Mihai Valentin Predoi

Finite element predictions for the dynamic response of thermo-viscoelastic material structures

In this paper, constitutive relations are solved in the Fourier domain using a finite-element-based commercial software. The dynamic responses of viscoelastic bars or plates to either thermal or mechanical loads are predicted by considering complex moduli (Young, Poisson, stiffness moduli) as input data. These moduli are measured in the same frequency domain as that which is chosen for modeling the wave propagation. This approach is simpler since it suppresses the necessity of establishing a rheological model. Specific output processing then allows the numerical predictions to be compared to analytical solutions, in the absence of scatterers. The performances of this technique and its potential for simulating more complicated problems like diffraction of waves or for solving inverse problems are finally discussed.

Wave propagation along transversely periodic structures

The dispersion curves for guided waves have been of constant interest in the last decades, because they constitute the starting point for NDE ultrasonic applications. This paper presents an evolution of the semianalytical finite element method, and gives examples that illustrate new improvements and their importance for studying the propagation of waves along periodic structures of infinite width. Periodic boundary conditions are in fact used to model the infinite periodicity of the geometry in the direction normal to the direction of propagation. This method allows a complete investigation of the dispersion curves and of displacement/stress fields for guided modes in anisotropic and absorbing periodic structures. Among other examples, that of a grooved aluminum plate is theoretically and experimentally investigated, indicating the presence of specific and original guided modes.

Numerical predictions and experiments on the free-plate edge mode

In this paper, te edge mode variation is studied with three different methods: the reciprocal work method, already used by Torvik [J. Acoust. Soc. Am. 41 (1967) 346] to model this phenomenon, the S-parameter method and a finite element model that are applied for the first time to the study of the edge resonance. Moreover, laser probe measurements of the edge mode have also been performed and compared to the numerical predictions. The good agreement between the numerical predictions and the experimental data allows full understanding of the resonant phenomenon. The edge resonance is linked to the strong increase in amplitude of two complex Lamb waves, and the edge mode is proved to radiate into the plate as the first symmetrical Lamb mode S(0). Displacements at the edge and away from the edge have been computed and measured to evaluate the spatial and temporal behaviour of the edge mode. The dependence of the edge resonance frequency and amplitude on the Poisson coefficient has also been studied.

An orthogonality relation-based technique for post-processing finite element predictions of waves scattering in solid waveguides

In this paper we propose an efficient way to post-process output data predicted by Finite Element (FE) or Boundary Element (BE) codes, when the scattering of Lamb modes by defects in plate-like structures is considered. The use of a general orthogonality relation is compared to classical post-processing made with spatial FFT. To get the amplitudes of incident or scattered modes, this orthogonality relation requires the numerical prediction of the through-thickness displacements, and stress-fields distributions, on each side of the scatterer. The distance between the location where these fields are predicted and the scatterer can be very small, thus allowing huge reductions in the size of the mesh. Through two examples, this orthogonality relation is used to calculate the reflection and transmission coefficients of a pure Lamb mode incident on a notch-like defect, in either an elastic or a viscoelastic plate. Thanks to efficient absorbing regions, the FE meshed domains are reduced to the vicinity of the de...

Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method.

Influence of material viscoelasticity on the scattering of guided waves by defects.

Guided waves are potential candidates for the nondestructive evaluation of viscoelastic structures due to their relatively long range of propagation. The major drawback is the difficulty in interpreting the scattered waves especially at high frequency-thickness values since many modes then exist. Moreover, in damping material waveguides, each mode of the scattered field has its own attenuation. Viscoelastic material characterization has been widely investigated by many authors in the past, but very few are treating multimodal scattering by discontinuities in viscoelastic guide. The scattering of a pure fundamental mode incident on a trough in a viscoelastic plate is investigated in this paper, over a relatively large frequency range, with up to five scattered modes. A hybrid two-dimensional finite element and modal projection method is used, based on modal orthogonality, to obtain the relative energy fluxes of each mode. Experiments are also made to validate the numerical predictions.

Use of shear horizontal waves to distinguish adhesive thickness variation from reduction in bonding strength

The capability of shear horizontal (SH) guided waves, to evaluate geometrical imperfections in a bonding layer, is investigated. SH waves are used in a three-layer structure in which the adhesive layer has variable thickness. It is proven that the SH waves are adapting to the local thickness of the adhesive layer (adiabatic waves). This is particularly useful in case of small thickness variations, which is of technical interest. The influence of thickness and stiffness of the adhesive layer on the wavenumbers are investigated. The selected SH2 mode is proven to be very sensitive to the adhesive layer thickness variation in the given frequency range and considerably less sensitive to the adhesive stiffness variation. This property is due to its specific displacement field and is important in practical applications, such as inspection techniques based on SH waves, in order to avoid false alarms.

Guided waves in plates with linear variation of thickness

Guided waves represent promising nondestructive evaluation (NDE) techniques. Their advantage of long distance propagation is however hampered by complex wave scattering at each discontinuity along the investigated structure. These scattered waves can be used to locate and size possible defects. Theoretical investigation is a prerequisite step in the development of a NDE technique. Planar metallic structures with localized thickness variation imposed by design represent possible new industrial structures that could be tested using guided waves. The waves scattered at the region of variable thickness must be theoretically predicted and experimentally measured before any defect could be detected. Very few authors have investigated waveguides with continuous variation of thickness. Our previous numerical and experimental studies have proven the complexity of the scattering phenomenon in such cases. Among other remarks is the curved shape of the wave front. The present work investigates properties of the waves...

Ultrasonic inspection of defects in welded plates and tubes

The characterization of defects, their size and orientation is of primary interest in quantitative NDE. A model for wave propagation through a weld between two plates is presented. An analytic method based on orthogonality relationship for Lamb modes is used to determine the reflected and transmitted fields for two welded plates. Some interesting experimental results have been obtained using guided waves inspection of hollow cylinders. Some frequencies are more sensitive to specific shapes and positions of defects.

Ultrasonic Measurements on β Cyclodextrin/Hydroxyapatite Composites for Potential Water Depollution

This paper presents structural, morphological and preliminary ultrasonic characterizations of the β-Cyclodextrin/hydroxyapatite (CD-HAp) composites synthesized by an adapted co-precipitation method. The structural and morphological properties were evaluated by Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Spectroscopy (EDX). The specific surface area, pore size and pore volume were determined using the methods of Brunauer–Emmett–Teller (BET) and Barrett–Joyner–Halenda (BJH), respectively. The novelty of our study consists in preliminary ultrasonic measurements conducted on CD-HAp composite, uniformly dispersed in distilled water. The benefit of this non-destructive method was to facilitate and simplify the characterization techniques of nanoparticles. Our experiments proved that the efficiency of lead ion removal by CD-HAp composites depended on the initial concentration of lead. The maximum adsorption capacity of the solid phase, for Pb2+ indicated a higher rate of removal by the CD-HAp_2. These adsorption results bring valuable insight into the beneficial contribution of our compounds, for the removal of heavy metal ions from aqueous solutions. Furthermore, in the present study, was evaluated the toxic effect of lead ions adsorbed by hydroxyapatite from contaminated water on HeLa cells.