Finite element implementation of efficient absorbing layers for time harmonic elastodynamics of unbounded domains

Fontara, Ioanna‐Kleoniki; Schepers, Winfried; Savidis, Stavros A.; Rackwitz, Frank

doi:10.1016/j.soildyn.2018.06.026

Cited by 14 publications

(6 citation statements)

References 27 publications

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“…The concept of PML was proposed by B erenger 26 to simulate an absorbing boundary condition for electromagnetic wave propagation in an unbounded domain. The application of PML is not limited to electromagnetic wave and has been spread to elastic wave [27][28][29] and acoustic wave. [30][31][32][33] Based on theories of PML to attenuate acoustic wave, 34 we truncate the infinite fluid domain by PML and discretize the unit cell by finite element method.…”

Section: An Important Cornerstone -Calculation Methodsmentioning

confidence: 99%

Optimization of sound transmission loss of open acoustic barriers with respect to unit cell topology

Tahar

Sui

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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Open acoustic barriers exhibit excellent sound transmission reduction property at a certain frequency/frequencies which highly depends on the configuration of its unit cell. Design of unit cell configuration for minimum sound transmission at predefined objective frequency remains an open question. This paper aims at providing an automatic design method for open acoustic barriers with multi-material unit cell. Firstly, a wave finite element method is developed to calculate the sound transmission through an infinite array of periodic scatterers. As the unit cell contains infinite fluid domain, the application of Floquet-Bloch theorem to the boundaries of perfectly match layers (PML) is necessary and has been resolved in this paper. This wave finite element method with the implementation of PML is validated by comparing to analytical solution of sound transmission through an array of steel cylinders. Then a genetic algorithm is employed to optimize the sound transmission loss with respect to material distribution of a bi-material unit cell. Finally, the effectiveness of this inverse design is demonstrated by examples with different predefined frequencies. Corresponding unit cell typologies are obtained and the dips of sound power transmission coefficient curve are successfully tuned to objective frequencies.

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Section: An Important Cornerstone -Calculation Methodsmentioning

confidence: 99%

Optimization of sound transmission loss of open acoustic barriers with respect to unit cell topology

Tahar

Sui

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Hence the dimensions of the PML layer must be chosen such that any reflections inside the PML will fully attenuate before travelling back into the regular FEM region of the model. Suggestions from several references concerning the extent of the regular domain of a FEM mesh comprising a PML domain for wave propagation into a half-space, as well as the dimensions of the PML itself have been summarized in [8]. With only one exception these references provide mesh dimensions and PML dimensions with respect to the length of a foundation only, with no hints which frequencies were used.…”

Section: Model Dimensionsmentioning

confidence: 99%

Recommendations on finite element modelling of non-seismic excitation in soil-structure interaction problems

Schepers,

Brinkgreve,

Appel

2024

J. Phys.: Conf. Ser.

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Nowadays geotechnical engineering firms have powerful software tools to extent their consulting business also into dynamic soil-structure interaction, which before has been restricted to a rather small community of specialized experts in this field, and they certainly do. This is particularly true with respect to non-seismic sources, that is all kinds of human induced vibrations. Hence, there is a demand from clients as well as from contractors to have guidance on the requirements as well as the limits of numerical modelling of soil-structure interaction. From the literature as well as from relevant standards, recommendations for the numerical modelling of soil-structure interaction problems involving seismic actions are well known, e. g. ASCE/SEI 4-16. There are, however, some particularities when dealing with human-induced vibrations, which are absent in seismic analyses. For human-induced excitations very little specific guidance has been published in the past. A machine foundation on a homogeneous half space excited by harmonic loads with excitation frequency between 4 Hz and 64 Hz has been analysed by means of several commercially available software packages. Parametric studies have been performed to verify if recommendations for seismic soil-structure analyses are valid for non-seismic analyses as well. This paper provides details on the benchmark example and the most important conclusions from the undertaken parametric studies.

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“…The absorption effect of the PML on outgoing waves depends highly on the value of the stretching function. Although there are many available stretching functions [39][40][41], there is a lack of research on the selection of the best parameters for actual use [37]. Furthermore, the PML cannot be directly applied to commercial finite element software and requires programming to implement [42].…”

Section: Introductionmentioning

confidence: 99%

Multi-Directional Viscous Damping Absorbing Boundary in Numerical Simulation of Elastic Wave Dynamic Response

Zhao,

Yu,

et al. 2024

Applied Sciences

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Numerical seismic wave field simulation is essential for studying the dynamic responses in semi-infinite space, and the absorbing boundary setting is critical for simulation accuracy. This study addresses spherical waves incident from the free boundary by applying dynamic equations and Rayleigh damping. A new multi-directional viscous damping absorbing boundary (MVDB) method is proposed based on regional attenuation. An approximate formula for the damping value is established, which can achieve absorbing the boundary setting by only solving the mass damping coefficients without increasing the absorbing region grid cells or depending on the spatial and temporal walking distance. The validity and stability of the proposed method are proven through numerical calculations with seismic sources incident from different angles. Meanwhile, the key parameters affecting the absorption of the MVDB are analyzed, and the best implementation scheme is provided. In order to meet the requirements of mediums with different elastic parameters for boundary absorption and ensure the high efficiency of numerical calculations, the damping amplitude control coefficients k can be set between 1.02 and 1.12, the thickness of the absorbing region L is set to 2–3 times of the wavelength of the incident transverse wave, and the thickness of the single absorbing layer is set to the size of the discrete mesh of the model Δl.

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Finite element implementation of efficient absorbing layers for time harmonic elastodynamics of unbounded domains

Cited by 14 publications

References 27 publications

Optimization of sound transmission loss of open acoustic barriers with respect to unit cell topology

Optimization of sound transmission loss of open acoustic barriers with respect to unit cell topology

Recommendations on finite element modelling of non-seismic excitation in soil-structure interaction problems

Multi-Directional Viscous Damping Absorbing Boundary in Numerical Simulation of Elastic Wave Dynamic Response

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