Modelisation analytique pour l'etude du comportement vibratoire en regime transitoire d'une plaque avec tampon amortissant contraint

This thesis aims at developing an analytical model for the study of a viscoelastic sandwich under the effect of an impact. The sandwich consists of a rectangular plate with a PCLD (Partial Constrained Layer Damping). This study includes the characterization of the vibration behaviour of the sandwich (frequencies and mode shapes), the damping performance (loss factors), and the characterization of radiated noise and wave propagation in the plate. The model provides the flexibility to vary the geometric and physical characteristics of the different layers and to study theirs influences on the aforementioned values.;The model is based on the application of Lagrange’s equations, which yield the equation of motion. The shear modulus of the viscoelastic layer is a function of frequency, and is represented by Prony series. The impact is represented by Heitkämper’s theoretical relation. Two methods of resolution were adopted for the transverse displacement of the viscoelastic sandwich. In the first method, the equation of motion is converted into the frequency domain using Fast Fourier Transform (FFT). Once solved, the transverse displacement obtained in the frequency domain is converted to the time domain with the Inverse Fast Fourier Transform (IFFT). The second method consists of solving the equation directly in the time domain with the Newmark and Wilson iterative method. Once the displacement is obtained, the acoustic pressure is calculated with Rayleigh’s integral.;The model is validated at different stages. The first validation is performed in harmonic response by comparing natural frequencies and loss factors with literature, both for full coverage and partial coverage. Moreover, an experimental setup was made to measure the transverse displacement of the sandwich due to an impact : these results were used for the second validation in transient response. In both cases, good accuracy is obtained. In harmonic response, the accuracy is around 0.3% on natural frequencies and 0.2% on loss factors. In transient response, the simulations provided the instantaneous motion of the sandwich with a minor difference with experimental results.;The model has proved its efficiency for the study of sandwiches with PCLD, in particular :;• the design of the PCLD – the model can be used to quantify the PCLD parameters to meet the requirements of the designer;;• defining areas of plate to promote maximum damping, these areas are related to the deformation mode, and are located in the vicinities of the corners, on the modal crests, and near plate central edges ;;• predicting the transient response not only in terms of displacement and sound pressure, but also in terms of transverse wave propagation, in fact, for a given impact and for any point of the plate, displacement can be visualized with respect to time and space, and the sound pressure generated can be quantified.;The model was used to prepare three papers. The objective of the first article is to explain and validate the model in both regimes (permanent and transient). The second article discusses the influence of geometric characteristics of the PCLD on the damping of the sandwich and on the acoustic pressure generated due to an impact. In the last article we studied the influence of PCLD on the bending wave propagation in the plate.