Dynamic model order reduction of blisks with nonlinear damping coatings using amplitude dependent mistuning

In this paper, a reduced order model is developed to simulate the dynamics of a bladed disk or blisk with nonlinear damping coatings adhered to its blades. The nonlinear forces exerted by these coatings on the underlying linear blisk structure are a function of the local strain. It is known that coatings modify the stiffness and damping of each blade depending on its amplitude. Blisks, which are designed as perfectly cyclic symmetric structures with identical blades, never behave as such in practice due to various uncertainties encountered during their manufacturing. This asymmetry in the structure is also referred to as mistuning. Mistuning in the linear blisk structure, which causes different blades to respond with non-identical amplitudes, interacts with the coating nonlinearity to yield a mistuning pattern which depends on the blade amplitudes. Additional stiffness and damping parameters that are dependent on the blade amplitude are introduced into a reduced linear model to formulate the nonlinear reduced order model. It is found that this model captures the nonlinear amplitude dependent mistuning effect and predicts the nonlinear coated blisk responses accurately near isolated blisk mode families in blade-dominated frequency regions where these coating effects are likely to be dominant. Significant reductions in the computational effort are achieved through this reduction.