On the properness condition for modal analysis of non symmetric second order systems

International audienceNon symmetric second order systems can be found in several engineering contexts, including vibroacoustics, rotordynamics, or active control. In this paper, the notion of properness for complex modes is extended to the case of non self-adjoint problems. The properness condition is related to the ability of a set of complex modes to represent in an exact way the behavior of a physical second order system, meaning that the modes are the solutions of a quadratic eigenvalue problem whose matrices are those of a physical system. This property can be used to identify the damping matrices which may be difficult to obtain with mathematical modeling techniques. The first part of the paper demonstrates the properness condition for non symmetric systems in general. In the second part, the authors propose a methodology to enforce that condition in order to perform an optimal reconstruction of the "closest" physical system starting from a given basis complex modes. The last part is dedicated to numerical and experimental illustrations of the proposed methodology. A simulated academic test case is first used to investigate the numerical aspects of the method. A physical application is then considered in the context of rotordynamics. Finally, an experimental test case is presented using a structure with an active control feedback. An extension of the LSCF identification technique is also introduced to identify both left and right complex mode shapes from measured frequency response functions

Robust design of spot welds in automotive structures : a decisionmaking methodology

International audienceAutomotive structures include thousands of spot welds whose design must allow the assembled vehicle to satisfy a wide variety of performance constraints including static, dynamic and crash criteria. The objective of a standard optimization strategy is to reduce the number of spot welds as much as possible while satisfying all the design objectives. However, a classical optimization of the spot weld distribution using an exhaustive search approach is simply not feasible due to the very high order of the design space and the subsequently prohibitive calculation costs. Moreover, even if this calculation could be done, the result would not necessarily be very informative with respect to the design robustness to manufacturing uncertainties (location of welds and defective welds) and to the degradation of spot welds due to fatigue effects over the lifetime of the vehicle. In this paper, a decision-making methodology is presented which allows some aspects of the robustness issues to beintegrated into the spot weld design process. The starting point is a given distribution of spot welds on the structure, which is based on both engineering know-how and preliminary critical numerical results, in particular criteria such as crash behavior. An over-populated spot weld distribution is then built in order to satisfy the remaining design criteria, such as static torsion angle and modal behavior. Then, an efficient optimization procedure based on energy considerations is used to eliminate redundant spot welds while preserving as far as possible the nominal structural behavior. The resulting sub-optimal solution is then used to provide a decision indicator for defining effective quality control procedures (e.g. visual post-assembly inspection of a small number of critical spot welds) as well as designing redundancy into critical zones. The final part of the paper is related to comparing the robustness of competing designs. Some decision-making indicators are presented to help the analyst to plan robust resistance spot welds designs along with quality controls in order to insure a specified level of structural performance. All examples are presented on a full body-in-white structure (one million dofs and thousands spot welds)

A robust component mode synthesis method for stochastic damped vibroacoustics

International audienceIn order to reduce vibrations or sound levels in industrial vibroacoustic problems, the low-cost and efficient way consists in introducing visco- and poro-elastic materials either on the structure or on cavity walls. Depending on the frequency range of interest, several numerical approaches can be used to estimate the behavior of the coupled problem. In the context of low frequency applications related to acoustic cavities with surrounding vibrating structures, the finite elements method (FEM) is one of the most efficient techniques. Nevertheless, industrial problems lead to large FE models which are time-consuming in updating or optimization processes. A classical way to reduce calculation time is the Component Mode Synthesis method (CMS), whose classical formulation is not always efficient to predict dynamical behavior of structures including visco-elastic and/or poro-elastic patches. Then, to ensure an efficient prediction, the fluid and structural bases used for the model reduction need to be updated as a result of changes in a parametric optimization procedure. For complex models, this leads to prohibitivenumerical costs in the optimization phase or for management and propagation of uncertainties in the stochastic vibroacoustic problem. In this paper, the formulation of an alternative CMS method is proposed and compared to classical (u,p) CMS method: the Ritz basis is completed with static residuals associated to visco-elastic and poro-elastic behaviors. This basis is also enriched by the static response of residual forces due to structural modifications, resulting in a so-called robust basis, also adapted to Monte Carlo simulations for uncertainties propagation using reduced models

Robust optimization and quality control in spot welded structures

International audienceThe performance characteristics (i.e., static, dynamic, crash, etc.) of a spot welded structure are strongly influenced by the number and the locations of the resistance spot welds. The design problem requires the number and locations of spot welds to be optimized so as to obtain reasonable trade-offs between manufacturing costs and structural performances. An optimization procedure is proposed which iterativelyadds and removes spot welds in order to correct for approximations made in the iterative process. Moreover, a robustness indicator is formulated that allows to analyze the impact of the number of defective or broken spot welds on the system performance. This indicator provides a useful decision making tool for deciding both how many spot welds should be inspected following assembly as well as pointing to a small number of critical spot welds that should be reinforced. The proposed methodology will be illustrated on a full body-in-white structure

