Dynamics of the Structures and Non Destructive Testing

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Authors: A. Mahi, E.A. Adda-Bedia, A. Benkhedda
Abstract: The purpose of this paper is to present exact solutions for the free vibration of symmetrically laminated composite beams. The present analysis includes the first shear deformation theory and the rotary inertia. The analytical solutions take into account the thermal effect on the free vibration characteristics of the composite beams. In particular, the aim of this work is to derive the exact closed-form characteristic equations for common boundary conditions. The different parameters that could affect the natural frequencies are included as factors (aspect ratio, thermal load-to-shear coefficient, ply orientation) to better perform dynamic analysis to have a good understanding of dynamic behavior of composite beams. In order to derive the governing set of equations of motion, the Hamilton’s principle is used. The system of ordinary differential equations of the laminated beams is then solved and the natural frequencies’ equations are obtained analytically for different boundary conditions. Numerical results are presented to show the influence of temperature rise, aspect ratio, boundary conditions and ply orientation on the natural frequencies of composite beams.
Authors: L. Elmaimouni, J.E. Lefebvre, F.E. Ratolojanahary, A. Raherison, B. Bahani, T. Gryba
Abstract: Legendre polynomial method which describes the structure and incorporates automatically the boundary conditions in constitutive and propagation equations is used to model acoustic wave cylindrical resonators. It is the first time this method is applied to study standing rather than propagative waves. The advantage of this approach is, in a unique formulation, to take into account electric sources. The analytical and numerical resolutions are presented to highlight the potentialities of the Legendre polynomial approach. The vibration characteristics of piezoelectric discs with regard to diameter to thickness D/H ratios are analyzed by the three dimensional modeling approach through both modal and harmonic analyses. Resonance and antiresonance frequencies, electric input impedance, dispersion curves, field profiles and electromechanical coupling coefficient, easily obtained, are presented for PZT5A resonator piezoelectric discs. To validate our approach, the results using our 3D polynomial modelling of acoustic wave resonator are compared with those obtained by an approximated analytical method. The developed software proves to be very efficient to retrieve the radial modes of all orders.
Authors: Taoufiq Belhoussine Drissi, Bruno Morvan, Mihai Predoi, Jean Louis Izbicki, Pascal Pareige
Abstract: We are interested in a right junction of two plates of different materials (aluminum and copper) placed in contact edge to edge. The aim of this study is the interaction of Lamb waves with a defect located at the junction. The reflection and transmission of the fundamental symmetrical S0 wave is analyzed. The theoretical coefficients of reflection and transmission are obtained by a multi-modal approach based on the orthogonality relations involving different modes. Using the Finite Element Method (FEM), we estimate the limit value of the ratio between the dimension of the defect and the thickness of the structure, for which the multi-modal approach is applicable. In experimental and numerical studies, it is also brought to light the effects of diffraction by the defect.
Authors: Kossi Atchonouglo, Olivier Bonneau, Pascal Jolly, Claude Vallée
Abstract: Within the linear region, the oil-film force increment of journal bearing is a fourdegree- of-freedom linear system. This paper presents an experimental method to identify hybrid bearing coefficients. Under various testing conditions described, experimental data are required on a complex test rig. An inverse technique based on least square method in time domain is developped for the coefficients identification. It results from the experimental data exploitation that the linear stiffness and damping coefficients are sensitive to the pressure feed, but the mass coefficients are insensitive.
Authors: Christian Garnier, Toufik Djilali, Romain Brault, Sébastien Mistou
Abstract: The first aim of this study is to analyze the impact behavior of pre-loaded composite. Indeed, a bi-axial load is applied to the composite specimen, in order to keep in touch with a real case of composite fuselage. Then, this pre-loaded specimen is impacted by a pendulum. The used energy and velocity are weak in order to be in the case of low-energy and low-velocity impact. The second aim of this study is to develop and design a pendulum device to be integrated to the bi-axial fatigue loading. Moreover, two Non Destructive Inspections (Sonoscan and InfraRed Thermography) is used in order to establish links between pre-load and induced impact damage.
