Experimental and numerical estimation of damping in composite plates with embedded viscoelastic treatments

This thesis summarizes the work done by the author in the frame of the Ph.D. Program in Aerospace, Naval and Quality Engineering at the University of Naples Federico II, following the research projects ARCA and COMFORT, which were aimed to develop innovating solutions for the noise and vibration control in the aeronautical field. In the last years, a constant pursuit in performance improve- ment has been demanded to the aeronautical products, mainly in reducing weight and fuel consumption, hence in reducing the emissivity of polluting agents (Nox). The employment of composite materials in bigger parts of the structures is one of the solutions found to reduce weight, culminating in the design of Boeing 787, the first airplane with a massive part of carbon fiber also in the main frames of the fuselage structure. However, like any other engineering solution, using composite materials has its own drawbacks; while they allow considerable weight reductions, they show high noise permeability thus negatively influencing the comfort level, when employed in the structural elements of an airplane fuselage. To contrast this behavior and comply with comfort requirements in the cabin, it was suggested the use of soundproof or damping materials. Adding one or more viscoelastic material layers within the laminate allows to increase the damping properties of the structure, hence limiting the noise, whether it is structure-borne or air-borne. This approach is called passive control of noise. Inserting a vis- coelastic material between composite plies increases the total weight of the panel, contrasting the weight gained by using composite materials. On the other hand, this technique only reduces the noise by increasing the structural damping of the system panel-viscoelastic layer. Damping is very important for noise and vibration control and for structural stability as well; however, the experimental characterization of the damping level of a structure and its numerical modeling are very hard to realize, especially when viscoelastic materials are employed. At the present day, few references can be found in literature on the subject of damp- ing measurements on composite structures with embedded damping treatment, depending on temperature. From the numerical point of view, things get even more complicated, since even fewer results are found in literature, given the lack of adequate modeling criteria and analysis procedures. This thesis was motivated by the need of further development in both the modeling and the prediction of viscoelastic damping materials properties, for the practical use in aeronautical applications. The aim of this work is to identify, define and validate a procedure for experimental-numerical analyses capable to characterize the behavior of structures with embedded viscoelastic damping treatments, as a function of temperature, in a range of values similar to that of flight conditions. The present research activity can thus be split up in two parts: the first one related to experimental tests and the second related to the numerical simulations. About the experimental part, the objectives have been primarily the identification and validation of a procedure capable to extract the loss factor with a low dispersion of the data in different temperature conditions and, subsequently, the characterization of the performance of two test panels in different environmental conditions like flight temperature conditions. About the numerical part, the objective has been the identification of a numerical procedure able to give as output the same result of the experimental tests, in terms of loss factor. In this direction, two ways have been undertaken by two different numerical approaches: explicit in time domain and direct in frequency domain. For the numerical part of the study, a FEM solver was used, NASTRAN. As it will be shown in the following, the damping extraction procedures were re- alized with dedicated routines written in Matlab. This thesis is organized as follows: in chapter 1, the state of the art about damping treatments is exposed, together with analytical and numerical models that allow to study it. In chapter 2, composite materials are described, as they are characterized as laminates starting from fiber and matrix characteristics. In chapter 3 viscoelastic materials are introduced, first describing viscous and elastic properties separately, then introducing the constitutive models already present in literature to describe such materials. Then these properties were described as functions of several external factors, such as temperature, frequency, etc. In chapter 4, the approach adopted for the experimental part is presented. A detailed description of the loss factor extraction procedure is proposed (IRDM) with the hypotheses to take into account to consider this procedure applicable to highly damped structures as well. The test bed set-up and the lay-up of analyzed panels are described. In the end, the results in terms of position effect (due to the accelerometers position) and temperature effect are shown. Then, in order to validate a procedure of experimental analysis on over 700 acqusitions, a statistical analysis is proposed. In chapter 5, the FEM modeling criterion is shown, in terms of element types, boundary conditions and constraints. Then, two possible approaches are confronted, a time-domain explicit approach and a frequency-domain direct approach. Thereafter, a numerical-experimental comparison is performed to define which procedure is the most suitable to the analysis at the subject of this thesis.