Equation-Free Analysis of Mechanical Vibrations

    Project Details

    Description

    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.
    StatusFinished
    Effective start/end date01/04/200931/03/2012

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