Statistics of response of a mistuned and frictionally damped bladed disk assembly subjected to random excitation.

摘要

In this thesis, analytical techniques have been developed to efficiently compute the statistics of the response of a mistuned bladed disk assembly (with and without friction dampers) subjected to random excitation. The accuracy of these analytical techniques has been tested by the simple discrete model which represents the basic characteristics of the blade disk vibration. Considering the circumferential pressure field of a turbomachinery, three different types of excitation are considered: white noise excitation, narrow band random excitation and sinusoidal excitation with unknown amplitudes. The narrow band random excitation can be generated as an output of the band-pass filter with the white noise as an input and the sinusoidal excitation with unknown amplitude is considered as a sinusoidal functions where the amplitude and phase shift are time-invariant random variables. The sensitivities of the response to mistuning have been examined as a function of the frequency bandwidth of random excitation and the structural coupling stiffness. Furthermore, the effects of correlation of narrow band excitation on the response variance of mistuned system are investigated.; To investigate the effect of normal load on the performance of a friction damper, the equivalent linearization method (ELM) is used for white noise and narrow band random excitations and the harmonic balance method (HBM) is used for sinusoidal excitation with unknown amplitudes. To examine the accuracy of ELM, the analytical results for a tuned and a mistuned system with friction dampers are compared with those from the numerical integration of differential equations. Then, the analytical techniques are used to calculate the statistics of response variance of a frictionally damped and mistuned bladed disk assembly subjected to random excitation. The performance of both types of friction dampers, blade-to-blade and blade-to-ground dampers, are represented by a new set of nondimensionalized variables, so that the optimal normal loads can be obtained without any direct information about the external force.