Short-fiber-reinforced-materials are widely used in industry today. In this paper, microstructure and modal analyses are performed on short-glass-fiber-reinforced polypropylene (PPGF) and short-natural-fiber-reinforced polypropylene (PPNF), to study possible links between the first natural frequency and fibers' orientation and quantify the associated variability. In view of this, different specimens were tested with clamped-free boundary conditions. The microstructural analysis, performed with micro-computed tomography studies fibers' properties in injection-molded plates. This study shows the importance of considering real fibers' orientation for modal predictions.

Despite numerous works over the past two decades, friction-induced vibrations, especially braking noises, are a major issue for transportation manufacturers as well as for the scientific community. To study these fugitive phenomena, the engineers need numerical methods to efficiently predict the mode coupling instabilities in a multiparametric context. The objective of this paper is to approximate the unstable frequencies and the associated damping rates extracted from a complex eigenvalue analysis under variability. To achieve this, a deep Gaussian process is considered to fit the non-linear and non-stationary evolutions of the real and imaginary parts of complex eigenvalues. The current challenge is to build an efficient surrogate modelling, considering a small training set. A discussion about the sample distribution density effect, the training set size and the kernel function choice is proposed. The results are compared to those of a Gaussian process and a deep neural network. A focus is made on several deceptive predictions of surrogate models, although the better settings were well chosen in theory. Finally, the deep Gaussian process is investigated in a multiparametric analysis to identify the best number of hidden layers and neurons, allowing a precise approximation of the behaviours of complex eigensolutions.

This paper presents a new method to efficiently approximate both linear buckling loads and associated mode shapes of finite element structures subject to perturbations. To achieve this, a coupling between a Reduced Order Model (ROM) based on the Homotopy Perturbation Method (HPM) and a Kriging model is presented here. The ROM maintains the link between eigenvalues, related eigenvectors and the dependencies between each eigenvector components, leading to a high precision level. The computational time is greatly reduced by the surrogate model which avoids the computation of modified finite element matrices for each prediction. Next, the capabilities of the method allow to efficiently handle the prediction, sensitivity and optimization steps of an uncertain propagation problem using fuzzy formalism. Additive Manufacturing is a powerful and impressive process but many factors can be responsible for relatively large discrepancies in the mechanical and geometrical characteristics of the manufactured structure. Lastly, a study shows how the proposed fuzzy strategy allows the prediction of the buckling variability of a set of lattice structures. (c) 2021 Elsevier Inc. All rights reserved.

ABSTRACT The evolution of mechanical properties of NR with carbon black fillers was examined after a thermal aging step through both experimentation and non-deterministic numerical simulations. A quantification of mechanical properties and associated variability is first proposed for a set of specimens exposed at different temperatures and exposure times. Second, a family of stretch–stress laws is numerically built with a James' hyperelastic model. Next, the whole of the behavior evolution is modeled with a Kriging model to quantify the effects of properties on a macroscopic stiffness, useful in dynamic simulations, and the least-favorable scenario is so determined. Finally, Arrhenius method is performed to numerically draw the evolution bounds of macroscopic stiffness as a function of aging exposure, followed by a comparison with a naturally aged suspension component. To our knowledge, the methodology developed has not already been proposed in this area.

This paper puts forward a projection technique for accurately calculating solutions of large Quadratic Eigenvalue Problem. The aim here is to stabilize the complex eigensolutions whilst reducing residual errors, especially when considering significant damping contribution or asymmetric stiffness matrices. Hence, more confident results can be obtained in the frequency band of interest. To achieve this, high order modes, calculated using the homotopy perturbation technique, are introduced in the projection step of the classical method. This numerical proposal is a generalization of the classical projection, based only on normal modes of the associated undamped problem. To evaluate the efficiency of the suggested method, a finite element application dedicated to a friction-induced vibration problem is investigated. (C) 2020 Elsevier Ltd. All rights reserved.

Injection-molded short-fiber-reinforced thermoplastics are widely used in today's industry. Nevertheless, their mechanical behavior is difficult to model, especially because of strong anisotropy induced by complex fiber distributions of orientation. Moreover, the intrinsic variability of plant fibers' properties leads to an even more complex behavior than with mineral fibers and therefore increase the uncertainty for behavior prediction of these materials. The aim of this review is to provide basic and more specific knowledge about dealing with the uncertainty related to injection molded short-plant-fiber-reinforced thermoplastics behavior, focusing on variability induced by both injection-molded process and natural variability of plant fibers properties. To achieve this goal, it is important to understand the behavior of SFRT before considering the uncertainty induced by the use of natural fibers. Thus, in the first place, the authors have chosen to limit the sources of uncertainty related to fibers by studying the case of a short-glass-fibers-reinforced thermoplastic. Then, after discussing the sources of uncertainty related to the use of natural fibers, the methods for the quantification, the propagation and the management of uncertainties are analyzed.

Transport industry and, more specifically, railway industry, is confronted with a permanent need of improvement of its products. The competitiveness of rolling stock does not come only from low-cost production, but also from wise-calculated lifecycle costs. Nowadays, many contracts for railway operators include not only rolling stock, but also its maintenance services throughout its lifetime, which may reach up to 30% of global costs. Hence, deep knowledge about the system’s ageing is a strong asset to ensure a good performance, both on quality of service and financial costs. Rubber parts are widely used in railway technology because of their mechanical properties, providing both stiffness and, to a certain extent, additional damping and vibration filtering. Unlike metallic parts, whose mechanical properties remain relatively stable, rubber’s behaviour can change throughout a lifecycle, due to service loads and environmental influence. Such changes might have an impact on the system’s overall behaviour and lead to undesirable scenarii. For a given bogie model, we seek to estimate the stiffness variation of some rubber parts, which are deemed critical for safe operation.

