Determinantal method for locally modified structures. Application to the vibration damping of a space launcher

Brizard, Denis; Besset, Sébastien; Jézéquel, L.; Troclet, Bernard

doi:10.1007/s00466-012-0695-9

Cited by 6 publications

(12 citation statements)

References 19 publications

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“…The number of boundary modes being equal to the number of boundary DOFs, another reduction was described with Balmes (Balmes, 1996) and (Brizard et al, 2012), and leads to a boundary condensation using branch modes. It permits to reduce the boundary to a certain number of "branch modes", depending on the frequency band we want to observe.…”

Section: Modal Reductions On a Mixed Finite Element Modelsmentioning

confidence: 99%

“…Many sub-structuring methods exist so as to reduce primal FEM such as "fixed interface mode" method (Craig & Bampton method (Craig and Bampton, 1968)), "free interface mode" method (Mac Neal method (MacNeal, 1971)) and "boundary mode" method (see Brizard et al (2012) and Tran (2001)). The principle of those methods is to split the structure into a few substructures, and to express the behavior of each one taking separately with its own eigenmodes (the type of eigenmodes depending on the method).…”

Section: Introductionmentioning

confidence: 99%

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Various double component mode synthesis and sub-structuring methods for dynamic mixed FEM

Garambois¹,

Besset²,

Jézéquel³

2015

European Journal of Mechanics - A/Solids

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International audienceMixed Finite Element Model Component Mode Synthesis (CMS) a b s t r a c t This paper presents various sub-structuring and component mode synthesis (CMS) reduction methods for dynamic mixed displacement-stress FEM. The idea is to imagine a new way of reducing a mixed FEM, by splitting the reduction of the displacement and the stress parameters and adapting primal existing modal reduction methods to each field of the mixed model. In this way, we can choose, for each sub-structure, different methods to truncate the displacements, the stresses and even the junction between the sub-structures. The results differ according to the combination of the methods used, and can show extremely promising results that significantly decrease the numerical size of the structures and still keep the benefits of the mixed method

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Section: Modal Reductions On a Mixed Finite Element Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Various double component mode synthesis and sub-structuring methods for dynamic mixed FEM

Garambois¹,

Besset²,

Jézéquel³

2015

European Journal of Mechanics - A/Solids

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“…This reduction (at the frictional interface) in connection with conventional reductions (for each of the sub-structures) must be able to reproduce the overall behavior of the system for the prediction of the squeal propensity. In this work, we propose a new original strategy based on the Double Modal Synthesis [17,18]: the reduced finite element model is performed by using the combination of the Craig & Bampton reduction procedure [19] with an interface reduction that allows to reduce the size of the internal interface between substructures. This paper is divided into four parts: firstly, the finite element model under study for brake squeal is presented with the modeling hypotheses.…”

Section: Introductionmentioning

confidence: 99%

A double modal synthesis approach for brake squeal prediction

Monteil

Besset

Sinou

2016

Mechanical Systems and Signal Processing

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a b s t r a c tThis paper is devoted to propose a new efficient reduction method for predicting the stability analysis of a brake system subjected to friction-induced vibration. The finite element brake system under study is composed of a disc and a pad. The contact is modeled by introducing contact elements at the friction interface with the classical Coulomb law and a constant friction coefficient. It will be demonstrated that it is possible to build efficient reduced finite element models by developing a reduced model based on a Double Modal Synthesis (i.e. a classical modal reduction via Craig & Bampton plus a condensation at the frictional interface). Special attention is being conducted to validate the convergence of the reduced model especially on the approximation of the unstable modes with respect to real and imaginary parts. This complete numerical strategy based on Double Modal Synthesis allows us to perform relevance squeal prediction of unstable vibration modes. It is demonstrated that the numerical results via the Double Modal Synthesis are in good agreement with those of the classical Craig & Bampton method.

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“…Many sub-structuring reduction methods called Component Mode Synthesis (CMS) methods exist in order as to reduce primal displacement FEM such as: "fixed interface mode" method (Craig & Bampton method [30,29,14]), "free interface mode" method (Mac Neal method [55]) and "boundary mode" method (see Brizard [14] and Tran [76]). The principle of these methods is to split the global structure into a few sub-structures, to describe each of them with a truncated basis made of their proper eigenmodes (the type of eigenmodes depending on the method) before re-assembling them.…”

Section: Introductionmentioning

confidence: 99%

“…Our work is to adapt them in order to build up a new reduced basis for each mixed sub-structure. The main idea is, for each substructure, to separate the condensation of each of the two fields, using the primal Craig & Bampton method [30,29,14] for the condensation of the displacements and a projection of this method on the stresses for the latter. Once the reduction of the two fields is made, we build up a whole mixed basis for each sub-structure and we assemble them through the displacement parameters.…”

Section: Introductionmentioning

confidence: 99%

A new component mode synthesis for dynamic mixed thin plate finite element models

2015

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International audienceThis paper presents a methodology for the reduction in dynamic mixed finite element models (DM-FEMs) based on the use of a sub-structuring primal methods adapted to such models. We implement a DM-FEM for Kirchhoff–Love thin plates using the Hellinger–Reissner variational mixed formulation adapted to dynamic, and give a quick insight of its convergence. This model uses both displacement and generalized stress fields within the plate, obtained as a primary result, but the numerical size of the model is bigger than with a primal displacement model. Thus, we choose to offset this complication by reducing the model with a totally new sub-structuring reduction method, especially adapted to DM-FEMs. The aim of our method is to adapt sub-structuring reduction methods commonly used for primal displacement FEM only (such as Craig and Bampton method) and split the reduction in the two fields. With these displacement methods, the whole structure is splitted into few smaller ones, and each of them is condensed with eigenmodes of the substructure and static connections between them. The principle of our method is to build, for each substructure, a reduced basis for the displacements according to the existing method, and a projection of the primal basis for the stresses. A new reduced basis for the whole mixed model is then built up exclusively with modes taken from the primal model. That method reduces significantly the number of degrees of freedom and keeps the properties and advantages of the mixed formulation

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Determinantal method for locally modified structures. Application to the vibration damping of a space launcher

Cited by 6 publications

References 19 publications

Various double component mode synthesis and sub-structuring methods for dynamic mixed FEM

Various double component mode synthesis and sub-structuring methods for dynamic mixed FEM

A double modal synthesis approach for brake squeal prediction

A new component mode synthesis for dynamic mixed thin plate finite element models

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