Investigation Of The Vibration Localization Problem Of The Mistuned Bladed Disk With Complicated Coupling

The bladed disk is an important component in the high performance aeronauticalengines. The blades on the disk will vibrate due to the excitation by the unsteadystream field and the unbalanced factors. The vibratory response of blades is verysensitive to the small variations of blade properties. These variations, which arereferred to mistuning, mainly come from the blade procession, wear in service, etc.The mistuning can lead to the localization of vibratory energy of a bladed disk,increase the vibratory stress in the resonant region, and even result in the high cyclicfatigue failure.In this dissertation, the vibration localization problem of the mistuned bladeddisk with complicated coupling is systematically investigated through the mass-stringmodels and the finite element model. The investigations focus on the fundamentalphysics and solution methods of the effects of mistuning on the natural properties andforced response of the bladed disks. Conclusions of the mistuning effects on thedynamics of the bladed disk are summarized.The bladed disk assemblies are cyclic symmetry structures. Mistuning destroysthe symmetric properties, and produce modal localization for a bladed disk. We definea modal localization parameter for the blade-disk system modes. This parameter canaccurately describe the degree of concentration of vibratory energy of the systemmodal shape in quantity. Using this parameter, the effects of mistuning on thelocalization of system modal shapes for various orders are studied. The reasons of themodal localization phenomenon are analyzed by the perturbation method. At the meantime, for some middle order modals, a singular change of the value of the localizationparameter was found in the weak coupling region. This singular change is hard toexplain by perturbation methods, and may result in unsteady vibrations for themistuned bladed disk. Few past investigations have documented this strangephenomenon.The deterministic and statistic methods are employed respectively to study theforced response of the mistuned bladed disk under various system parameters withrespect to the deterministic and random mistuning. In the statistic analysis, wepropose a method that calculates and compares the statistics of the maximum andaverage vibratory responses. This method can analyze the concentration degree of thevibratory energy so that the characteristics of the vibration localization of themistuned bladed disk can be investigated.The perturbation methods are the common analyzing method for studying thevibratory response of the mistuned bladed disk, but different perturbation methodshave their own relying conditions on the system parameters. In this dissertation, threekey perturbation methods are studied for their application conditions. Their relyingconditions on the system parameters are summarized. For the adaptive perturbationmethod, an auto-selecting-modal method (ASMM) is proposed to improve the originaladaptive perturbation method on the mode-selecting mechanism. By this proposedmethod, the accuracy and the efficiency are both improved. The ASMM is especially suitable for statistics analyzing.The approximations of past analyzing methods can hardly give accurate resultwhen the coupling degree is in the middle range. To solve this problem, a new modelcombined analyzing method (MCAM) which can predict the vibratory response of themistuned bladed disk in entire range of coupling is proposed. This method employs apartial-entire-combined mistuning model to predict the vibratory response of amistuned bladed disk. Meanwhile, a reasonable error correction ratio is proposed tofurther increase the accuracy of the solution. Because the error mainly comes from theresonant region, the error correction method can only be used in resonant region, andcan effectively improve the efficiency of the statistical analyzing solutions.Two types of the mistuned bladed disks, whose friction damping are blade dryfriction damping and blade-to-blade dry friction damping, are modeled respectively. Amulti-harmonic method (MHM) which can employ the fast Fourier transformationtechnique is proposed to investigate the vibratory response of the bladed disks withthese two types of nonlinear friction damping. Formulations of the solution for thesetwo types of motion functions are deduced. The characteristics of the forced responseof the bladed disks with these two dry friction damping are analyzed and summarizedunder various system parameters. The vibratory response of the bladed disk with dryfriction scatter mistuning is investigated. The effects of this special mistuning type onthe features of the vibratory response of the bladed disk are studied and summarized.The reciprocal effects between the frequency veering and the sensitivity ofmistuning for a bladed disk are studied. The investigation is based on a finite elementmodel. The reason and features of frequency veering of the bladed disk are analyzed.By using the localization parameter, the effects of mistuning on the system modallocalization of the bladed disk are analyzed in the frequency veering region. Theeffects of mistuning on the forced response are also analyzed in the frequency veeringregion.The outcomes of this dissertation improve the fundamental theories of thevibration localization of the mistuned bladed disk. They can be a support for thedesigner to look insight of the vibration mechanism of the mistuned bladed disk, andto predict its forced response. Therefore, the researches of this dissertation canprovide fundamental theories for studying and designing the power systems of thenew high performance aero-engines.