Abstract
The Helmholtz equation for exterior acoustic problems can be solved by the finite element method in combination with conjugated infinite elements. Both provide frequency-independent system matrices, forming a discrete, linear system of equations. The homogenous system can be understood as a quadratic eigenvalue problem of normal modes (NMs). Knowledge about the only relevant NMs, which — when doing modal superposition — still provide a sufficiently accurate solution for the sound pressure and sound power in comparison to the full set of modes, leads to reduced computational effort. Properties of NMs and criteria of modal reduction are discussed in this work.
Highlights
Exterior acoustic problems comprehend the propagation and distribution of sound pressure in fluid-filled domains of infinite extent
According to the work by Marburg et al.,[18,19,20] normal modes (NMs) in numerical exterior acoustic problems can be determined as follows: For the description of the spatial sound pressure field p(x) at a frequency f, the Helmholtz differential equation is used. It is discretized by the finite element method (FEM) and the infinite element method (IFEM) according to Astley and Leis
The NM eigenvectors are found in the whole computational fluid domain including FE and IFE DOFs
Summary
Exterior acoustic problems comprehend the propagation and distribution of sound pressure in fluid-filled domains of infinite extent This implies sound sources under free-field conditions in full- or half-space problems, with or without open cavities. For the description of sound sources, e.g. by means of their radiated sound power, free-field conditions are required in order to only determine the characteristics of the source and to exclude the influence of the measurement environment. This applies for the numerical simulation of sound radiation, since in the context of virtual prototyping, it is desired for estimating acoustical properties in the development process. Rabinovich et al.[5] compare the
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