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.

No 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.

This paper presents the Acoustics Apps, an e-learning platform that offers an interactive and playful environment for teaching and learning the principles of acoustics and vibration. The Acoustics Apps address the increasing demand for digitized teaching methods, which might be suitable for home schooling or as a complement to physical experiments by adding interactive simulation. The apps combine learning by experimenting, observing, and exploring using state-of-the-art scientific methods and numerical simulations. The ability to visualize and control acoustic phenomena facilitates understanding of the relevant physical principles. The apps are designed to be used intuitively and can be tailored to suit the existing knowledge of the user. As such, a wide range of users can benefit from this learning aid. It has been developed to allow barrier-free access to modern educational tools, requiring only a device with a browser and Internet access. The necessary computing power is provided by an external server using the COMSOL ServerTM technology. The Acoustics Apps are freely available for academic and teaching purposes at apps.vib.mw.tum.de.

A novel method to solve exterior Helmholtz problems in the case of multipole excitation and random input data is developed. The infinite element method is applied to compute the sound pressure field in the exterior fluid domain. The consideration of random input data leads to a stochastic infinite element formulation. The generalized polynomial chaos expansion of the random data results in the spectral stochastic infinite element method. As a solution technique, the non-intrusive collocation method is chosen. The performance of the spectral stochastic infinite element method is demonstrated for a time-harmonic problem and an eigenfrequency study.