The paper focuses on the definition of a reduced order model for linear modal analysis. The aim is to supply a suitable mathematical alternative tool compatible for multiparametric analysis of large finite element model considering numerous variable parameters, numerous mode shapes and significant levels of variation. The initial full eigenvalue problem is so replaced by a reduced one considering an efficient projection basis. To build it, we propose to combine homotopy transformation and perturbation technique for each parameter direction to define a reduced order model compatible with the design space. Finally, a complete finite element application highlights the capabilities of the proposal in terms of precision and computational time. (C) 2017 Elsevier Ltd. All rights reserved.

The train/track interaction models available in the literature introduce defects on wheel or rail but they usually do not consider combination of them. The aim of this paper is to provide a dynamic model of wheel/rail interaction able to take into account any kind of defects. For this purpose, a time-domain investigation is done to predict the normal contact force and displacements of wheel and rail. The model includes a multi-body representation of vehicle and track, coupled by a contact model based on the Distributing Points Reacting Spring (DPRS) procedure which allows the local three-dimensional description of the surfaces in contact and the use of actual geometries. After comparison with a finite-element model, it appears that the present model gives accurate results while being little-time consuming. An example of combination of defects is then presented and discussed.

The aim of this paper is to improve the correlation between the experimental and the numerical prediction of unstable frequencies for automotive brake systems considering uncertainty. First, an experimental quantification of uncertainty and a discussion analysing the contributions of uncertainty to a numerical squeal simulation are proposed. Frequency and transient simulations are performed considering nominal values of model parameters, determined experimentally. The obtained results are compared with those derived from experimental tests to highlight the limitation of deterministic simulations. The effects of the different kinds of uncertainty detected in working conditions of brake system, the pad boundary condition, the brake system material properties and the pad surface topography are discussed by defining different unstable mode classes. Finally, a correlation between experimental and numerical results considering uncertainty is successfully proposed for an industrial brake system. Results from the different comparisons reveal also a major influence of the pad topography and consequently the contact distribution.

This paper presents a complete method to carry out a fuzzy study of a friction-induced vibration system and to analyze the effects of uncertainty on the output data of a stability problem. The proposed approach decomposes the fuzzy problem into interval problems and calculates interval output solutions by optimization. Next, each calculation of the stability problem output data, which is useful during the optimization process, is reanalyzed by integrating fuzzy logic controllers for the static step and homotopy development and projection techniques for the modal step. Finally, the obtained results are compared with Zadeh's extension principle reference.

This paper presents a numerical strategy to reanalyze the modified frequency stability analysis of friction induced vibration problem. The stability analysis of a mechanical system relies on several coupling steps, namely a non-linear static analysis followed by linear and complex eigenvalue problems. We thus propose a numerical strategy to perform more rapidly multiple complex eigenvalue analyses. This strategy couples three methods namely, Fuzzy Logic Controllers to manage frictional contact problem, homotopy developments and projection techniques to reanalyze the projection matrices and component mode synthesis to calculate the modified eigensolutions. A numerical application is performed to highlight the efficiency of the strategy and a discussion is proposed in terms of precision and computational time.

Purpose– The purpose of this paper is to expand the previously published fuzzy logic controller for contact method to normal frictionless contact for solving mechanical frictional contact problems. The secondary aim is to integrate a reduction model for each component in contact to decrease the size of the global finite element contact problem.Design/methodology/approach– The proposed strategy relies on the design of two fuzzy logic controllers currently used in the automation domain. These controllers are considered to link normal and tangential gaps (for sticking conditions) with normal and tangential contact loads. A direct consequence of integrating a control-based approach into the numerical solving approach is the decomposition of the non-linear problem into a set of linear problems.Findings– With this new strategy, no tangent or coupling matrix is defined for the contact problem that allows to consider a projection matrix to reduce the size of each component in contact and subsequently to decrease the associated computational time. As in condensation techniques, this matrix is composed of both modal bases of each component in contact and static modes that capture behaviors at the contact interface. Moreover, the proposed numerical application highlights the efficiency of the proposal in terms of computation time and precision of contact data.Research limitations/implications– The developments are currently implemented in Matlab only for 2D static numerical applications. Therefore, as obtained results are very promising in terms of precision and computational time, the objective is to complete the proposed method in future research to manage frictional contact for 3D finite element models in a dynamic context.Originality/value– In conclusion, this paper highlights the interest of studying mechanical frictional contact problems by considering fuzzy logic control approaches.

Purpose – The purpose of this paper is to present a new way to solve numerically a mechanical frictionless contact problem within a context of multiple sampling, frequently used to design robust structures. Design/methodology/approach – This paper proposes to integrate a control-based approach, currently used in automation domain, for the solving of non-linear mechanical problem. More precisely, a fuzzy logic controller is designed to create a link between the normal gaps identified between the bodies and the normal contact pressures applied at the interface. Findings – With this new strategy, the initial non-linear problem can be decomposed into a set of reduced linear problems solved using the finite element method. A projection built from the modal bases of each component in contact is considered to reduce computational time. Moreover, the proposed numerical applications highlight an interesting compromise between computation time and precision of contact data. Research limitations/implications – Currently, the proposed Fuzzy Logic Controller for Contact method has been developed for a frictionless contact problem in the case of 2D numerical applications. Therefore, as obtained results are very interesting, it will be possible to expand on these works in a future works for more complex problems including friction, 3D model and transient dynamic responses by adding other controllers. Originality/value – In conclusion, this paper highlights the interest of studying a contact problem by considering automation approaches and defines the basis of future multidisciplinary works.