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

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.

Normal Modes and Modal Reduction in Exterior Acoustics

“…This observation was confirmed by the authors in Ref. 21, however, the influence on NMs and ARMs was negligible. The number of DOFs in the used meshes is given in Table 1.…”

“…As observed by the authors in Ref. 21, an even number for the polynomial order n rad leads to a line of purely real eigenvalues (cf. Fig.…”

“…In previous work, the authors used the MAC in order to track the eigenvalues in convergence studies with different meshes and increasing orders of radial interpolation polynomials. 21 The MAC values of the left and right eigenvectors of the second geometry are depicted in Fig. 8(a).…”

A greedy reduced basis scheme for multifrequency solution of structural acoustic systems

“…These results lead to the conclusion that an a priori estimation of the condition numbers in the frequency range could provide indication of suitable tolerances tol and consequently facilitate the decision whether to use the greedy algorithm or a conventional strategy. Relatively inexpensive algorithms for estimating 1-norm condition numbers exist 49,50 and the thereby gained knowledge could also be incorporated into the choice of the next sample (10). This is certainly an issue requiring future research.…”

“…7,8 The use of conjugated Astley-Leis IFEM results in frequency independent coefficient matrices giving rise to the formulation of a generalized eigenvalue problem for determining acoustic radiation modes and normal modes. 9,10 However, making informed choice of the contributing modes for a superposition is still an active field of research. 11 While BEM is particularly advantageous due to the implicit satisfaction of the far field radiation condition, its major drawback stems from the frequency dependence of the coefficient matrices.…”