Keywords: wave propagation, finite element, loss factor, laminates, constrained layer damping treatment.

The main aim of this paper is to show the capability of a wave finite element (WFE) method for fast and accurate modelling of the vibroacoustical behaviour of multi-layer panels treated with viscoelastic layers. In particular the method is applied to predict dispersion curves and loss factors of laminated plates with constrained layer damping (CLD) treatment including the frequency dependence of the viscoelastic material.

The WFE method involves the systematic post-processing, using periodicity conditions, of element matrices of a small segment of the structure which is modelled using a stack of solid elements meshed through the cross section [1]. This allows the shear distribution, in particular in soft layers, to be correctly represented and hence to accurately represent the energy dissipation due to the CLD. The element matrices are typically found using a commercial FE package, in this case ANSYS. This is one of the main advantages of the WFE technique since the full power of existing FE packages and their extensive element libraries can be exploited.

In this paper the formulation of the method is presented and is extended to account for viscoelastic material behaviour, enabling the prediction of dispersion, attenuation and damping in composite structures for which inherent material damping is not negligible. Estimation of the damping loss factor using the WFE method is shown. Then a formulation for evaluating the average loss factor considering the variation of the modal density with the direction of wave propagation is proposed. Numerical examples are presented. As a first example the flexural loss factor of an aluminum plate with an attached CLD treatment is considered. The WFE results for this case are compared with those obtained by other authors [2,3]. Good agreement is seen. Laminated plates with CLD treatment are considered as a second example. Both the frequency dependence of the viscoelastic material and the contribution to the energy dissipation of the fibre reinforced materials are taken into account. Results concerning dispersion curves, global loss factor as a function of the frequency and of the heading direction and average loss factor are presented for a wide frequency range.

The method is seen to provide a useful tool for evaluating the vibroacoustic behaviour of composite panels treated with viscoelastic layers and for optimizing, at the design stage, using important parameters, such as material selection, layer thickness, stacking sequence, treatment position and operating temperature and frequencies.

1

B.R. Mace, E. Manconi, "Modelling wave propagation in two-dimensional structures using a Wave/Finite Element", COMPDYN Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rethymno, Crete, Greece, 2007.

2

E.M. Kerwin, "Damping of flexural waves by constrained viscoelastic layer", Journal of the Acoustical Society of America, 31, 952-962, 1959. doi:10.1121/1.1907821

3

S. Ghinet, N. Atalla, "Wave approach modeling of sandwich and laminate composite structures with viscoelastic layers", ICA 19th International congress on acoustics, Madrid, 2007.

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