A Reduced Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons

Abstract

This paper draws upon the theoretical basis and applicability of the threedimensional (3D) reducedorder spectralbased “meshlessâ€‌ energy technology presented in a companion paper (McGee et al., 2013, “A ReducedOrder Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis,â€‌ ASME J. Turbomach., to be published) to predict free and forced responses of bladed disks comprised of randomly mistuned blades integrally attached to a flexible disk. The 3D reducedorder spectralbased model employed is an alternative choice in the computational modeling landscape of bladed disks, such as conventionallyused finite element methods and component mode synthesis techniques, and even emerging elementfree Hamiltonian–Galerkin, Petrov–Galerkin, boundary integral, and kernelparticle methods. This is because continuumbased modeling of a full disk annulus of mistuned blades is, at present, a steep task using these latter approaches for modaltype mistuning and/or rogue blade failure analysis. Hence, a considerably simplified and idealized bladed disk of 20 randomly mistuned blades mounted to a flexible disk was created and modeled not only to analyze its free and forced 3D responses, but also to compare the predictive capability of the present reducedorder spectralbased “meshlessâ€‌ technology to generalpurpose finite element procedures widelyused in industry practice. To benchmark future development of reducedorder technologies of turbomachinery mechanics analysts may use the present 3D findings of the idealized 20bladed disk as a new standard test model. Application of the 3D reducedorder spectralbased “meshlessâ€‌ technology to an industry integrallybladed rotor, having all of its blades modally mistuned, is also offered, where reasonably sufficient upperbounds on the exact free and forced 3D responses are predicted. These predictions expound new solutions of 3D vibration effects of modal mistuning strength and pattern, interblade mechanical coupling, and localized modes on the free and forced response amplitudes.