Читать книгу Vibroacoustic Simulation - Alexander Peiffer - Страница 37

As clean harmonic signals are rare in technical systems we need a mathematical toolbox to deal with nonharmonic signals. Due to the Fourier theory (Nelson and Elliott, 1993) every deterministic time signal can be synthesized by a sum of harmonic components. This provides a theoretical link between periodic and harmonic but also transient signals. See appendix A.1 for a brief introduction.

The same theory can also be applied to stochastic or random signals but in a slightly different manner. Fourier analysis and methods for investigating the random processes and the description of mechanical systems by impulse response or frequency response functions is an important toolset for the description of vibroacoustic systems. In addition and due to digitalisation most signals or spectra are given as a discrete, digital set of values. This discrete formulation creates some pitfalls that may also lead to misinterpretations. Even though the signal analysis is not a major subject in vibroacoustic simulation it is a very important especially when acoustic experiments are performed.

Signals from technical processes are often not predictable and are generated randomly like pressure fluctuations in a turbulent flow, the impact of raindrops on a roof, or the stochastic combustion in a jet. For dealing with such signals the above described methods must be adapted. In addition we need formulations that allow for the definition of the statistics of random processes as there is no deterministic functionality between time or frequency and the physical quantity, for example force or displacement.