More Than Six Elements Per Wavelength: The Practical Use of Structural Finite Element Models and Their Accuracy in Comparison with Experimental Results

Langer, Philipp; Maeder, Marcus; Guist, Christian; Krause, Michael; Marburg, Steffen

doi:10.1142/s0218396x17500254

Cited by 72 publications

(33 citation statements)

References 30 publications

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“…The normal mesh consists of 1021 finite elements with a maximum element size of h max = 3.78 cm to ensure reliable results at about 3 kHz to 4 kHz. 38,39 The coarse and the fine mesh consist of 707 and 2102 elements, respectively, with maximum element sizes of h max = 11.33 cm and h max = 2.27 cm. The total numbers of DOF for the sound pressure are 1569, 2197 and 4368 for the coarse, normal and fine meshes, respectively.…”

Section: Recordermentioning

confidence: 99%

Infinite Elements and Their Influence on Normal and Radiation Modes in Exterior Acoustics

Moheit

Marburg

2017

J. Comp. Acous.

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Acoustic radiation modes (ARMs) and normal modes (NMs) are calculated at the surface of a fluid-filled domain around a solid structure and inside the domain, respectively. In order to compute the exterior acoustic problem and modes, both the finite element method (FEM) and the infinite element method (IFEM) are applied. More accurate results can be obtained by using finer meshes in the FEM or higher-order radial interpolation polynomials in the IFEM, which causes additional degrees of freedom (DOF). As such, more computational cost is required. For this reason, knowledge about convergence behavior of the modes for different mesh cases is desirable, and is the aim of this paper. It is shown that the acoustic impedance matrix for the calculation of the radiation modes can be also constructed from the system matrices of finite and infinite elements instead of boundary element matrices, as is usually done. Grouping behavior of the eigenvalues of the radiation modes can be observed. Finally, both kinds of modes in exterior acoustics are compared in the example of the cross-section of a recorder in air. When the number of DOF is increased by using higher-order radial interpolation polynomials, different eigenvalue convergences can be observed for interpolation polynomials of even and odd order.

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Section: Recordermentioning

confidence: 99%

Infinite Elements and Their Influence on Normal and Radiation Modes in Exterior Acoustics

Moheit

Marburg

2017

J. Comp. Acous.

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“…Helmholtz equation or elastodynamics). A priori error estimators for the Helmholtz equations are provided in [5] and numerical evidences of the convergence in elastodynamics problems are shown in [25].…”

Section: Derivation Of Discrete Analogue Of Boundary Integral Equationsmentioning

confidence: 99%

A Boundary Algebraic Formulation for Plane Strain Elastodynamic Scattering

Poblet-Puig¹,

Shanin²

2018

SIAM J. Appl. Math.

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Solving of elastodynamic problems arises in many scientific fields such as wave propagation in the ground, non-destructive testing, vibration design of buildings, or vibroacoustics in general. An integral formulation based on boundary algebraic equations is presented here. This formulation leads to a numerical method with a discretised boundary. An important advantage of the method over the standard boundary element method (BEM) is that no contour (2D) or surface (3D) integral needs to be computed. This feature is helpful in order to obtain a discrete version of the combined field integral equations (designed to damp numerically the fictitious eigenfrequencies) without difficulties caused by the evaluation of hypersingular integrals. The key aspects are: (i) the approach deals with discrete equations from the very beginning; (ii) discrete (instead of continuous) tensor Green's functions are considered (the methodology to evaluate them is demonstrated); (iii) the boundary must be described by means of a regular square grid. In order to overcome the drawback of this third condition the boundary integral is coupled, if needed, with a thin layer of finite elements. This improves the description of curved geometries and reduces numerical errors. The properties of the method are demonstrated by means of numerical examples: the scattering of waves by objects and holes in an unbounded elastic medium, and an interior elastic problem.

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“…In general, for Helmholtz problems with uniform grids the gridsize and thus the number of necessary ansatz functions N is dependent on the wavenumber k = 2πf c where f is the frequency and c the speed of sound (cf. [5,6]). Therefore, for high frequencies the computational effort becomes very large, and calculations of wave scattering problems can last between hours to several days on modern computers.…”

Section: Introductionmentioning

confidence: 99%

Using B-spline frames to represent solutions of acoustics scattering problems

Kreuzer

2019

Journal of Computational and Applied Mathematics

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Although frames, which are a generalization of bases, are important tools used in signal processing, their potential in other fields of engineering and applied mathematics (e.g. acoustics) has not been fully explored yet. Gabor frames, that are specific type of frames, are very well adapted to oscillating functions, and therefore have a great potential to efficiently represent functions in connection with the Helmholtz operator. In this paper representations of the solution of a scattering problem in 2D using Gabor frames based on B-splines as building blocks are investigated. Practical issues concerning the implementation of frames like the restriction of the frame elements to a finite interval and methods to determine the unknown coefficients for the representation, i.e. by using dual frames or by solving a least squares problem, are discussed. Numerical experiments are made comparing the different ways to determine the unknown expansion coefficients and the representations are compared in terms of their efficiency, i.e. the number of used frame coefficients versus the accuracy of the approximation. In all cases the coefficients calculated with a slightly modified orthogonal matching pursuit algorithm provide the best accuracy versus sparsity ratio.

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More Than Six Elements Per Wavelength: The Practical Use of Structural Finite Element Models and Their Accuracy in Comparison with Experimental Results

Cited by 72 publications

References 30 publications

Infinite Elements and Their Influence on Normal and Radiation Modes in Exterior Acoustics

Infinite Elements and Their Influence on Normal and Radiation Modes in Exterior Acoustics

A Boundary Algebraic Formulation for Plane Strain Elastodynamic Scattering

Using B-spline frames to represent solutions of acoustics scattering problems

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