Enforcing Reciprocity in Numerical Analysis of Acoustic Radiation Modes and Sound Power Evaluation

Abstract

By identifying the efficiently radiating acoustic radiation modes of a fluid loaded vibrating structure, the storage requirements of the acoustic impedance matrix for calculation of the sound power using the boundary element method can be greatly reduced. In order to compute the acoustic radiation modes, the impedance matrix needs to be symmetric. However, when using the boundary element method, it is often found that the impedance matrix is not symmetric. This paper describes the origin of the asymmetry of the impedance matrix and presents a simple way to generate symmetry. The introduction of additional errors when symmetrizing the impedance matrix must be avoided. An example is used to demonstrate the behavior of the asymmetry and the effect of symmetrization of the impedance matrix on the sound power. The application of the technique presented in this work to compute the radiated sound power of a submerged marine vessel is discussed.

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

“…The distribution of eigenvalues at each frequency is related to the share of the corresponding mode shape in the total superimposed pressure field at the surface of the solid structure, since ARM eigenvalues are related to the radiation efficiency σ by λ = ρ f c f σ. 16 Three notable peaks can be found for the largest eigenvalue at approximately 840 Hz, 1760 Hz and 2880 Hz. The corresponding mode shapes -which can be found as eigenvectors of the acoustic impedance matrix Z R -are depicted in Fig.…”

“…(23). Peters et al 16 show that Z R = {Z} is required to be symmetric or -if not the case -can easily be symmetrized.…”

“…9 Cunefare and Currey 13-15 focus on the grouping behavior of the eigenvalues and radiation efficiencies. This line of research is further explored by Peters et al 16 who investigate the symmetry characteristics of the real impedance matrix. Recent studies by Wu et al 17 investigate fast multipole BEM and iterative methods for efficiently and accurately calculating the ARMs and the radiation efficiencies in the example of a baffled plate.…”

“…16,22 Recent studies on BEM in exterior acoustics were published by Ramesh et al 23 and Marburg. 24,25 The method is also applied for eigenvalue analysis in the exterior acoustic problem by Zheng et al 26 The convergence of the infinite elements was shown by Demkowicz and Gerdes 27,28 and proves the reliability of the approach, but there have been no studies yet on the influence of the infinite elements on modes in exterior acoustics.…”

Decoupling Structural Acoustic Systems: Investigation of Radiation Damping Mechanisms

“…where the acoustic impedance matrix Z can be identified. It can be replaced by its symmetric part 1 2 (Z + Z T ) without introducing any relevant numerical error [11]. Instead of evaluating Z for each individual frequency, a polynomial approximation is calculated over the frequency range of interest.…”