Narrow Results

The solution of time-harmonic acoustic problems suffers from a frequency dependency which usually requires to solve the systems for many discrete frequencies independently. Among others, the Padé-via-Lanczos approximation provides an efficient solution. Herein, this method is applied to the external acoustic problem by using a finite and infinite element formulation. The state-space system matrix is first reduced to a condensed transfer matrix which is approximated in a power series, i.e. Padé approximation. The coefficients of this power series are reconstructed by using a Krylov basis, i.e. Lanczos method. Based on this method, the authors provide a formulation for the radiated sound power. The necessary integration over the boundary for the sound power is done in the first vectors of the Lanczos method. Thus the scalar sound power can be approximated in a certain frequency band by means of a transfer matrix, which is several orders of magnitude smaller than the total numbers of degrees of freedom of the overall problem. The error of this additional approximation can be estimated. The method is tested in an example of an open cavity including two loadcases, one representing a cavity with an open window, the other one being a radiating obstacle.

A combination of a commercially available finite element software package and additional user-written programs is used to modify the shape of a square plate made of steel. The structure's local geometry modification values at the selected surface key-points are considered as design variables. The objective of the optimization includes the minimization of the root mean square level of structure borne sound. The optimization process continues automatically until the predefined maximum number of function evaluations is reached. A statistical approach is followed for the comparison of seven different optimization methods. It will be shown that the method of moving asymptotes and the mid-range multi-point method produce the best results to find a substantial improvement of the objective function within a limited number of function evaluations.

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.

The sound radiation inside an acoustic canyon has been analyzed for a surface sound source located at the bottom. Based on rigorous mathematical manipulations, the formulas of a high computational efficiency describing the sound pressure and sound power have been obtained. They can be easily adapted to describe the sound radiation of an arbitrary system of sound sources. As an example of their application, the sound radiation of a piston has been investigated. The asymptotic formulas of the sound power modal coefficients have been obtained. They can be used to significantly improve the numerical calculation of the sound power.

Sound power estimation is a widely investigated research topic. Some of its state-of-the-art measurement solutions include taking velocity values on the source boundary, discrete pressure assessment on a virtual outer surface or evaluations with a sound intensity probe. The increased availability of microphone arrays proposes a new tool to obtain these results. The inverse boundary element method, the equivalent source method, the Helmholtz equation least-squares, and an approach based on the radiation resistance matrix provide vectorized formulations for estimating sound power. In this study, the results for different regularization techniques on the sound power deviation from a discrete line source are presented based on a backward reconstruction scheme from simulated sound pressure field points on four microphone arrays. Additionally, in this study, time improvement between single-frequency calculations and multi-frequency execution on multiple graphics processing units is presented. The outcome shows good accuracy and reduced computation time in graphics card implementations.