Vibration reduction on city buses: Determination of optimal position of engine mounts

International audience; This study is composed of three essential parts. The first part describes an indirect semi-experimental method which is used to reconstruct the excitation force of an operating diesel engine from the acceleration data measured at the mounting points. These internal forces can not be directly measured with force sensors; they have to be derived from the dynamic deformation of the engine support, so a theoretical analysis is carried out to derive the equations for the force re-construction.The second part deals with prevention of low frequency vibration of the powertrain from spreading to the rest of the vehicle. Three uncoupling techniques are used to minimize these v…

Latin hypercube sampling with inequality constraints

International audience; In some studies requiring predictive and CPU-time consuming numerical models, the sampling design of the model input variables has to be chosen with caution. For this purpose, Latin hypercube sampling has a long history and has shown its robustness capabilities. In this paper we propose and discuss a new algorithm to build a Latin hypercube sample (LHS) taking into account inequality constraints between the sampled variables. This technique, called constrained Latin hypercube sampling (cLHS), consists in doing permutations on an initial LHS to honor the desired monotonic constraints. The relevance of this approach is shown on a real example concerning the numerical w…

Numerical support for laser welding of zinc-coated sheets process development

Abstract A lap welding process for zinc-coated sheets has been developed with the help of numerical simulations. This process has been improved and is now compatible with industrial requirements. The zinc boiling point (1180 K) is lower than the steel melting point (1800 K). Consequently, a violent boiling of zinc in melted steel produces serious defects in the seam. To get round this difficulty, we choose to consider a two-spots process: the first spot vaporizes the zinc coating at the interface; the second one welds the sheets. Previously, we develop a numerical model that permits a process parameters choice and limits the plan of experimentations. The zinc ablation spotlight shape is cho…

Numerical vibroacoustic analysis of plates with constrained-layer damping patches

International audience; 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-Ritz's 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 distri…

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

International audience; 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 …

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 functio…

Numerical Study of Zinc Coated Car Body Laser Welding

A theoretical model for laser and powder particles interaction during laser cladding

Abstract Interactions between the laser and the powder particles lead to attenuation of the laser and make the powder particles temperatures raise. According to given stream spread and speed of the powder particles, their temperature distribution at the surface of the workpiece is calculated. The attenuation of the laser induced by the cloud is also computed. These results are plotted for the case of a Gaussian distribution. Results show that with the increasing of the powder jet incidence angle, both temperature distribution of powder particles and attenuation of the laser have very different profiles. Their effects on the clad should be considered for modelling of laser cladding.

Complex power distribution analysis in plates covered with passive constrained layer damping patches

International audience; The vibration of a plate partially covered with a passive constrained layer damping (PCLD) patch is studied from an energetic point of view. The damped plate is excited by an acoustic plane wave. The study is done with a numerical two-dimensional multilayer plate model. Results of the present model are compared to those obtained with three-dimensional finite element models. It is shown that the present model gives accurate results, even for the layer's inner behavior. It is less expansive in terms of computational cost; hence, it can simulate efficiently the structure for higher frequencies. Mathematical formulas for complex mechanical power are presented, and the li…

A Multilayered Plate Theory with Transverse Shear and Normal Warping Functions

A multilayered plate theory which takes 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 behaviour, the fifth is related 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 s…

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 method…

Generalized inverse of the compliance tensor, and behaviour of incompressible anisotropic materials - Application to damage

Before the final rupture, most structural materials exhibit an import damage in the form of microvoids. The overall behaviour of a damaged elastic material depends on the void volume fraction f. Undamaged polymers are generally considered as incompressible elastic. Metals at high temperature may be considered as linearly viscoplastic. Thus the undamaged material may be described by an incompressible behaviour, while the overall behaviour of the damaged material is compressible depending on the void volume fraction. The transition from a compressible to an incompressible behaviour leads to a singular compliance matrix and an undefined rigidity matrix. The generalized inverse of the complianc…

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 p…

Global sensitivity analysis in welding simulations -- what are the material data you really need ?

In this paper, the sensitivity analysis methodology is applied to numerical welding simulation in order to rank the importance of input variables on the outputs of the code like distorsions or residual stresses. The numerical welding simulation uses the finite element method, with a thermal computation followed by a mechanical one. Classically, a local sensitivity analysis is performed, hence the validity of the results is limited to the neighbourhood of a nominal point, and cross effects cannot be detected. This study implements a global sensitivity analysis which allows to screen the whole material space of the steel family mechanical properties. A set of inputs of the mechanical model-ma…

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 be…

Heat transfer in semi-transparent materials during laser interaction

Abstract A model of energy exchange, based on the finite element method is specially developed to determine the thermal field for semi-transparent polymers irradiated by laser. Our model, which uses the finite element method, allows to define the laser and specific structure characteristics in terms of density of power, speed and shape of the spotlight, material coefficient absorption, etc. The model has been experimentally validated by measuring the thermal response induced by the laser source. The experimental part of the study has been performed using a semiconductor laser diode source and an infrared thermography camera.

A family of higher-order single layer plate models meeting Cz0-requirements for arbitrary laminates

Abstract In the framework of displacement-based equivalent single layer (ESL) plate theories for laminates, this paper presents a generic and automatic method to extend a basis higher-order shear deformation theory (polynomial, trigonometric, hyperbolic…) to a multilayer C z 0 higher-order shear deformation theory. The key idea is to enhance the description of the cross-sectional warping: the odd high-order C z 1 function of the basis model is replaced by one odd and one even high-order function and including the characteristic zig-zag behaviour by means of piecewise linear functions. In order to account for arbitrary lamination schemes, four such piecewise continuous functions are consider…