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978-3-8439-4411-3, Reihe Luftfahrt
Numerical analysis of flutter-induced multi-wave vibrations of bladed disks with tip-shroud friction
94 Seiten, Dissertation Universität Stuttgart (2019), Softcover, A5
Measurements of a low pressure turbine (LPT) blade row with tip-shrouds revealed that multiple traveling wave modes can simultaneously contribute to bounded flutter vibrations. This phenomenon is referred to as multi-wave flutter vibrations (MWFV) and cannot be explained with the available theory. Whether geometrical blade-to-blade variations (mistuning) or strongly nonlinear tip-shroud friction is a likely cause for the experimentally observed MWFV is not known. In order to investigate this question, a state-of-the-art aeroelastic model of a LPT blade row with tip-shrouds is considered in this thesis.
Indeed, it is found that tip-shroud friction can lead to multi-wave flutter vibrations. The oscillations in this case are quasi-periodic. Here, multiple wave components arise due to strongly nonlinear interaction between distinct traveling wave modes. An internal combination resonance between the associated frequencies is found to be the necessary condition.
Even in the linear case, mistuning can destroy the symmetry of the mode shapes so that they generally contain multiple wave components. In this case, the limit states are dominated by a single mistuned mode shape, and the oscillations are periodic.
Time and frequency domain methods for computing the quasi-periodic limit states are assessed in this thesis. An available multi-dimensional harmonic balance method (MDHB) is completed by a systematic construction of a good initial guess and a strategy to exclude degenerate solutions. The computation of friction-damped, quasi-periodic oscillations in the frequency domain requires the introduction of auxiliary variables, which can only be represented well using a very high number of Fourier terms. This compromises the expected efficiency benefit of the frequency domain method compared to numerical time integration. Moreover, MDHB does neither give any information about the stability of the found solution nor, and if stable, which initial conditions lead to it.