Vibroacoustic Simulation

6 Random Description of Systems

In the academic examples from Chapters 4 and 5 all parameters of the problem are given: Material constants, wave speed and damping, boundary conditions, and the excitation. However, even for those simple cases the resonant and deterministic response at low frequencies moves on to noisy but asymptotic signal history for high frequencies.

Obviously, real systems such as cars, buildings, or ships are much more complex. There are many subsystems and different materials, and there is complex geometry and a large combination of shapes. In addition, the environmental conditions lead to further changes. Thus, all real engineering systems are subject to uncertainty.

The test cases reveal that the small changes in the parameters don’t change the dynamics of the system too much as long as the wavelength is just an order of magnitude below the length scale of the system. For high frequencies, the impact of small changes becomes high. The response of the dynamic system becomes very uncertain and varies strongly. Shorter and Langley (2005) introduced the term dynamically complex system for a system with fuzzy or uncertain parameters and small wavelengths compared to the system’s length scale. Consequently, such a system is dealt with by statistical methods.

In statistical energy analysis (and statistical physics) we deal with this randomness by statistical parameters such as mean or root mean values. As this corresponds to energy quantities, there is the word ...