A reduced-order meshless energy (ROME) model for the elastodynamics of mistuned bladed disks

A careful Monte Carlo simulation of the statistical mechanics of a randomly mistuned bladed disk requires, in the ideal sense, a Reduced-Order Meshless Energy (ROME) model that captures the three-dimensional (3-D) elastodynamical physics of the bladed disk at a reasonable cost. Such a modeling technique has been unavailable until now. In this work, a significant order reduction of the elastodynamics of a bladed disk assembly has been achieved. The system studied was regarded as a 3-D annulus of shroudless, arbitrarily-shaped and randomly mistuned blades attached to a flexible disk for interblade mechanical coupling. Specifically, the annulus was modeled as a meshless continuum structure utilizing only nodal data to describe the arbitrary volume in which the system's dynamical energy was minimized. An extended Ritz variational procedure was used to minimize this energy, subjected to constraints imposed by an assumed 3-D displacement field of mathematically complete, orthonormal “blade-disk” polynomials newly constructed for the title problem. From this the governing equations of motion were yielded and recasted into their usual forms to calculate the free and forced responses of bladed disks.; The ROME model, which required no conventional finite elements and element connectivity or component substructuring data, employed constituted a considerable advantage over conventionally used finite element methods and component mode synthesis techniques, and even emerging element-free Galerkin methods. The present work outlines the theoretical foundation of the ROME model, and through fundamental case studies, establishes the analytical basis and predictive accuracy of the approach.; Hence, an idealized 20-bladed disk was created and modeled to analyze their free and forced responses and to compare the predictive capability and computational efficiency of the ROME technology to general-purpose finite element technology. The ROME model was also used to examine the effect of mistuning strength and pattern, interblade coupling, and localized modes on the free and forced response of an industry Integrally Bladed Rotor (IBR) in this work.