A non-linear vibration spectroscopy model for structures with closed cracks

International audienceEnsuring an uninterrupted service in critical complex installations requires parameter health monitoring of the vibrating structures. Tools for monitoring structural modifications through changes in the measured dynamic responses are necessary in order to detect the advent and evolution of cracks before the occurrence of catastrophic failures. It is shown, both theoretically and experimentally, that the equation for the modes of vibration of a structure with closed (breathing) cracks and whose surfaces enter into contact during vibration can be modeled using the Hertz contact theory. The damping chosen is a fractional order derivative to investigate the order matching the experimental data. A perturbation solution technique, combining the Multiple Time Scales and Lindsted-Poincaré methods, has been employed to construct analytical approximations to the resulting non-linear equation of vibration. A 3D finite element model of the structure has been employed to compute the eigenvalues of the sound structure, providing a means to validate the measured resonance frequencies and also allowing the visualization of the modal deformations thus giving greater insight into the physics of the problem

Identification of the mechanical moduli of closed-cell porous foams using transmitted acoustic waves in air and the transfer matrix method

International audienceClosed-cell cellular polymer foams are the most efficient insulating materials commercially available. Their lightweight and mechanical resistance also make them ideal materials for packaging protection in the transport industry. A new method using guided \emph{acoustic waves in air} transmitted through samples of cellular foam panels, has been developed to recover their P-wave moduli and Poisson's ratios. These parameters were recovered from measured transmission coefficients of the foams through fitting to an elastodynamic transfer matrix method (TMM). The TMM integrates both the P and shear waves propagating in the layer. It was shown by using a finite element fluid-solid (elastic) interaction and an analytic P-waves-only model, that the two types of waves should be modeled to give a more precise representation of the data. The retrieved values were validated using vibration spectroscopy and from the measured velocity of a transient mechanical stress wave propagating in thin, long rod specimens cut from the panels. The problems inherent to these simple 1D characterization methods were pointed out and solved

Investigation of long acoustic waveguides for the very low frequency characterization of monolayer and stratified air-saturated poroelastic materials

International audienceWhen sound propagates in a porous medium, it is attenuated via several energy loss mechanisms which are switched on or o as the excitation frequency varies. The classical way of measuring acoustic energy loss in porous materials uses the Kundt impedance tube. However, due to its short length, measurements are made in the steady state harmonic regimes. Its lower cuto frequency is often limited to a few hundreds of Hertz. Two long acoustic waveguides were assembled from water pipes and mounted to create test-rigs for the low-frequency acoustic characterization of monolayer and stratied air-waveguides were found to be equivalent and provided data down to frequencies of the order of ≈ 12 Hz