Modal Analysis:

Modal analysis is a tool that allows to compare measurements and calculation in the low frequency region.

The modes are mainly calulated using the finite element method (FEM).

The measurement is recorded with an artifical excitation either by a shaker or an instrumented hammer. The admittances of the structure are derived using the power spectral density (PSD) of the excitation and the cross power spectral density of the response and the excitation.

The admittances of a discrete model as it is given in the FEM can be described by a quotient of two polynomials. The polynomial in the denominator is the same for all admittances of a structure. The zeros of the polynomial in the denominator are the complex resonances of the structure.

A large number of methods exist for the esimation of the complex modes from the admittances. In the institute the Global Rational Fractional Polynomial (GRFP) method was implemented. An extension of the method allows to derivate directly the mode shape.

A project for the future is the combination of Comutational Fluid Dynamics (CFD) especially the Large Eddy Simulation (LES) with the Fast Multipole Boundary Element Method (FMBEM). The flow acoustics of a panthograph can be simulatied by this combination.

A flutter instability in water was observed on rotor blades. The instability leads to high noise levels. A simple tool for the rapid simuation was developed. The panel method was combined with the finite element model of the blade to estimate the critical velocity of the fluid.

The project extends isotropic computation of vibrations in the soil to anisotropic material. Up to now mainly deterministic models have been used in practice.

Read more: Vibrations in Stratified Anisotropic or Random Material

**gear orders** in a multiple motor component environment a specific method for the generation of order spectrograms has been implemented into S_TOOLS-ST^{x}. The method applies smoothing on the rpm-signal and uses re-sampling as well as the Discrete Fourier Transform (DFT) in combination with the anti aliasing filter to create **order analysis spectrograms** at reasonable computational cost.

Blind source seperation is based on PCA and ICA.

The principal component analysis (PCA) and independent component analysis (ICA) are methods to devide a mixture of sounds into uncorrelated or indendent components.

The PCA is based on the singular value decomposition (SVD) of a matrix or on the eigenvalue and eigenvector determination of a centered covarince or correlation matrix.

PCA is applied in the method Spatial Transfrom of sound fields (STSF) to receive uncorrelated components from a mixture. The components are assumed to be coherent and projected by the method acoustic holography.

The method PCA was applied to simultaneous measurements of vibrations on the structure and sound in the far field. The components from the PCA are seperated into near field and far field components using the reaction of the far field microphone.

The Doppler effect of moving sources in the far field was compensated either by correcting the transformation kernel from time to frequency domain or by re-sampling.

A better seperation of independent sources is possible, if ICA is applied. ICA in theory is based on the Kulback-Leibler divergency related to a Gaussian distribution to maximize a non-Gausianity. Approximations to this feature that are more stable and faster to optimize are used in the FastICA algorithms.

The FastICA code was applied to short pices of music and the notes were separated by this algorithm.

**64 microphone array **is applied when instationary or moving sound sources have to be processed. Numeric simulation corresponds with measurements of monopole sources in an anechoic room concerning dynamic relations and side lobe influence.

Measurements of noise of high speed trains (ICE-S from 200 km/h to 300 km/h) have been performed. Beam forming on horizontal as well as on vertical axis enables the identification of distinctive noise emissions generated from different sections of the trains passing by. Noise radiated from wheel-rail contact dominates at speeds up to 240km/h. At higher speeds flow noise originating from roof components and pantographs is clearly distinguishable.

Read more: Noise Emissions of Moving Sources (High Speed Trains)

The picture compares (left) the traditional Boundary Element Method (BEM) with the MLFMM (see larger picture).

The BEM is an important tool used in Acoustics. But the computational effort for traditional BEM, which is O(n^{2}) (n is the number of unknowns), makes the solution of real life problems for high frequencies almost impossible. The combination with the Fast Multipole Method (FMM) reduces this effort to O(n·log^{2}(n)), thus making it possible to also solve problems in the high frequency region.

Read more: Boundary Element Method (BEM) - Multilevel Fast Multipole Method (MLFMM)