Denis Duhamel

Finite element prediction of wave motion in structural waveguides

A method is presented by which the wavenumbers for a one-dimensional waveguide can be predicted from a finite element (FE) model. The method involves postprocessing a conventional, but low order, FE model, the mass and stiffness matrices of which are typically found using a conventional FE package. This is in contrast to the most popular previous waveguide/FE approach, sometimes termed the spectral finite element approach, which requires new spectral element matrices to be developed. In the approach described here, a section of the waveguide is modeled using conventional FE software and the dynamic stiffness matrix formed. A periodicity condition is applied, the wavenumbers following from the eigensolution of the resulting transfer matrix. The method is described, estimation of wavenumbers, energy, and group velocity discussed, and numerical examples presented. These concern wave propagation in a beam and a simply supported plate strip, for which analytical solutions exist, and the more complex case of a viscoelastic laminate, which involves postprocessing an ANSYS FE model. The method is seen to yield accurate results for the wavenumbers and group velocities of both propagating and evanescent waves.

Viscoroute 2.0 : a tool for the simulation of moving load effects on asphalt pavement

ABSTRACT As shown by strains measured on full-scale experimental aircraft structures, traffic of slow-moving multiple loads leads to asymmetric transverse strains that can be higher than longitudinal strains at the bottom of asphalt pavement layers. To analyze this effect, a model and software called ViscoRoute have been developed. In these tools, the structure is represented by a multilayered half-space, the thermo-viscoelastic behaviour of asphalt layers is accounted for by the Huet-Sayegh rheological law, and loads are assumed to move at constant speed. The paper presents a comparison of results obtained with ViscoRoute to results stemming from the specialized literature. For thick asphalt pavement and several configurations of moving loads, other ViscoRoute simulations confirm that it is necessary to incorporate viscoelastic effects in the model to predict the pavement behaviour and to anticipate possible damages in the structure.

IDENTIFICATION OF POLYNOMIAL CHAOS REPRESENTATIONS IN HIGH DIMENSION FROM A SET OF REALIZATIONS

This paper deals with the identification in high dimensions of a polynomial chaos expansion of random vectors from a set of realizations. Due to numerical and memory constraints, the usual polynomial chaos identification methods are based on a series of truncations that induce a numerical bias. This bias becomes very detrimental to the convergence analysis of polynomial chaos identification in high dimensions. This paper therefore proposes a new formulation of the usual polynomial chaos identification algorithms to avoid this numerical bias. After a review of the polynomial chaos identification method, the influence of the numerical bias on the identification accuracy is quantified. The new formulation is then described in detail and illustrated using two examples.

Karhunen-Loève expansion revisited for vector-valued random fields: Scaling, errors and optimal basis.

Due to scaling effects, when dealing with vector-valued random fields, the classical Karhunen-Loeve expansion, which is optimal with respect to the total mean square error, tends to favorize the components of the random field that have the highest signal energy. When these random fields are to be used in mechanical systems, this phenomenon can introduce undesired biases for the results. This paper presents therefore an adaptation of the Karhunen-Loeve expansion that allows us to control these biases and to minimize them. This original decomposition is first analyzed from a theoretical point of view, and is then illustrated on a numerical example.

Influence of Road Texture on Tyre/Road Contact in Static Conditions: Numerical and Experimental Comparison

ABSTRACT This paper deals with the influence of road texture on normal pressure distribution for tyre/road contact in statics, within the framework of rolling noise prediction. A contact model is developed in statics where the tyre tread is modelled by an elastic half-space and the road surface by several perfectly rigid asperities. The problem is solved using a Two-scale Iterative Method (TIM) which is fast and efficient. The numerical results give high resolution contact patterns for real road surfaces. Predicted results are compared to contact pressures measured between a slick tyre and several road surfaces. The agreement is fairly acceptable by keeping in mind both the precision of the measurement device and the simplicity of the model. The best correlations are obtained for model surfaces composed of spherical punches and real road surfaces of moderated or high macro-texture. The results are less conclusive for road surfaces of fine macro-texture. The efficiency of the TIM at a tyre/road contact scale is an encouraging first step before introducing dynamical effects.

A Posteriori Error and Optimal Reduced Basis for Stochastic Processes Defined by a Finite Set of Realizations

The use of reduced basis has spread to many scientific fields for the past 50 years to condense the statistical properties of stochastic processes. Among these bases, the classical Karhunen--Loeve basis corresponds to the Hilbertian basis that is constructed as the eigenfunctions of the covariance operator of the stochastic process of interest. The importance of this basis stems from its optimality in the sense that it minimizes the total mean square error. When the available information about this stochastic process is characterized by a limited set of independent realizations, the covariance operator is not perfectly known. In this case, there is no reason for the Karhunen--Loeve basis associated with any estimator of the covariance that is not converged to still be optimal. This paper therefore presents an adaptation of the Karhunen--Loeve expansion in order to characterize optimal basis for projection of stochastic processes that are characterized only by a relatively small set of independent realizat...

A recursive approach for the finite element computation of waveguides

Abstract The finite element computation of structures such as waveguides can lead to heavy computations when the length of the structure is large compared to the wavelength. Such waveguides can in fact be seen as one-dimensional periodic structures. In this paper a simple recursive method is presented to compute the global dynamic stiffness matrix of finite periodic structures. This allows to get frequency response functions with a small amount of computations. Examples are presented to show that the computing time is of order log 2 N where N is the number of periods of the waveguide.

A continuum model for granular materials taking into account the no-tension effect

This paper presents a phenomenological continuum model describing no-tension effects observed in granular materials. Constitutive laws are derived from a strain-energy function, which must vanish in the positive stress directions. Computational aspects are then investigated, wherein the finite element formulation is developed in the principal deformation directions. Last, a numerical example of a ballast structure will be outlined for illustrative purposes.

Measurement of active control efficiency around noise barriers

Abstract This paper presents results of measurements of active noise control efficiency around noise barriers in an outdoor experiment around a real wall. The study is here limited to stationary noise, either harmonic or pink noise, created by a loudspeaker and controlled with the help of loudspeakers as secondary sources. The aim is to reduce the sound pressure in the shadow zone where error microphones are placed. The purpose of the experiment is mainly to find the space and frequency domains over which the control is efficient and to give an estimate of the supplementary attenuation provided by the actively controlled noise barrier over a classical one. The second purpose is to estimate the influence of the secondary source and error microphone positions and the influence of the number of sources and microphones used on the performances of the system. In each case comparisons are made with values calculated by a boundary integral equation software in order to validate this tool and then to be able to simulate the system efficiency from the knowledge of its different parameters.

A discrete element study of settlement in vibrated granular layers: role of contact loss and acceleration

This paper deals with the vibration of granular materials due to cyclic external excitation. It highlights the effect of the acceleration on the settlement speed and proves the existence of a relationship between settlement and loss of contacts in partially confined granular materials under vibration. The numerical simulations are carried out using the Molecular Dynamics method, where the discrete elements consist of polygonal grains. The data analyses are conducted based on multivariate autoregressive models to describe the settlement and permanent contacts number with respect to the number of loading cycles.