Alexandre Loredo

Numerical vibroacoustic analysis of plates with constrained-layer damping patches

A numerical vibroacoustic model that can manage multilayered plates locally covered with damping patches is presented. All the layers can have an on-axis orthotropic viscoelastic behavior. Continuity of displacements and transverse shear stresses at each interface is enforced, which permits to write the entire displacement field in function of the displacements of the--common--first layer, leading to a two-dimensional plate model. The problem is then discretized by Rayleigh-Ritzs method using a trigonometric basis that includes both sine and cosine functions in order to treat various boundary conditions. The excitation can be of mechanical kind (concentrated or distributed forces) or of acoustic kind (plane wave of any incidence, diffuse field, etc.). The model permits to compute different vibroacoustic indicators: the mean square velocity of the plate, the radiation efficiency, and the transmission loss. Comparisons between the present model and numerical results from literature or finite element computations show that the model gives good results in both mechanical and acoustical aspects. Then, a comparison of the effects of different distributions of patches is presented. The role of the surface covering rate is first discussed, followed by a study involving different geometries for the same surface covering rate.

Exact 3D solution for static and damped harmonic response of simply supported general laminates

Abstract The state-space method is adapted to obtain three dimensional exact solutions for the static and damped dynamic behaviors of simply supported general laminates. The state-space method is written in a general form that permits to handle both cross-ply and antisymmetric angle-ply laminates. This general form also permits to obtain exact solutions for general laminates, albeit with some constraints. For the general case and for the static behavior, either an additive term is added to the load to simulate simply supported boundary conditions, or the plate bends in a particular way. For the dynamic behavior, the general case leads to pairs of natural frequencies for each order, with associated mode shapes. Finite element simulations have been performed to validate most of the results presented in this study. As the boundary conditions needed for the general case are not so straightforward, a specific discussion has been added. It is shown that these boundary conditions also work for the two aforementioned laminate classes. The damped harmonic response of a non-symmetrical isotropic sandwich is studied for different frequencies around the fundamental frequency. The static and undamped dynamic behaviors of the [−15/15], [0/30/0] and [−10/0/40] laminates are studied for various length-to-thickness ratios.

Characterisation of cw Nd : YAG laser keyhole dynamics

Abstract The paper concerns laser–matter interaction characterisation. In this work, we use a rapid CCD camera located coaxially to the laser beam and we compare recorded images with those obtained by numerical modelling. Because images are difficult to understand, we compute thermal radiation emitted by a keyhole of fixed geometry and we adjust it trying to approach the camera record. The modelling treats radiative heat transfer within the keyhole and determines the sensor illumination map. By adjusting the geometrical characteristics of the hole, we seek to obtain the image that corresponds as well as possible to the realised experiment. Results are compared with other experimental methods simultaneously performed plume characterisation with an electric probe and spectrometric analysis. They show the existence of two distinct behaviours of the keyhole: a pseudo-steady state associated with regular and pseudo-constant keyhole shapes, low frequencies of electric current in the plume, and generally good welding results, and a highly dynamic mode associated with irregular and rapidly varying keyhole shapes, high frequencies in the plume current and generally poor welding results.

A multilayer anisotropic plate model with warping functions for the study of vibrations reformulated from Woodcock's work

Abstract In this paper, a suitable model for static and dynamic analysis of inhomogeneous anisotropic multilayered plates is described. This model takes into account the variations of the transverse shear strains through the thickness of the plate by means of warping functions. Warping functions are determined by enforcing kinematic and static assumptions at the interfaces. This model leads to: a 10×10 stiffness matrix coupling to each other the membrane strains, the bending and torsion curvatures, and the x and y-derivatives of the transverse shear strains; and a classical 2×2 transverse shear stiffness matrix. This model has been proven to be very efficient, especially when high ratios between the stiffnesses of layers – up to 106 – are present. This work is related to Woodcocks model, so it can be seen as a reformulation of his work. However, it brings several enhancements: the displacement field is made explicit; it is reformulated with commonly used plate notations; laminate equations of motion are fully detailed; the place of this model among other plate models is now easy to see and is discussed; the link between this formulation and the original one is completely written with all necessary proofs; misses and errors have been found in the energy coefficients of the original work and have been corrected; it is now easy to improve or to adapt the model for specific applications with the choice of refined or specific warping functions. Static deflection and natural frequencies for isotropic and anisotropic sandwich plates are given and compared to other models: they show that the present model is very accurate for the simulation of such structures.

Numerical investigation of laser beam shaping for heat transfer control in laser processing

This article presents a thermal finite volume model adapted to investigate laser processes. It is specially developed to treat moving heat sources with phase changes, melting and vapourisation. Heat transfer control in laser processing is particularly useful when processes must respect prescribed temperatures, or more generally, prescribed constraints. These processes involve generally several laser sources, or non-conventional power distribution. Hence, they have numerous parameters to set. Experimental optimisation is difficult and may be expansive. The numerical model is a useful and cheaper tool for development of those complex processes. For example in this article, two special laser processes are investigated: control of high carbon steel welded line cooling, zinc-coated sheets lap welding.

A multilayered plate theory with transverse shear and normal warping functions

Abstract A multilayered plate theory taking into account transverse shear and normal stretching is presented. The theory is based on a seven-unknowns kinematic field with five warping functions. Four warping functions are related to the transverse shear, the fifth to the normal stretching. The warping functions are issued from exact three-dimensional solutions. They are related to the variations of transverse shear and normal stresses computed at specific points for a simply supported bending problem. Reddy, Cho–Parmerter and (a modified version of) Beakou–Touratier theories have been retained for comparisons. Extended versions of these theories, able to manage the normal stretching, are also considered. These theories, which use the same kinematic field with different warping functions, are compared to analytical solutions for the bending of simply supported plates. Various plates are considered, with special focus on low length-to-thickness ratios: an isotropic plate, two homogeneous orthotropic plates with ply orientation of 0° and 5°, a [ 0 / c / 0 ] sandwich panel and a [ - 45 / 0 / 45 / 90 ] s composite plate. Results show that models are more accurate if their kinematic fields (i) depend on all material properties (not only the transverse shear stiffnesses), (ii) depend on the length-to-thickness ratios and (iii) present a coupling between the x and y directions.

Two multilayered plate models with transverse shear warping functions issued from three dimensional elasticity equations

Abstract A multilayered plate theory which uses transverse shear warping functions is presented. Two methods to obtain the transverse shear warping functions from three-dimensional elasticity equations are proposed. The warping functions are issued from the variations of transverse shear stresses computed at specific points of a simply supported plate. The first method considers an exact 3D solution of the problem. The second method uses the solution provided by the model itself: the transverse shear stresses are computed integrating equilibrium equations. Hence, an iterative process is applied, the model is updated with the new warping functions, and so on. Once the sets of warping functions are obtained, the stiffness and mass matrices of the models are computed. These two models are compared to other models and to analytical solutions for the bending of simply supported plates. Four different laminates and a sandwich plate are considered. Their length-to-thickness ratios vary from 2 to 100. An additional analytical solution that simulates the behavior of laminates under the plane stress hypothesis – shared by all the considered models – is computed. Both presented models give results very close to this exact solution, for all laminates and all length-to-thickness ratios.