Sébastien Besset

Optimization of the dynamic behavior of vehicle structures by means of passive interface controls

As a form of passive control, padding rubber layers onto the most heavily deformed zones of a system can improve the dynamic behavior and the acoustic comfort of a vehicle system. This paper proposes an extensive hybrid modal synthesis method in order to study coupled fluid-structure systems, in retaining a few degrees of freedom. Modal criteria, corresponding to noise transmission paths between substructures in the system, have been derived to characterize the dynamic phenomenon from a modal view. These criteria were then substituted by Kriging interpolation models to avoid prohibitive simulation steps during optimization of the complex system. Once the mathematical models of the investigated modal criteria were established and the multi-objective functions for rubber characteristics defined, an approximate optimal solution leading to superior dynamic performance could be obtained based on a genetic algorithm. The analytical results and numerical experiments conducted have also justified the efficiency of our proposed strategy.

Shape Optimization Under Vibroacoustic Criteria in the Mid-High Frequency Range

This paper deals with shape optimization issues under vibroacoustic criteria. The aim of the conducted research is to minimize the energy density in the cavity by changing its geometry parameters. The energy density is obtained through an energy method called simplified energy method (MES). The optimization method is based on a transformation function mapping 3D cavity surface on a 2D domain. The optimization process directly relies on this function and thus avoids remeshing of the geometry. The proposed method allows to describe the geometry through Bezier, Bspline and NURBS parametrization. To illustrate the method, we process a shape optimization on a simple acoustic cavity.

Reduction Methods Applied to Aircraft Brake Squeal Prediction and Simulation

Aircraft braking systems may be subjected to friction-induced vibrations, during which the brake is unstable and behaves as a source of mechanical vibrations. This is an issue for aircraft brake manufacturers because it may jeopardize structural integrity due to accelerated fatigue life or generate discomfort for the aircraft crew and passengers. Hence, there is a need for instability simulation and prediction methods that can be used as early as the design stage. At this stage, finite element models are available, but their sizes are prohibitive as far as vibration-level prediction is concerned, thus requiring model reduction. This paper presents a comparative study between several modal reduction methods, among them the well-known Craig–Bampton method. The reference model to be reduced is a full brake system finite element model. The system stability is assessed by means of the classical complex eigenvalue analysis. Convergence of the implemented reduction strategies is studied. Double modal synthesis i...

Influence of Physical Parameters and Operating Conditions for Structural Integrity of Mechanical System Subjected to Squeal Noise

This work proposes to study the effects of physical parameters and loading conditions on both dynamic and acoustic responses of a brake system subjected to squeal. A simplified brake system model composed of a disc and a pad is investigated. The friction interface is modeled by introducing linear and non-linear stiffnesses at several local nodes to model contact. The classical Coulomb law is applied to model friction and the friction coefficient is assumed to be constant. A stability analysis of this system is performed with respect to the friction coefficient and the hydraulic brake pressure. Then self-excited vibrations are investigated for two cases of loading conditions: static loading and ramp loading. Time responses for these cases are significantly different: the case with ramp loading presents higher amplitude of velocity than the static loading case. For the case with ramp loading, the spectrum analysis performed by the Continuous Wavelet Transform, shows the appearance of the fundamental frequencies of unstable modes but also their harmonics and combinations frequencies. Sound pressures radiated during squeal event present different peculiar patterns of directivity for both cases and for a progressive load, the levels are significantly higher.

Optimization of the Dynamic Behaviour of Complex Structures Based on a Multimodal Strategy

