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

Lennart Moheit,Steffen Marburg

doi:10.1142/s0218396x1650020x

Lennart Moheit, Steffen Marburg

Open Access

https://doi.org/10.1142/s0218396x1650020x

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Abstract

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.

Highlights

The discretization and calculation of an acoustic exterior problem involves the problem of an infinite, unbounded domain with a nonreflecting boundary condition at the outside of the fluid-filled domain
Tests performed by the authors of this paper have confirmed this observation, the choice between the four polynomials had no considerable effect on the modes in exterior acoustics, as will be shown subsequently
The obtained discrete system matrices were used for modal decomposition into Acoustic radiation modes (ARMs) and normal modes (NMs)

Summary

Introduction

The discretization and calculation of an acoustic exterior problem involves the problem of an infinite, unbounded domain with a nonreflecting boundary condition at the outside of the fluid-filled domain. Two approaches have been established in order to calculate acoustic exterior problems numerically: Perfectly matched layers (PML)[1] and the infinite element method (IFEM).[2,3] The method of conjugated Astley–Leis infinite elements is applied by the authors, since these elements provide the frequency-independent system matrices of stiffness, damping and mass on the basis of the corresponding FE matrices. These system matrices are required for further investigations in modal decomposition. The sound pressure field in the radial direction in the domain with the infinite elements is interpolated by polynomials such as Lagrange polynomials, Legendre polynomials or Jacobi polynomials, which lead to differences in the matrix condition number of the discrete, global system matrices.[5,6]

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