel; Elejabarrieta, María Jesús
Highlights: A finite element formulation for time analysis of free layer damping plates is proposed. The damping layer is modelled by a five-parameter fractional derivative model. The proposed formulation is based on the homogenisation of plates. Grünwald-Letnikov and Newmark methods are used for the numerical integration. The validation is completed by means of a model with hexahedral finite elements. Abstract: This paper presents a finite element formulation specifically developed for the transient dynamic analysis of free layer damping plates, in which the viscoelastic behaviour of damping layers is modelled by means of fractional derivatives. This formulation is based on the homogenisation of thin multi-layered plates, adapted to consider fractional derivatives. Then, a fractional matrix equation system is reached, and the time response is solved by means of the implicit Newmark method in conjunction with the Grünwald-Letnikov discretisation of the fractional derivatives. The validation of the method is carried out by comparing the results of three different numerical applications with the ones provided by a finite element model built with hexahedral elements. As conclusion, it can be pointed out that the proposed finite element formulation based on the homogenisation of multi-layer plates reproduces accurately the time response of plates with surface damping treatments. In addition, this method allows conventional plate mass and stiffness matrices to be used to model each individual layer, without requiring specific formulations.