Applications of the Mortar Finite Element Method in Vibroacoustics and Flow Induced Noise Computations

Triebenbacher, Simon; Wohlmuth, Barbara; Flemisch, Bernd

doi:10.3813/aaa.918305

Cited by 24 publications

(24 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[25,27], the general procedure is based on the determination of the intersection between the elements of the different meshes. For arbitrary elements in a general three-dimensional problem, this task is expected to be quite complex [22,25].…”

Section: Integration Of Coupling Matrices Over Nonconforming Meshesmentioning

confidence: 99%

“…The latter have received attention during the last two decades, particularly in problems that concern solid and contact mechanics [22][23][24]. Regarding the numerical modelling of acoustic and vibroacoustic problems, some reported attempts have been found in the literature related to nonconforming meshes [25][26][27], with a view to taking advantage of more flexible discretization techniques. In these works, the authors considered nonmatching discretizations in coupled mechanical-acoustic systems and also acoustic-acoustic coupling problems, without including the presence of a transfer matrix.…”

Section: Introductionmentioning

confidence: 99%

“…Applications are related to flow induced noise calculations [27], where the interface separates two regions: the aeroacoustic subdomain, with a smaller element size, associated with the fluid flow problem (and therefore the source terms), and the purely acoustic subdomain, where the homogeneous wave equation is solved. Since the FE mesh is nonconforming at the interface, the continuity of acoustic pressure is not fulfilled directly, and must be enforced in a weak sense with suitable Lagrange multipliers [23,27] In some cases [25], this procedure exhibits better computational behaviour than the conforming FE version, where a small transition region from fine to coarse mesh is considered.…”

Section: Introductionmentioning

confidence: 99%

“…Here, the continuity conditions of the acoustic fields at the interfaces [25][26][27] are replaced by four-pole relationships between the acoustic pressure and velocity at both sides of the subsystem represented through a transfer matrix. …”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices

et al. 2012

View full text Add to dashboard Cite

Elsevier Denia, FD.; Martínez-Casas, J.; Baeza, L.; Fuenmayor, FJ. (2012). Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices. Applied Acoustics. 73 (8) ABSTRACTTransfer matrices are commonly considered in the numerical modelling of the acoustic behaviour associated with exhaust devices in the breathing system of internal combustion engines, such as catalytic converters, particulate filters, perforated mufflers and charge air coolers. In a multidimensional finite element approach, a transfer matrix provides a relationship between the acoustic fields of the nodes located at both sides of a particular region. This approach can be useful, for example, when one-dimensional propagation takes place within the region substituted by the transfer matrix. As shown in recent investigations, the sound attenuation of catalytic converters can be properly predicted if the monolith is replaced by a plane wave four-pole matrix. The finite element discretization is retained for the inlet/outlet and tapered ducts, where multidimensional acoustic fields can exist. In this case,

show abstract

Section: Integration Of Coupling Matrices Over Nonconforming Meshesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices

et al. 2012

View full text Add to dashboard Cite

show abstract

“…Thus, these techniques provide a very flexible and computationally attractive setting to handle numerically coupled multi-physics problems. Mortar methods have been applied successfully in many engineering applications, such as, e.g., contact problems [4][5][6][7], dynamic and static structural analysis [8][9][10], flow problems [11][12][13] and coupled problems in acoustics [14,15]. Further, the mortar method is used to simulate eigenvalue problems in [16,17].…”

Section: Introductionmentioning

confidence: 99%

A new mortar formulation for modeling elastomer bedded structures with modal-analysis in 3D

Horger

Kollmannsberger

Frischmann

et al. 2014

Adv. Model. and Simul. in Eng. Sci.

View full text Add to dashboard Cite

Background: It is a well-known fact that cross-laminated timber structures are sensitive to rumbling noises. These transmissions are best captured by a fully three-dimensional mathematical model. Since the discretization of such models with hexahedral elements in a conforming manner is highly complex, we chose the mortar method to reduce the algorithmic complexity for the mesh generation. Moreover we consider high-order finite elements in order to deal with the high aspect ratios in three-dimensionally resolved, cross-laminated walls and slabs. The geometric models and material specification was derived from a building information model. Methods: This paper derives a new mortar formulation designed to replace an explicitely discretized elastomer with a new coupling condition. To this end, tailored Robin conditions are applied at the interface as coupling conditions instead of the more standard continuity constraints. Having demonstrated the suitability of the mortar method for high order finite elements, we proceed with the derivation of the dimensional reduced model with the new coupling condition and to show its stability by numerical experiments. We then test the performance of the new formulation on benchmark examples and demonstrate the engineering relevance for practical applications. Results: The newly derived mortar formulation performs well. We tested the new formulation on fully three-dimensional examples of engineering relevance discretized by high-order finite elements up to degrees of p = 10 and found the reproduction of both eigenvalues and eigenmodes to be accurate. Moreover, the mortar method allows for a significant reduction in the algorithmic complexity of mesh generation while simultaneously reducing the overall computational effort. Conclusion: The newly derived modified mortar method for replacing an elastomer layer is not only an academically interesting variant but is capable of solving problems of practical importance in modal-analysis of cross-laminated timber structures.

show abstract

Structural‐acoustic coupling on non‐conforming meshes with quadratic shape functions

Peters

Marburg

Kessissoglou

2012

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARY Fully coupled finite element/boundary element models are a popular choice when modelling structures that are submerged in heavy fluids. To achieve coupling of subdomains with non‐conforming discretizations at their common interface, the coupling conditions are usually formulated in a weak sense. The coupling matrices are evaluated by integrating products of piecewise polynomials on independent meshes. The case of interfacing elements with linear shape functions on unrelated meshes has been well covered in the literature. This paper presents a solution to the problem of evaluating the coupling matrix for interfacing elements with quadratic shape functions on unrelated meshes. The isoparametric finite elements have eight nodes (Serendipity) and the discontinuous boundary elements have nine nodes (Lagrange). Results using linear and quadratic shape functions on conforming and non‐conforming meshes are compared for an example of a fluid‐loaded point‐excited sphere. It is shown that the coupling error decreases when quadratic shape functions are used. Copyright © 2012 John Wiley & Sons, Ltd.

show abstract

Applications of the Mortar Finite Element Method in Vibroacoustics and Flow Induced Noise Computations

Cited by 24 publications

References 24 publications

Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices

Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices

A new mortar formulation for modeling elastomer bedded structures with modal-analysis in 3D

Structural‐acoustic coupling on non‐conforming meshes with quadratic shape functions

Contact Info

Product

Resources

About