Parametric reduced-order models for predicting the vibration response of complex structures with component damage and uncertainties

Modeling and fast reanalysis techniques are proposed for predicting the dynamic response of complex structures with uncertainty represented by parameter variability (in geometric and material properties) at component-level. The novel models allow for accurate reanalyses and are useful in many applications where the model of the pristine structure may not capture the changes in the system-level response due to component-level parameter variations. Herein, such models are obtained by using a novel approach based on a modified concept of component mode synthesis. The novel models, referred to as parametric reduced-order models, are developed for the general case of multiple substructures with parameter variabilities. Three types of parameteric variabilities are considered: (a) geometric (thickness) variability, (b) structural deformations (dents), and (c) cracks. For the first case, a novel parametrization of component-level mass and stiffness matrices is employed to predict the system-level response. For the second case, a novel approximate method based on static mode compensation is implemented. For the third case (cracks), a generalized formulation for the bi-linear frequency approximation is used. The predicted vibration responses of complex structures are shown to agree very well with results obtained using a much more computationally expensive commercial tool.