Equation-Free Analysis of Mechanical Vibrations

Mechanical vibrations are the cause of substantial operational and
safety related problems with many mechanical systems of major
importance, in particular in transportation, energy production, and
industry. This project aims towards the development of new
mathematical techniques to systematically investigate the dependence
of vibrations on model parameters (e.g. bearing or material
coefficients). To achieve this, equation-free techniques (also called
coarse analysis) will be used which allow to obtain an understanding
of the dynamic behaviour on a macroscopic scale by disregarding large
amounts of unimportant information on the microscopic scale.

The method fills the gap between time simulations of complex numerical
models, such as nonlinear finite element models (FEM), and stability
and bifurcation analyses with much simpler analytical models. The
reason is that it enables such informative analyses directly on the
complex microscopic models without the (often approximative)
derivation of equations of motion on a macroscopic level. Due to the
high-dimensional variable and parameter spaces and resulting
computational costs, it is not possible to obtain similar information
by direct simulations. The scientific goal is to clarify the
potential of this approach within an important area of mechanics,
rotating machinery (e.g. a turbocharger), where the detailed
understanding of time dependent complex models play important roles in
the design process.