The focus of this investigation is on the optimum placement of a limited number of dampers, fewer than the number of blades, on a bladed disk to induce the smallest amplitude of blade response. The optimization process considers the presence of random mistuning, i.e. small involuntary variations in blade stiffness properties resulting, say, from manufacturing variability. Designed variations of these properties, known as intentional mistuning, is considered as an option to reduce blade response and the pattern of two blade types (A and B blades) is then part of the optimization in addition to the location of dampers on the disk. First, this study focuses on the formulation and validation of dedicated algorithms for the selection of the damper locations and the intentional mistuning pattern. Failure of one or several of the dampers could lead to a sharp rise in blade response and this issue is addressed by including, in the optimization, the possibility of damper failure to yield a fail-safe solution. The high efficiency and accuracy of the optimization algorithms is assessed in comparison with computationally very demanding exhaustive search results. Second, the developed optimization algorithms are applied to nonlinear dampers (underplatform friction dampers), as well as to blade-blade dampers, both linear and nonlinear. Further, the optimization of blade-only and blade-blade linear dampers is extended to include uncertainty or variability in the damper properties induced by manufacturing or wear. It is found that the optimum achieved without considering such uncertainty is robust with respect to it. Finally, the potential benefits of using two different types of friction dampers differing in their masses (A and B types), on a bladed disk are considered. Both A/B pattern and the damper masses are optimized to obtain the largest benefit compared to using identical dampers of optimized masses on every blade. Four situations are considered: tuned disks, disks with random mistuning of blade stiffness, and, disks with random mistuning of both blade stiffness and damper normal forces with and without damper variability induced by manufacturing and wear. In all cases, the benefit of intentional mistuning of friction dampers is small, of the order of a few percent.

This thesis concerns the role of geometric imperfections on assemblies in which the location of a target part is dependent on supports at two features. In some applications, such as a turbo-machine rotor that is supported by a series of parts at each bearing, it is the interference or clearance at a functional target feature, such as at the blades that must be controlled. The first part of this thesis relates the limits of location for the target part to geometric imperfections of other parts when stacked-up in parallel paths. In this section parts are considered to be rigid (non-deformable). By understanding how much of variation from the supporting parts contribute to variations of the target feature, a designer can better utilize the tolerance budget when assigning values to individual tolerances. In this work, the T-Map®, a spatial math model is used to model the tolerance accumulation in parallel assemblies. In other applications where parts are flexible, deformations are induced when parts in parallel are clamped together during assembly. Presuming that perfectly manufactured parts have been designed to fit perfectly together and produce zero deformations, the clamping-induced deformations result entirely from the imperfect geometry that is produced during manufacture. The magnitudes and types of these deformations are a function of part dimensions and material stiffnesses, and they are limited by design tolerances that control manufacturing variations. These manufacturing variations, if uncontrolled, may produce high enough stresses when the parts are assembled that premature failure can occur before the design life. The last part of the thesis relates the limits on the largest von Mises stress in one part to functional tolerance limits that must be set at the beginning of a tolerance analysis of parts in such an assembly.

The focus of this investigation is on the renewed assessment of nonlinear reduced order models (ROM) for the accurate prediction of the geometrically nonlinear response of a curved beam. In light of difficulties encountered in an earlier modeling effort, the various steps involved in the construction of the reduced order model are carefully reassessed. The selection of the basis functions is first addressed by comparison with the results of proper orthogonal decomposition (POD) analysis. The normal basis functions suggested earlier, i.e. the transverse linear modes of the corresponding flat beam, are shown in fact to be very close to the POD eigenvectors of the normal displacements and thus retained in the present effort. A strong connection is similarly established between the POD eigenvectors of the tangential displacements and the dual modes which are accordingly selected to complement the normal basis functions. The identification of the parameters of the reduced order model is revisited next and it is observed that the standard approach for their identification does not capture well the occurrence of snap-throughs. On this basis, a revised approach is proposed which is assessed first on the static, symmetric response of the beam to a uniform load. A very good to excellent matching between full finite element and ROM predicted responses validates the new identification procedure and motivates its application to the dynamic response of the beam which exhibits both symmetric and antisymmetric motions. While not quite as accurate as in the static case, the reduced order model predictions match well their full Nastran counterparts and support the reduced order model development strategy.