Vibration analysis is fundamental in the analysis and design of rotating machinery designs, such as turbines, pumps and bearings. It is equally important in the theory of sound and is also related to the properties of electromagnetic waveguides. Its application extends to vehicle structures, equipment and design machines, both for reference and comfort. However, a vibrational analysis also has more daring purposes, directed to the definition of seismic attributes, to the dispersion of phenomena related to acoustics in infinite media. This solution can be adapted as the frequency of vibrations and how outdoor environments are designed for self-balancing devices are designed for Helmholtz self-balancing devices, which are directly adjusted. Typical pressure media situations, Boundary Element Method (BEM) is considered as one of the technical circumstances or more considered, due to its pressure field accuracy, especially differentiated by barriers and scattering of general circumstances, whose frequencies are complex numbers. This work aims to present the various particularities of BEM in approaching these problems, which involve determining the acoustic eigenvalues in open and closed domains, highlighting its operational advantages and numerical difficulties.
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