Structural energy flow optimization through adaptive shunted piezoelectric metacomposites

International audienceIn this article, a numerical approach for modeling and optimizing two-dimensional smart metacomposites is presented. The proposed methodology is based on the Floquet-Bloch theorem in the context of elastodynamics including distributed shunted piezoelectric patches. The dedicated numerical technique is able to cope with the multimodal wave dispersion behavior over the whole first Brillouin zone for periodically distributed two-dimensional shunted piezomechanical systems. Some indicators allowing the optimization of the shunt impedance for specific performance objectives are presented and applied for illustration purposes on the design of an adaptive metacomposite with specific functionalities. In order to validate the strategy, the designed metacomposite is integrated in a support structure, and a full three dimensional model is derived to illustrate the efficiency of the approach

Integrated and Distributed Adaptive Metacomposites for vibroacoustic control of Aerospace Structures

International audienceResearch activities in smart materials and structures represent a significant potential for technological innovation in mechanics and electronics. The necessity of controlling vibroacoustic behavior of industrial systems motivates a broad research effort for introducing active or passive technologies to control noise and vibrations. New processes are now available which allow active transducers and their driving electronics to be directly integrated into otherwise passive structures. This new approach could allow fine control of the material physical behavior for implementing new functional properties that do not exist in nature. In this sense, we can speak of "integrated distributed adaptive metacomposites" that merges with the notion of programmable material. Through two different examples dealing with active acoustical impedance and elastodynamical interface, this paper presents used theoretical tools for designing specific applications of this new technology

Kirigami Auxetic Pyramidal Core: Mechanical Properties and Wave Propagation Analysis in Damped Lattice

International audienceThe work describes the manufacturing, mechanical properties, and wave propagation characteristics of a pyramidal lattice made exhibiting an auxetic (negative Poisson's ratio) behavior. Contrary to similar lattice tessellations produced using metal cores, the pyramidal lattice described in this work is manufactured using a kirigami (origami pluscutting pattern) technique, which can be applied to a large variety of thermoset and thermoplastic composites. Due to the particular geometry created through this manufacturing technique, the kirigami pyramidal lattice shows an inversion between in-plane and out-of-plane mechanical properties compared to classical honeycomb configurations. Long wavelength approximations are used to calculate the slowness curves, showing unusual zero-curvature phononic properties in the transverse plane. A novel 2D wave propagation technique based on Bloch waves for damped structures is also applied to evaluate the dispersion behavior of composite (Kevlar/epoxy) lattices with intrinsic hysteretic loss. The 2D wave propagation analysis shows evanescence directivity at different frequency bandwidths and complex modal behavior due to unusual deformation mechanism of the lattice

Adaptive metacomposites : design strategy and experimental validation

International audienceRecent advances in modeling of multiphysics periodic systems allow designers to investigate new concepts for vibroacoustic absorption. In this work, we present a strategy to design adaptive metacomposites, namely host structures with periodic piezoelectric patches shunted with semi-passive electric circuits, together with experimental implementation

Computation of 2D vibroacoustic waves dispersion for optimizing acoustic power flow in interaction with adaptive metacomposites

International audienceThis paper presents an integrated methodology for optimizing vibroacoustic energy flow in interaction between an adaptive metacomposite made of periodically distributed shunted piezoelectric material glued onto passive plate and open acoustic domain. The computation of interacting Floquet-Bloch propagators is also used to optimize vibroacoustic behavior. The main purpose of this work is first to propose a numerical methodology to compute the fluid-structure multi-modal wave dispersions. In a second step, optimization of electric circuit is used to control the acoustic power flow. 3D standard computation is used to confirm the efficiency of the designed metacomposite in terms of acoustic emissivity and absorption

ROM for nonlinear vibroacoustic problems with structural and acoustic nonlinearities

International audienceThis paper presents a reduced order method dedicated to nonlinear vibroacoustic problems. Both structural and acoustics behavior are nonlinear. The structural nonlinearity is due to large displacements while the acoustic nonlinearity is due to the high intensity level in the fluid. The Kuznetsov equation is used to formulate the nonlinear acoustic problem. The reduced order model is based on the Ritz bases of the uncoupled linear problem. Nonlinear behavior is considered as a perturbation of the linear model so that the resolution is compared to a reanalysis problem. The Combined Approximation method dedicated to reanalysis problems is used to enriche the Ritz reduced basis