This paper presents an analysis of the dynamic behaviour of constrained layer damping (CLD) beams with thick viscoelastic layer. A homogenised model for the flexural stiffness is formulated using Reddy-Bickford's quadratic shear in each layer, and it is compared with Ross-Kerwin-Ungar (RKU) classical model, which considers a uniform shear deformation for the viscoelastic core. In order to analyse the efficiency of both models, a numerical application is accomplished and the provided results are compared with those of a 2D model using finite elements, which considers extensional and shear stress and longitudinal, transverse, and rotational inertias. The intermediate viscoelastic material is characterised by a fractional derivative model, with a frequency dependent complex modulus. Eigenvalues and eigenvectors are obtained from an iterative method avoiding the computational problems derived from the frequency dependence of the stiffness matrices. Also, frequency response functions are calculated. The results show that the new model provides better accuracy than the RKU one as the thickness of the core layer increases. In conclusion, a new model has been developed, being able to reproduce the mechanical behaviour of thick CLD beams, reducing storage needs and computational time compared with a 2D model, and improving the results from the RKU model.

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This paper presents finite element formulations for transient dynamic analysis in structural systems with damping treatments in which viscoelastic materials are characterized by means of fractional derivative models. In contrast to other formulations, such as that of Padovan employing the principle of virtual work, the proposed formulations begin from the local equation of linear momentum and make use of the weighted residual method, providing a matrix equation of motion involving fractional operators. The numerical approximations of these are developed through the Grünwald–Letnikov definition, which allows to formulate explicit and implicit numerical schemes. The principal advantage of the proposed formulations is that the history of the displacements and external forces must be stored, but not that of the stress, which reduces computational time and storage needs. Numerical applications are presented for a cantilever beam, where a viscoelastic treatment has been applied using damping material modelled by a five‐parameter fractional derivative model. The results of the proposed formulation are compared among them and with those of Padovan for different damping values and for different load cases. The influence of the truncation of Grünwald coefficients and of the integration time‐step is also investigated. Copyright © 2006 John Wiley & Sons, Ltd.

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ABSTRACT:The effects of processing parameters on the strength of the fusion bonding interface have been investigated. The interface was generated when an isotactic polypropylene homopolymer was injection molded on a solid self-reinforced polypropylene substrate. The interface strength was measured in shear configuration, and the melting behavior of substrate was studied using differential scanning calorimetry. The results show that strong bonding interface can be achieved when the correct processing parameters are chosen. The interfacial strength is largely improved if the interface temperature is higher than the melting temperature of the substrate layer, and in these specimens failure does not take place at the interface. Furthermore, for a fixed interface temperature, interface strength increases with thermal gradient. Finally, in the analyzed holding pressure range, pressure apparently has no effect on strength.

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a b s t r a c tIn 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.

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