A Continuous Model for the Dynamical Analysis of Mistuned Bladed Rotors

Abstract

Ideal bladed rotors are rotationally symmetric, as a consequence they exhibit couples of degenerate eigenmodes at coinciding frequencies. When even small imperfections are present destroying the periodicity of the structure (disorder or mistuning), each couple of degenerate eigenfrequencies splits into two distinct values (frequency split) and the corresponding modal shapes exhibit vibration amplitude peaks concentrated around few blades (localization phenomenon). In this paper a continuous model describing the in-plane vibrations of a mistuned bladed rotor is derived via the homogenization theory. Imperfections are accounted for as deviations of the mass and/or stiffness of some blades from the design value; a perturbation approach is adopted in order to investigate the frequency split and localization phenomena arising in the imperfect structure. Numerical simulations show the effectiveness of the proposed model, requiring much lower computational effort than classical finite element schemes.

Study and Quantitative Analysis of Mode Localization in Wind Turbine Blades

“…Matrix perturbation theory is a powerful tool for studying the modal localization of structures [28][29][30][31]. The basic concept of this method is to approximately express the eigenvalues and eigenvectors of structures after disturbance by utilizing the eigenvalues and eigenvectors before disturbance.…”

Passive Vibration Reduction Analysis of the Mistuned Blisk Deposited Hard Coating Using Modified Reduced-Order Model

“…In order to apply this vibration reduction technology, the dynamic model and the prediction of vibration characteristics of the HCM blisk need to be investigated, such as the spring-mass models (or lumped parameter models) [36][37][38][39], the beam-plate models (or continuous parameter model) [40,41], and the FEMs (finite element models) [42,43]. In spring-mass models, each sector of the blisk was usually modeled using just one or a few lumped masses connected by springs, and the qualitative results were useful for gaining a rough understanding of the influence of the mistuning on the vibration characterizes of the blisk, most notably the identification of critical blades and the increase in forced response levels which can be caused by mistuning.…”

Application of the hard-coating damper on the mistuned blisk for passive vibration reduction

“…Some kinds of models have been developed for forced response analysis of the mistuned blisk, such as the spring-mass (lumped mass) model, 36,37 the beam-plate (continuous parameter) model 38,39 and the finite element model (FEM). 40 The spring-mass model and the beam-plate model were usually used to understand rough effects of the blade mistuning on dynamics of the blisk.…”