A model reduction strategy for computing the forced response of elastic waveguides using the wave finite element method

Mencik, Jean‐Mathieu

doi:10.1016/j.cma.2012.03.024

Cited by 31 publications

(33 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The strategy to determine the number m of wave modes to be computed by means of the Lanczos method may be carried out by considering an error analysis like the one proposed in [18] (see Section 3.3). Notice that this number can be large to ensure the convergence of the WFE method for describing the vectors of nodal displacements/rotations and forces/moments of the structure.…”

Section: Motivation and Frameworkmentioning

confidence: 99%

“…Besides, the Lanczos method [17] is used to speed up the computation of the WFE eigenproblem with a view to calculating a reduced number of wave modes only. To achieve this task, an error indicator already proposed in [18] is considered to select in an a priori process the number of wave modes that need to be computed. As a second feature of this work, an efficient model reduction technique is proposed which consists in partitioning a whole periodic structure into one central structure surrounded by two extra substructures.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A wave-based model reduction technique for the description of the dynamic behavior of periodic structures involving arbitrary-shaped substructures and large-sized finite element models

Mencik¹,

Duhamel²

2015

Finite Elements in Analysis and Design

Self Cite

View full text Add to dashboard Cite

International audienceThe wave finite element (WFE) method is investigated to describe the dynamic behavior of periodic structures like those composed of arbitrary-shaped substruc-tures along a certain straight direction. Emphasis is placed on the analysis of non-academic substructures that are described by means of large-sized finite element (FE) models. A generalized eigenproblem based on the so-called S + S −1 transformation is proposed for accurately computing the wave modes which travel in right and left directions along those periodic structures. Besides, a model reduction technique is proposed which involves partitioning a whole periodic structure into one central structure surrounded by two extra substructures. In doing so, a few wave modes are only required for modeling the central periodic structure. An error indicator is also proposed to determine in an a priori process the number of those wave modes that need to be considered. Their computation hence follows by considering the Lanczos method, which can be achieved in a very fast way. Numerical experiments are carried out to highlight the relevance of the proposed reduction technique. A comprehensive validation of the technique is performed on a 2D periodic structure. Also, its efficiency in terms of CPU time savings is highlighted regarding a 3D periodic structure that exhibits substructures with large-sized FE models

show abstract

Section: Motivation and Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A wave-based model reduction technique for the description of the dynamic behavior of periodic structures involving arbitrary-shaped substructures and large-sized finite element models

Mencik¹,

Duhamel²

2015

Finite Elements in Analysis and Design

Self Cite

View full text Add to dashboard Cite

show abstract

“…The selection of the number m of right-going and left-going wave modes in the central periodic structure that need to be computed from the Lanczos method is addressed here using the strategy proposed in [11]. In this work, it is suggested to bound the relative errors, for the vectors of nodal displacements/rotations and forces/moments, as follows:…”

Section: Error Indicatormentioning

confidence: 99%

“…One of the features of the proposed error analysis is that the error bound E s is to be computed at the maximum discrete frequency considered within the frequency band of interest, only, as explained in [11].…”

Section: Error Indicatormentioning

confidence: 99%

“…Besides, the Lanczos method [10] is used to speed up the computation of the WFE eigenproblem with a view to calculating a reduced number of wave modes only. To achieve this task, an error indicator already proposed in [11] is considered to select in an a priori process the number of wave modes that need to be computed. As a second feature of this work, an efficient model reduction technique is proposed which consists in partitioning a whole periodic structure into one central structure surrounded by two extra substructures.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Wave-Based Reduction Technique for the Dynamic Behavior of Periodic Structures

Duhamel¹,

Mencik²

2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

View full text Add to dashboard Cite

Abstract. The wave finite element (WFE) method is investigated to describe the dynamic behavior of periodic structures like those composed of arbitrary-shaped substructures along a certain straight direction. A generalized eigenproblem based on the so-called S + S −1 transformation is proposed for accurately computing the wave modes which travel in right and left directions along those periodic structures. Besides, a model reduction technique is proposed which involves partitioning a whole periodic structure into one central structure surrounded by two extra substructures. In doing so, a few wave modes are only required for modeling the central periodic structure. A comprehensive validation of the technique is performed on a 2D periodic structure. Also, its efficiency in terms of CPU time savings is highlighted regarding a 3D periodic structure that exhibits substructures with large-sized FE models.

show abstract

A wave finite element‐based formulation for computing the forced response of structures involving rectangular flat shells

Mencik

2013

Numerical Meth Engineering

View full text Add to dashboard Cite

International audienceThe harmonic forced response of structures involving several noncoplanar rectangular flat shells is investigated by using the Wave Finite Element method. Such flat shells are connected along parallel edges where external excitation sources as well as mechanical impedances are likely to occur. Also, they can be connected to one or several coupling elements whose shapes and dynamics can be complex. The dynamic behavior of the connected shells is described by means of numerical wave modes traveling towards and away from the coupling interfaces. Also, the coupling elements are modeled by using the conventional finite element (FE) method. A FE mesh tying procedure between shells having incompatible meshes is considered, which uses Lagrange multipliers for expressing the coupling conditions in wave-based form. A global wave-based matrix formulation is proposed for computing the amplitudes of the wave modes traveling along the shells. The resulting displacement solutions are obtained by using a wave mode expansion procedure. The accuracy of the wave-based matrix formulation is highlighted in comparison with the conventional FE method through three test cases of variable complexities. The relevance of the method for saving large CPU times is emphasized. Its efficiency is also highlighted in comparison with the component mode synthesis technique

show abstract

A model reduction strategy for computing the forced response of elastic waveguides using the wave finite element method

Cited by 31 publications

References 18 publications

A wave-based model reduction technique for the description of the dynamic behavior of periodic structures involving arbitrary-shaped substructures and large-sized finite element models

A wave-based model reduction technique for the description of the dynamic behavior of periodic structures involving arbitrary-shaped substructures and large-sized finite element models

A Wave-Based Reduction Technique for the Dynamic Behavior of Periodic Structures

A wave finite element‐based formulation for computing the forced response of structures involving rectangular flat shells

Contact Info

Product

Resources

About