Franck Renaud

A new identification method of viscoelastic behavior: Application to the generalized Maxwell model

This paper focuses on the generalized Maxwell model (GMM) identification. The formulation of the transfer function of the GMM is defined, as well as its asymptotes. To compare identification methods of the parameters of the GMM, a test transfer function and two quality indicators are defined. Then, three graphical methods are described, the enclosing curve method, the CRONE method and an original one. But the results of graphical methods are not good enough. Thus, two optimization recursive processes are described to improve the results of graphical methods. The first one is based on an unconstrained non-linear optimization algorithm and the second one is original and allows constraining identified parameters. This new process uses the asymptotes of the modulus and the phase of the transfer function of the GMM. The result of the graphical method optimized with the new process is very accurate and fast.

EXPERIMENTAL CHARACTERIZATION, MODELING AND PARAMETRIC IDENTIFICATION OF THE HYSTERETIC FRICTION BEHAVIOR OF VISCOELASTIC JOINTS

Viscoelastic joints connecting solids are essential components of mechanical systems. Viscoelastic components have inherent damping in their structure. Moreover, energy losses in structural vibrations are strongly linked to the friction properties of joints. In this work, a new visco-tribological model was developed by coupling the rheological linear generalized Maxwell model and Dahl friction model. A method for parametric identification is proposed. Parameters of the model are identified from dynamic mechanical analysis (DMA) tests for different excitation frequencies. Comparison between measurements and simulations is performed and the validity of the proposed model is discussed.

ASYMPTOTIC NUMERICAL METHOD FOR THE DYNAMIC STUDY OF NONLINEAR VIBRATION ABSORBERS

Vibrations are usually undesired phenomena as they may cause discomfort, disturbance, damage, and sometimes destruction of machines and structures. It must be reduced or controlled or eliminated. One of the most common methods of vibration control is the use of the dynamic absorber. The paper is interested in the study of a nonlinear two degrees of freedom (DOF) model. To solve nonlinear equation of motion a high order implicit algorithm is proposed. It is based on the introduction of a homotopy, an implicit scheme of Newmark and the use of techniques of Asymptotic Numerical method (ANM). We propose also a regularization of the contact force to overcome the difficulty of the singularity in this model. A comparison will be presented between the results obtained by the proposed algorithm and those using the classical Newton–Raphson and Newmark time scheme.

Viscoelasticity Measurement and Identification of Viscoelastic Parametric Models

Generally speaking, the behaviour of viscoelastic material is more complicated than the behaviour proposed by classical models as Voigt, Maxwell or Zener. The stiffness of such materials is a frequency dependent complex function. Above 1000Hz, classical measurements techniques are unable to achieve accurate measurements of the stiffness. In this paper, a new Dynamical Mechanical Analysis (DMA) tester is presented. It allows the characterization of the shear stiffness of preloaded viscoelastic materials between 200 and 3500Hz and without using frequency-temperature equivalences. Then the Generalized Maxwell model is used to describe behaviours measured with the DMA tester. A new iterative identification method of the parameter of the Generalized Maxwell model is described. This identification method is based on the asymptotes of the model.Copyright

The Skateboard Speed Wobble

The speed wobble is a phenomenon in nonlinear dynamics that can occur in many vehicles such as bicycles, motorbikes, skateboards and airplanes nose landing gear. The dynamic instability affects the steerable wheels of a vehicle and can lead to the loss of control. While for bikes, motorbikes and airplanes the dynamics and causes of the wobble are well known and the literature fully describes the subject, for the skateboard the literature is very poor and there is no paper which investigates this type of instability.In order to do that, the skateboard equations of motion were obtained through Lagrange formalism and Lagrange multipliers method was used to solve the non-holonomic constraints. A parametric stability study was carried out on the linearized equations of motion and the influence of different skateboard parameters was investigated.The main discovery is that the wobble doesn’t strictly depend on skateboard configuration, but the human control characteristics are predominant in the vehicle dynamics.© 2015 ASME

Non-Linear Generalized Maxwell Model for Dynamic Characterization of Viscoelastic Components and Parametric Identification Techniques

Viscoelastic components are incorporated into automobile and aerospace structures system in order to damp mechanical vibrations. Viscoelastic components are a key element in designing desired dynamic behaviour of mechanical systems. Viscoelastic components dynamic characteristics are often very complex, due to the dependence of its response on several variables, such as frequency, amplitude, preload, and temperature. These dependencies can be critical in capturing the mechanical proprieties and so non linear dynamical behaviour may appear. Assuming that non linearities are due to non linear elasticity, the non linear Generalized Maxwell Model (GMM) is proposed to characterize dynamics of viscoelastic components. Parameters of GMM are identified from Dynamic Mechanical Analysis (DMA) tests for different excitation frequencies. A particular result from identification is that the non linear stiffness is dependent upon displacement amplitude and static displacement under static preload. The significance of this result is that the non linear dynamics of the viscoelastic component can be represented by a simple analytical model capable to produce accurate results. Comparison between measurements and simulations of dynamic stiffness of viscoelastic component has been carried on.Copyright

Viscoelastic Damping Effect on Brake Squeal Noise

Brake squeal remains a widespread cause for discomfort in automobiles. Manufacturers overcome this problem by adding damping materials in their systems. The purpose of this work is to take into account the damping in the modeling. As the materials exhibit a viscoelastic behavior, the authors chose to model the damping with the Generalized Maxwell model. Moreover, the authors have tested their method on a detailed Finite Element-model of a brake system. To compute the complex poles of the model, the authors have established a state-space formulation of the viscoelastic model with a new assumption that allows one to reduce the number of states. Making the computation on the whole model is rather difficult due to the number of Degrees Of Freedom, the model is thus reduced on a basis constituted with the eigenvectors of the undamped model. Several results are also presented and discussed as the observed phenomena are rather different from the results obtained with undamped systems.Copyright

A Reduction Methodology Using Free-Free Component Eigenmodes and Arnoldi Enrichment

In order to perform faster simulations, the model reduction is nowadays used in industrial contexts to solve large and complex problems. However, the efficiency of such an approach is sometimes cut by the interface size of the reduced model and its reusability.In this article, we focus on the development of a reduction methodology for the build of modal analysis oriented and updatable reduced order model whose size is not linked to their contacting interface. In order to allow latter model readjusting, we impose the use of eigenmodes in the reduction basis. Eventually, the method introduced is coupled to an Arnoldi based enrichment algorithm in order to improve the accuracy of the reduced model produced.In the last section the proposed methodology is discussed and compared to the Craig and Bampton reduction method. During this comparison we observed that even when not enriched, our work enables us to recover the Craig and Bampton accuracy with partially updatable and smaller reduced order model.Copyright

Dynamic Characterization of Viscoelastic Components

Characterizing frictional behavior of viscoelastic joints is investigated in the present work. A new visco-tribological model was developed by coupling the rheological Generalized Maxwell model (GMM) and Dahl friction model. Parameters of the proposed model are identified from Dynamic Mechanical Analysis (DMA) tests for different excitation frequencies. Comparison between measurements and simulations of hysteretic friction of the viscoelastic component has been carried on.

Compact Model Synthesis for Partially Observed Operational Systems

This work proposes a Compact Model Synthesis (CMS) for Partially Observed Operational Systems (POOS) without using the complete knowledge of models. Series of “grey boxes” fed with partial observations are built in order to synthesize target variables with compact models. The recursive process for real time computation is based on Kalman Filters (KF). This stochastic approach allows to converge in line toward deterministic models with estimated uncertainties and without intrusion on the complete model process. Mathematical context is described first and illustrated secondly with two examples.Copyright