The use of a modal approach to describe a structure from the standpoint of optimizing its dynamic behavior offers multiple advantages. Once modal matrices have been computed, optimization criteria can be readily defined. Both the dynamic amplification phenomena and dynamic coupling between substructures can then be described using just a small number of degrees of freedom. Furthermore, it becomes possible to link the criteria to the modal parameters used in the systemic procedure. In this chapter, we will propose optimization criteria based on a multimodal description of complex structures. The modal synthesis technique presented herein is based on the double and triple-modal synthesis proposed by Besset & Jezequel (2008a;d), as well as on classical component mode synthesis methods like those developed by Craig & Bampton (1968) or Hurty (1965). According to these modal synthesis techniques, many boundary degrees of freedom are capable of remaining; in such cases, numerical costs will also remain high. In order to avoid a high-cost situation, we are proposing generalized modal synthesis methods that operate by introducing generalized boundary coordinates in order to describe substructure connections: this procedure is called a “double modal synthesis”. In addition, we are proposing another procedure to analyze structures coupled with fluid. This second procedure will then be called “triple modal synthesis”. The first modal synthesis is classical; it consists of representing the interior points of the fluid by acoustic modes. When considering a formulation in force, the pressure on boundary points is set equal to zero. Using a formulation in displacement, cavity modes are introduced, generating a correspondence to the free modes of a structure. The second modal synthesis consists of describing the boundary forces between the fluid and each substructure through use of a set of loadedmodes. Lastly, the third modal synthesis consists of describing the boundary forces between each substructure by introducing another set of loaded modes. Complex structures often include hollow parts and stiffeners, both of which require very accurate analysis in order to obtain satisfactory results. In this chapter, the term “hollow parts” will denote the formed steel and stiffeners that make up the skeleton of a structure. In complex structures such as automobiles, stiffeners and formed steel parts, which compose the skeleton of the structure, these parts are most responsible for overall structural behavior. To analyze these elements, the method used is the one proposed in Besset & Jezequel (2008b). 5

Sensitivity of Shape Parameters of Brake Systems Under Squeal Noise Criteria

We propose in this paper to deal with squeal noise reduction of brake systems through their shape optimization during the design step. We first expose the FEM model used to generate the stability diagram representing the squeal noise behavior of a given brake system shape. We then propose an objective function able to be included in a minimization problem and based on the stability diagram. We use then a parallel code to browse the objective function response surface through a Latin Hypercube Sampling design of experiment. A Self Organizing Map is then generated to expose the sensibility of our objective function to seven shape parameters of the FEM brake system. We present and analysis the SOM results for further optimization steps.

Hydro-Mechanical Coupling in Unstable Aircraft Braking Systems

Aircraft braking systems may be subjected to friction-induced vibrations, during which the brake is unstable and behaves as a source of mechanical vibrations. This is an issue for aircraft brake manufacturers as it may jeopardize structural integrity due to accelerated fatigue life, or generate discomfort for the aircraft crew and passengers. The important cost associated to the occurrence of this phenomenon motivates the development of instability simulation and prediction methods that can be used as early as the design stage.

Reducing noise levels in vehicles by padding rubber layers at structural interfaces

This paper deals with the noise reduction of coupled fluid-structure system in a low frequency band. Passive rubber layer is introduced to junction between substructures to reduce noise in the cavity. The noise level and the vibration in the system can be modified by changing rubber layer configurations. A hybrid modal synthesis is proposed to investigate the forced responses of fluid-structure system, which allows studying the system behavior with few degrees of freedom. An optimization procedure following an interpolation process is provided in the interest of reducing noise level in the cavity. The optimal design configuration is then analyzed from a modal overview. The efficiency of this noise reduction strategy is demonstrated by a numerical example.

Methodology for the Design of the Geometry of a Cavity and Its Absorption Coefficients as Random Design Variables Under Vibroacoustic Criteria

Reducing the noise level in the acoustic cavities is the important problem when treating inflight conditions of commercial planes or boats. Shape optimization of the acoustic cavity that will take into account the geometrical and material uncertainties, arising during the manufacturing process, is presented in this paper. The noise level is controlled by minimizing the energy density in the cavity, obtained through an energy method called Simplified Energy Method. Such formulation is based on our previous published work where transformation function mapping 3D cavity surface on a 2D domain was proposed. The optimization process directly relies on this function and thus avoids remeshing of the geometry. Robust optimization is performed using the nondominated sorting genetic algorithm (NSGA-II) together with the Kriging surrogate model. Influence of geometrical and material characteristics on the optimal solution is identified.

Surrogate models for efficient stability analysis of brake systems

This study assesses capacities of the global sensitivity analysis combined together with the kriging formalism to be useful in the robust stability analysis of brake systems, which is too costly when performed with the classical complex eigenvalues analysis (CEA) based on finite element models (FEMs). By considering a simplified brake system, the global sensitivity analysis is first shown very helpful for understanding the effects of design parameters on the brake systems stability. This is allowed by the so-called Sobol indices which discriminate design parameters with respect to their influence on the stability. Consequently, only uncertainty of influent parameters is taken into account in the following step, namely, the surrogate modelling based on kriging. The latter is then demonstrated to be an interesting alternative to FEMs since it allowed, with a lower cost, an accurate estimation of the systems proportions of instability corresponding to the influent parameters.