Mathematical models of elastic structures have become very sophisticated: given the crucial material properties (mass density and the several elastic moduli), computer-based techniques can be used to construct exotic finite element models. By contrast, the modeling of damping is usually very primitive, often consisting of no more than mere guesses at “modal damping factors.” The aim of this paper is to raise the modeling of viscoelastic structures to a level consistent with the modeling of elastic structures. Appropriate material properties are identified which permit the standard finite element formulations used for undamped structures to be extended to viscoelastic structures. Through the use of “dissipation” coordinates, the canonical “M , K ” form of the undamped motion equations is expanded to encompass viscoelastic damping. With this formulation finite element analysis can be used to model viscoelastic damping accurately.

Dynamics of viscoelastic structures: a time-domain finite element formulation

Acoustic metamaterial plates for elastic wave absorption and structural vibration suppression

Reduced bases for model updating in structural dynamics based on constitutive relation error

https://hal.archives-ouvertes.fr/hal-00855074/document

A global strategy based on experiments and simulations for squeal prediction on industrial railway brakes

This paper addresses the damage localization problem with a statistical model-based approach applied to vibration-based measurements. Damages are viewed as changes in modal parameters. Damage detection is achieved with a subspace-based residual and a global test, which performs a sensitivity analysis of the residual to the modal parameters, relative to uncertainties in those parameters and noises on the data. Damage localization is achieved by plugging the sensitivities of the modal parameters with respect to structural (finite element model) parameters in this decision framework. For large structures that have thousands of elements, a statistical substructuring method, in which the columns of the latter sensitivity matrix are clustered into different classes, is employed. This paper investigates further the clustering step. Numerical results obtained on the finite element model of a bridge deck with a large number of elements are reported. Copyright © 2007 John Wiley & Sons, Ltd.

Statistical model‐based damage localization: A combined subspace‐based and substructuring approach

Experimentally, modal damping is known to allow a relatively accurate representation of damping for wide frequency ranges. For transient simulation of full finite element models, viscous damping is very often the only formulation that is associated with an acceptable computation time. In the absence of a proper material damping model, it is common to assume Rayleigh damping, where the viscous matrix is a linear combination of the mass and stiffness, or piece-wise Rayleigh damping. This representation very often results in modal damping ratios that do not correspond to the physical reality that can be tested. One thus introduces an implicit representation of the viscous matrix that allows transient time simulation with minor time penalty, while using a much more appropriate damping representation. Modal amplitudes are also considered to postprocess time simulations and analyze damping levels. When studying vibrations induced by the passage of pantographs under a catenary, the high modal density of catenaries and the load moving over a large part of the model is a strong motivation to use full model transient analysis. Modal damping is shown to be a practical tool to analyze the properties of this complex system.

https://hal.archives-ouvertes.fr/hal-00589953/document

Using modal damping for full model transient analysis. Application to pantograph/catenary vibration

The computation of frequency and mode shape sensitivities with respect to design parameters is essential to many, structural optimization and finite element updating algorithms. Approximating the gradients may lead to poor estimates and loss of convergence, but on the other hand the cost of exact methods, such as Nelson's (Nelson, R.,, "Simplified Calculations of Eigenvector Derivatives," A1AA Journal, Vol. 14, No. 9,1976, pp. 1201-1205), is often not acceptable for industrial-size models. The present study thus analyses existing approximation methods, suggests a first-order improvement of Fox and Kapoor's modal basis (Fox, R., and Kapoor, M., "Rate of Change of Eigenvalues and Eigenvectors"' A1AA Journal, Vol. 6, No. 12, 1968, pp. 2426-242, 9) and proposes a residual iteration technique allowing accurate computations of modeshape sensitivities. An engine cover model and a model of the Ariane 5 main cryogenic stage are used to analyze, for models of realistic sizes, the accuracy and computational costs of the proposed methods.

Iterative computation of modal sensitivities

Constrained viscoelastic layers have traditionally been considered as damping enhancement mechanisms. More recently bonding has appeared as an alternative to traditional welding strategies and sandwich shells with thick plastic cores have been considered to provide high flexural stiffness for a low overall weight. The present study focuses on computational strategies that can be used to analyze and design the vibroacoustic behavior of such assemblies. Difficulties of the task are the use of experimentally derived complex moduli for the viscoelastic materials, studies in the frequency and temperature domains, integration of the bonded shells into large finite element models, ability to modify the geometry of a particular assembly in an optimization phase or the ability to account for changes in the viscoelastic material properties during the part forming process. The study is illustrated by applications to an automotive oil pan.

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Analysis and design tools for structures damped by viscoelastic materials

Minimum Dynamic Residual Expansion (MDRE) seeks to estimate the response of test modeshapes at all degrees of freedom of a model by minimizing the weighted sum of a test error defined at sensors and a modeling error takento be the strain energy of the dynamic residual associated with the estimated modeshape. Theoretically the computation of the dynamic residual gives a simple mechanism to localize modeling errors. While various forms of MDRE have been often considered in the literature, few systematic analyses of the exact resolution have been attempted on industrial models in good part because of excessive computational costs. The present paper introduces an iterative method allowing the exact solution of MDRE for large problems. Exact solutions, either direct or iterative, are compared with reduced basis versions that were proposed in earlier papers. The ability to localize errors is then evaluated for simulated tests with known modifications. The evaluations are shown for a small 1032 DOF model of the GARTEUR SM-AG-19 testbed and a more industrial 16840 DOF model of an engine cover.

Solving minimum dynamic residual expansion and using results for error localization

L'expansion par minimisation du residu dynamique (MDRE) cherche a estimer la reponse de modes propres experimentaux sur tous les Degres De Liberte (DDLs) d'un modele elements Finis (EF) en minimisant la somme ponderee d'une erreur de modele et d'une erreur sur les mesures. On presente ici une methode de resolution iterative de ce probleme d'expansion, qui permet son application a des modeles de taille industrielle. La capacite des residus dynamiques issus de l'expansion a localiser des erreurs est ensuite evaluee pour des experiences simulees avec des defauts connus, sur un modele de couvre-culasse Renault comportant 16,840 DDLs.

Adrien Bobillot

Papers

Using modal damping for full model transient analysis. Application to pantograph/catenary vibration

Iterative computation of modal sensitivities

Analysis and design tools for structures damped by viscoelastic materials

Solving minimum dynamic residual expansion and using results for error localization

Expansion par minimisation du résidu dynamique