Authors: Ali Badidi Bouda, Mohammed S. Aljohani, Ahmed Mebtouche, Rafik Halimi, Wahiba Djerir
Abstract: A mechanical or thermal treatment of a material can change, among other things, the average grains size. It depends on temperature, holding time, cooling condition or rolling stress. The average grain size, as well as its influence on the propagation velocity and attenuation coefficient of ultrasonic waves, also affects the wave frequency propagating through the material. Grain size is an indicator of material fatigue. It can therefore be used in monitoring or fatigue damage prevention. In this paper, we study the effect of various heat treatments hence different steel average grain sizes on the ultrasonic wave frequency after crossing the material. We have performed the same experimental study on aluminum samples. The different grain sizes are obtained by rolling. The frequency shift measurement of longitudinal waves is achieved by immersion with two probes of different frequencies 2.25 and 5 MHz. The experimental results are shown as curves giving the frequencies depending on the grain size. Heat treatments on steel and aluminum rolling performed on the samples have yielded a grain sizes gradient. Our results are consistent with the theory because of the important path in the sample and in this case the down shift frequency is paramount. They show a direct relationship between the frequency shift and the average grain size. It is therefore possible to trace quantitatively to an average grains size from the frequency of an ultrasonic wave that has passed through this material and hence its thermal or mechanical fatigue state.
Authors: Marina Fazzini, Olivier Dalverny, Sébastien Mistou
Abstract: The aim of this work is to identify parameters driving constitutive equations of materials with displacement field measurements carried out by image stereo-correlation during an unidirectional tensile test. We evaluate two identification techniques. The first one is the virtual fields method which consists in writing the principle of virtual work with particular virtual fields. It is generally used in the case of linear elasticity and it requires a perfect knowledge of the model in terms of boundary condition since the virtual fields used must be kinematically admissible. This method allows to determine parameters by a direct and fast calculation, without iterations. The second method is the finite element model updating method. It consists in finding constitutive parameters that achieve the best match between finite element analysis quantities and their experimental counterparts. This method is more adaptable than the virtual field method but it needs to spend more calculation time.
Authors: Kamal Ait Tahar, Nora Harb
Abstract: The specific properties of material, such as resistance, the cost and the weight, become key factors in the decision making and the choice of vulgarization of material in its industrial and technological aspect. The choice of a resinous system used like stamps in the design of composites, depends on the mechanical performances and the cost of the resin. Currently the prohibitory cost of composite materials slows down the rise of their applications in certain technical fields. In this study, the physical and the mechanical characterization is presented, bearing on the resin of the type RESOW 55 E reinforced out of powders of different nature at different rate. The results of the mechanical tests carried out, show clearly, that the fracture is strongly influenced by the type and the rate of powder added in the matrix. In reinforcement, according to the results obtained with x-rays, one notes that there are no new chemical compounds formed in elaborate materials. The presence of powder does not modify the structure of polymer and that is confirmed by the x-rays analysis and spectrometric analysis. Based on experimental results, a model of Weibull strength distribution function has been established for each specimen. Finally, a confrontation of the theoretical and experimental results is carried out, based on probabilistic models.
Authors: Fabien Duco, Jean Pierre Faye, Serge Caperaa, Eric Reubrez
Abstract: France is a country composed of moderate seismic hazard regions but however vulnerable to earthquakes. Indeed, only a few parts of existing buildings have been built using paraseismic regulation. Several current large-scale seismic vulnerability assessment methods are used, as Hazus or Risk-UE, but they are inappropriate to the analysis of a specific building. In our case, we use an experimental approach to study the elastic behaviour of existing buildings: ambient vibration analyses seem to be an interesting way to determine the vulnerability. Ambient noise testing with Output-Only Modal Identification is a low-cost non-destructive method to provide vibration data from civil engineering structures like buildings. The interest of this method is to obtain dynamic parameters with only natural excitations: wind, traffic, human activity... In the frame of the “Plan séisme des Hautes-Pyrénées”, the building considered is the relatively regular 18-storey Ophite Tower located in Lourdes, France. The vibration measurements are conducted using a 24-channel system connected to an acquisition station. The modal parameters of this building (natural frequencies, modal shapes and damping) are calculated using the stochastic subspace identification method. These parameters, extracted from in situ data, are then used to calibrate a model. Having defined damage level criterion, the response motion, produced by seismic events, will lead to the determination of the vulnerability curves of Ophite Tower.

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