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Crack detection made by the observation of structural dynamic responses has been implemented for several years in non-destructive control using ultrasound transducers. More recently, detection methods have been proposed based upon the analysis of modal properties. As it has been shown that the modal frequencies are not very sensitive to the presence of a breathing crack, alternative detection techniques have been proposed. They are based upon the analysis of the dynamic non-linear effects of the crack. These effects essentially fall into two categories: the harmonic lobes of the main pure tone or modal excitations and the modulation lobes between these excitations. In order to test them, various simulation methods can be used. This paper presents the test of two simple one-dimensional finite element models and the comparison of their results with a two-dimensional finite element model for the representation of the stiffness loss of an open crack as well as the non-linear behaviour of a breathing crack. The configuration considered is a simply supported beam with a crack at its middle point. Two distinct damage rates are proposed as descriptors to characterize the presence of the crack in the beam: the harmonic damage rate and the modulation damage rate. It is found that the simple one-dimensional models can accurately determine the damage rates associated with the breathing crack, when compared to the results obtained with the two-dimensional model. It is also found that the proposed damage rates can be efficiently used as descriptors of the presence of a crack as their magnitude increases faster than the crack size and in a monotonic way.

This method provides the variation, versus frequency, of the absorption coefficient of a given Helmholtz resonator. We present a numerical method which allows one to foresee the sound pressure field in a room, where some parts of the walls are covered by an array of resonators

The aim of this work is to solve problems of active damping of vibrations in some given domain of a continuous viscoelastic structure. A mathematical model of the mechanical system, the sources of perturbing vibrations, the control system, and the different absorption criteria to be compared are defined. The problems are set in infinite dimension spaces, and the approximate problems are derived in finite dimension spaces. Two methods of resolution are proposed and the solutions are compared. Numerical results simulating the response of a square plate submitted to flexural vibrations are presented for three different absorption criteria, thus permitting a quick evaluation of the comparative effectiveness of the chosen criteria.

The problem of active protection of continuous structure domains is developed by using the well known results of optimal control theory. A mathematical model of the mechanical system is defined and a spatial approximation process is presented according to the basis theory of functional analysis applied to the discretization problem. In finite dimension spaces, the state analysis is developed, including the models of the structure and the perturbation sources, and the corresponding state equations are presented. Various protection criteria compatible with the state analysis scheme are proposed and after presentation of the observer problem, the solution of the optimal regulator problem is developed. Numerical results simulating the time response of a simply supported beam under control are presented for two different protection criteria. The results allow one to proceed to a qualitative comparison of the relative merits of the chosen criteria.

Presentation d'une theorie (Analyse Statistique de l'Energie) pour modeliser le transfert d'energie entre une structure vibrante et un espace acoustique, en caracterisant le couplage entre les divers sous-systemes par des coefficients de perte

The theoretical problem of sound source identification in an enclosed space is solved by minimizing a positive definite functional which is expressed in terms of the distance between the space distributions of the measured and the calculated acoustic pressures in a domain of the space. Two numerical methods for sound source identification are presented, it being assumed that the acoustic propagation in the space can be represented by geometrical acoustic models. The first method is used to determine the acoustic power of geometrically distinct, “point-like” sources, the reverberent sound field being assumed to be “almost” uniform. The second method, based on geometric acoustics ray theory, is designed for large scale sources which may generate non-uniform reverberant fields. For each method, an illustrative example is presented and the calculated acoustic powers are compared to measured ones.