Structural vibration of flexural beams with thick unconstrained layer damping

Abstract

In this paper, the dynamic behaviour of free layer damping beams with thick viscoelastic layer is analysed. A homogenised model for the flexural stiffness is formulated employing Reddy and Bickford’s quadratic shear in each layer, in contrast to the classical model of Oberst and Frankenfeld for thin beams, which does not take into account shear deformations. The results provided by these two models in free and forced vibration are compared by means of finite element procedures with those of a 2D model, which considers extensional and shear stress, and longitudinal, transverse and rotational inertias. The viscoelastic material is characterised by a fractional derivative model, which takes into consideration the variation of the complex modulus with frequency. To avoid the frequency dependence of the stiffness matrices, the extraction of the eigenvalues and eigenvectors is completed by a new iterative method developed by the authors. The frequency response to a harmonic force is deduced by the superposition of modal contribution functions. From these numerical applications it can be concluded that the model for thick beams provides sufficient accuracy for practical applications, able to reproduce the mechanical behaviour of free layer damping beams with thick viscoelastic layer, reducing the storage needs and computational time with respect to a 2D model.