Sound in Vibrating Cabins: Physical Effects, Mathematical Formulation, Computational Simulation with FEM

Ihlenburg, Frank

doi:10.1007/978-3-211-89651-8_3

Cited by 6 publications

(7 citation statements)

References 22 publications

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“…A common approach for solving Equation (15) (for example, in the automotive industry, e.g., [32][33][34]), which works fine for weakly-coupled systems, is as follows: one first determines the eigenpairs of the symmetric and definite eigenvalue problems:…”

Section: Discretization By Finite Elementsmentioning

confidence: 99%

On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations

Voß

2016

Aerospace

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Small amplitude vibrations of a structure completely filled with a fluid are considered. Describing the structure by displacements and the fluid by its pressure field, the free vibrations are governed by a non-self-adjoint eigenvalue problem. This survey reports on a framework for taking advantage of the structure of the non-symmetric eigenvalue problem allowing for a variational characterization of its eigenvalues. Structure-preserving iterative projection methods of the the Arnoldi and of the Jacobi-Davidson type and an automated multi-level sub-structuring method are reviewed. The reliability and efficiency of the methods are demonstrated by a numerical example.

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Section: Discretization By Finite Elementsmentioning

confidence: 99%

On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations

Voß

2016

Aerospace

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“…Accurate modeling of acoustics can be a formidable task [21], particularly due to complicated noise sources and boundary impedances. Finite/boundary element method (FEM/BEM) can be used to simulate acoustical fields in ANC systems [22][23][24][25], and these methods have also been combined with a optimization methods to optimize for example sensor/actuator locations and the acoustic source strengths [26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

An optimal local active noise control method based on stochastic finite element models

Airaksinen

Toivanen

2013

Journal of Sound and Vibration

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An optimal local active noise control method based on stochastic finite element models Airaksinen, T.; Toivanen, J.Airaksinen, T. & Toivanen, J. (2013). An optimal local active noise control method based on stochastic finite element models. Journal of Sound and Vibration, 332 (2013) pp.6924-6933. doi:10.1016/j.jsv.2013 AbstractA new method is presented to obtain a local active noise control that is optimal in stochastic environment. The method uses numerical acoustical modeling that is performed in the frequency domain by using a sequence of finite element discretizations of the Helmholtz equation. The stochasticity of domain geometry and primary noise source is considered. Reference signals from an array of microphones are mapped to secondary loudspeakers, by an off-line optimized linear mapping. The frequency dependent linear mapping is optimized to minimize the expected value of error in a quiet zone, which is approximated by the numerical model and can be interpreted as a stochastic virtual microphone. A least squares formulation leads to a quadratic optimization problem. The presented active noise control method gives robust and efficient noise attenuation, which is demonstrated by a numerical study in a passenger car cabin. The numerical results demonstrate that a significant, stable local noise attenuation of 20-32 dB can be obtained at lower frequencies (< 500 Hz) by two microphones, and 8-36 dB attenuation at frequencies up to 1000 Hz, when 8 microphones are used.

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“…Different formulations have been proposed to model this problem ( [1][2][3][4], e.g. ), the most obvious of which describes the structure by its relative displacement field and the fluid by its pressure [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

“…The efficiency of the method is demonstrated by the free vibrations of a structure completely filled with water.where Ω s and Ω f denotes the region occupied by the structure and the fluid, respectively, Γ O the outer boundary of the structure, Γ I the interface between the fluid and the structure, and n the outward pointing normal of Ω s on Γ I . u refers to the solid displacement, p to the fluid pressure, ω indicates the eigenfrequency, σ(u) the linearized stress tensor, and ρ s and ρ f the density of the solid and the fluid, respectively.Discretizing by finite elements yields the unsymmetric matrix eigenvalue problem [5,7,8]…”

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confidence: 99%

Structural-Acoustic Vibration Problems in the Presence of Strong Coupling

Voß¹,

Stammberger

2012

Journal of Pressure Vessel Technology

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Free vibrations of fluid-solid structures are governed by unsymmetric eigenvalue problems. A common approach which works fine for weakly coupled systems is to project the problem to a space spanned by modes of the uncoupled system. For strongly coupled systems however the approximation properties are not satisfactory. This paper reports on a framework for taking advantage of the structure of the unsymmetric eigenvalue problem allowing for a variational characterization of its eigenvalues, and structure preserving iterative projection methods. We further cover an adjusted automated multi-level sub-structuring method for huge fluidsolid structures. The efficiency of the method is demonstrated by the free vibrations of a structure completely filled with water.where Ω s and Ω f denotes the region occupied by the structure and the fluid, respectively, Γ O the outer boundary of the structure, Γ I the interface between the fluid and the structure, and n the outward pointing normal of Ω s on Γ I . u refers to the solid displacement, p to the fluid pressure, ω indicates the eigenfrequency, σ(u) the linearized stress tensor, and ρ s and ρ f the density of the solid and the fluid, respectively.Discretizing by finite elements yields the unsymmetric matrix eigenvalue problem [5,7,8]

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Sound in Vibrating Cabins: Physical Effects, Mathematical Formulation, Computational Simulation with FEM

Cited by 6 publications

References 22 publications

On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations

On a Non-Symmetric Eigenvalue Problem Governing Interior Structural–Acoustic Vibrations

An optimal local active noise control method based on stochastic finite element models

Structural-Acoustic Vibration Problems in the Presence of Strong Coupling

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