<p>Two state of the art finite element reduction techniquespreviously validated against the direct finite element method,one based on classical modal analysis and another based oncomponent mode synthesis, are applied for efficient mistunedfree vibration and forced response analysis of several bladeddisk geometries. The methods are first applied to two testcases in order to demonstrate the differences in computationalefficiency as well as to validate the methods againstexperimental data. As previous studies have indicated, nonoticeable differences in accuracy are detected for the currentapplications, while the method based on classical modalanalysis is significantly more efficient. Experimental data(mistuned frequencies and mode shapes) available for one of thetwo test cases are compared with numerical predictions, and agood match is obtained, which adds to the previous validationof the methods (against the direct finite element method).</p><p>The influence of blade-to-blade coupling and rotation speedon the sensitivity of bladed disks to mistuning is thenstudied. A transonic fan is considered with part span shroudsand without shrouds, respectively, constituting a high and alow blade-to-blade coupling case. For both cases, computationsare performed at rest as well as at various rotation speeds.Mistuning sensitivity is modelled as the dependence ofamplitude magnification on the standard deviation of bladestiffnesses. The finite element reduction technique based onclassical modal analysis is employed for the structuralanalysis. This reduced order model is solved for sets of randomblade stiffnesses with various standard deviations, i.e. MonteCarlo simulations. In order to reduce the sample size, thestatistical data is fitted to a Weibull (type III) parametermodel. Three different parameter estimation techniques areapplied and compared. The key role of blade-to-blade coupling,as well as the ratio of mistuning to coupling, is demonstratedfor the two cases. It is observed that mistuning sensitivityvaries significantly with rotation speed for both fans due toan associated variation in blade-to-blade coupling strength.Focusing on the effect of one specific engine order on themistuned response of the first bending modes, it is observedthat the mistuning sensitivity behaviour of the fan withoutshrouds is unaffected by rotation at its resonant condition,due to insignificant changes in coupling strength at thisspeed. The fan with shrouds, on the other hand, shows asignificantly different behaviour at rest and resonant speed,due to increased coupling under rotation. Comparing the twocases at resonant rotor speeds, the fan without shrouds is lessor equally sensitive to mistuning than the fan with shrouds inthe entire range of mistuning strengths considered.</p><p>This thesis’scientific contribution centres on themistuning sensitivity study, where the effects of shrouds androtation speed are quantified for realistic bladed diskgeometries. However, also the validation of two finite elementreduction techniques against experimental measurementsconstitutes an important contribution.</p>

One of the most important problems that plague turbomachinery rotors is the existence of rogue blades -- lone blades that exhibit unexpected fatigue failure. It has been recognized that rotor mistuning might be the cause of rogue blades through a phenomenoncalled normal mode localization, whereby vibration energy is confined to a few blades of the assembly. The goals of this dissertation are (1) to achieve a thorough understanding of the fundamental mechanisms governing mistuning effects, (2) the development of mathematical models of turbomachinery rotors suitable for mistuning analysis, and (3) the development of techniques for designers interested in the mistuning sensitivity of a particular rotor design.

Two state of the art finite element reduction techniquespreviously validated against the direct finite element method,one based on classical modal analysis and another based oncomponent mode synthesis, are applied for efficient mistunedfree vibration and forced response analysis of several bladeddisk geometries. The methods are first applied to two testcases in order to demonstrate the differences in computationalefficiency as well as to validate the methods againstexperimental data. As previous studies have indicated, nonoticeable differences in accuracy are detected for the currentapplications, while the method based on classical modalanalysis is significantly more efficient. Experimental data(mistuned frequencies and mode shapes) available for one of thetwo test cases are compared with numerical predictions, and agood match is obtained, which adds to the previous validationof the methods (against the direct finite element method). The influence of blade-to-blade coupling and rotation speedon the sensitivity of bladed disks to mistuning is thenstudied. A transonic fan is considered with part span shroudsand without shrouds, respectively, constituting a high and alow blade-to-blade coupling case. For both cases, computationsare performed at rest as well as at various rotation speeds.Mistuning sensitivity is modelled as the dependence ofamplitude magnification on the standard deviation of bladestiffnesses. The finite element reduction technique based onclassical modal analysis is employed for the structuralanalysis. This reduced order model is solved for sets of randomblade stiffnesses with various standard deviations, i.e. MonteCarlo simulations. In order to reduce the sample size, thestatistical data is fitted to a Weibull (type III) parametermodel. Three different parameter estimation techniques areapplied and compared. The key role of blade-to-blade coupling,as well as the ratio of mistuning to coupling, is demonstratedfor the two cases. It is observed that mistuning sensitivityvaries significantly with rotation speed for both fans due toan associated variation in blade-to-blade coupling strength.Focusing on the effect of one specific engine order on themistuned response of the first bending modes, it is observedthat the mistuning sensitivity behaviour of the fan withoutshrouds is unaffected by rotation at its resonant condition,due to insignificant changes in coupling strength at thisspeed. The fan with shrouds, on the other hand, shows asignificantly different behaviour at rest and resonant speed,due to increased coupling under rotation. Comparing the twocases at resonant rotor speeds, the fan without shrouds is lessor equally sensitive to mistuning than the fan with shrouds inthe entire range of mistuning strengths considered. This thesis’scientific contribution centres on themistuning sensitivity study, where the effects of shrouds androtation speed are quantified for realistic bladed diskgeometries. However, also the validation of two finite elementreduction techniques against experimental measurementsconstitutes an important contribution. / NR 20140805

High cycle fatigue (HCF) failure has been studied extensively over the last two decades. Its impact on jet engines is severe enough that may result in engine losses and even life losses. The main requirement for fatigue life predictions is the stress caused by mechanical vibrations. One of the factors which have major impact on the vibratory stresses of bladed disk assemblies is a phenomenon called &ldquo / mistuning&rdquo / which is defined as the vibration localization caused by the loss of cyclic periodicity which is a consequence of inter&amp / #8208 / blade variations in structural properties. In this thesis, component mode synthesis method (CMSM) is combined with nonlinear forced response analysis in modal domain. Newton&amp / #8208 / Raphson and arc length continuation procedures are implemented for the solution. The component mode synthesis method introduces the capability of imposing mistuning on the modal properties of each blade in the assembly. Forced response analysis in modal domain reduces the problem size via mode truncation. The main advantage of the proposed method is that it is capable of calculating nonlinear forced response for all the degrees&amp / #8208 / of&amp / #8208 / freedom at each blade with less computational effort. This makes it possible to make a stress analysis at resonance conditions. The case studies presented in this thesis emphasize the importance of number of modes retained in the reduced order model for both CMSM and nonlinear forced response analysis. Furthermore, the results of the case studies have shown that both nonlinearity and mistuning can cause shifts in resonance frequencies and changes in resonance amplitudes. Despite the changes in resonance conditions, the shape of the blade motion may not be affected.