Loïc Le Marrec

Determination of the bulk elastic moduli of various concretes by resonance frequency analysis of slabs submitted to impact echo

ABSTRACT The presented study aims at evaluating the bulk elastic Youngs modulus of six different concrete mixes as a function of porosity and water content. The impact echo method consists of a frequency analysis of ultrasonic waves generated by the impact of a steel ball. It is commonly used to measure the thickness of large concrete slabs, to detect voids in concrete structural elements considered as infinite. This method was employed on reduced size slabs (0.5 × 0.25 × 0.12 m3). As a consequence, it was necessary to identify the frequencies corresponding to resonance modes or pseudo-stationary modes. This modal analysis was performed with simplified models (for beam in particular) and used to extract the dynamic Youngs modulus Edyn and the Poissons ratio. The results are then analysed. The Edyn-modulus, inverted for all concrete mixes, is compared to static Youngs modulus Estat measured by destructive testing, to the porosity and to the water content of the specimens.

A Continuous Model for the Wave Scattering by a Bounded Defective Domain

Elastic wave propagation and scattering in a media containing a continuous density of defect is modeled with a geometrical approach. The material is supposed to be a Riemann–Cartan manifold with a connection enriched by a nonzero torsion. The study is followed until to reveal analytical solutions. The scattering of a defective domain shows explicitly some non-classical phenomena.

2D‐ultrasonic tomography using first‐order Born and canonical approximations

This paper deals with the two‐dimensional image reconstruction of an elastic tubes using ultrasonic tomographic method based on first‐Born approximation and a canonical approximations. The latter improvement makes it possible to extend the scope of tomography from lower impedance contrast media to higher impedance contrast situations, even when the ultrasonic propagation is greatly perturbed by the difference in acoustic impedance between the scatterer and the surrounding medium. The strategy used to solve this problem was based on comparisons between the experimental diffracted field and the canonical solution approached as a forward problem. The algorithm adopted, using the analytical solution to the local forward problem and an iterative process to recover the unknowns, is fast enough to yield real‐time information about the shape. A single frequency does not suffice to determine the real solution as the global minimum of the cost function, and the inversion is improved by using all the frequencies pre...

Influence of the pre‐stress state on the wave propagation in a shearable Timoshenko beam

It is very common to use pre‐stressed beam models in the structure design. However in the nonlinear domain, the modal analysis remains difficult especially when shearability is taken into account. This work aims to study the natural vibrations of pre‐stretched nonlinear shearable Timoshenko beam using Cosserat continuum mechanics. In this paper, a three dimensional nonlinear beam model is first developed. Then we analyse waves which are superimposed on a finite pre‐stretch state. Namely, analytical dispersion relations are given for different values of pre‐strech. The complete spectrum, including propagating and evanescent traction/compression, shear and bending modes, of a pre‐ stretched shearable beam is calculated through dispersion pattern. Spectrum strongly depends on initial pre‐stress value. A significant qualitative and quantitative difference with the classical Timoshenko beam theory is pointed out even for small pre‐stretch values.