Parametric reduced order models for predicting the nonlinear vibration response of cracked structures with uncertainty

Abstract

Modeling and re-analysis techniques are proposed for predicting the dynamic response of complex structures that have suffered damage in one or more of their components. When such damages are present, the model of the healthy structure may no longer capture the system-level response or the loading from the rest of the structure on the damaged components. Hence, novel models that allow for an accurate re-analysis of the response of damaged structures are needed in important applications, including damage detection. Herein, such models are obtained by using a reduced order modeling approach based on component mode synthesis. Because the resonant response of a complex structure is often sensitive to component uncertainties (in geometric parameters such as thickness, material properties such as Young's modulus, etc.), novel parametric reduced order models (PROMs) are developed. In previous work, PROMs have been applied for handling uncertainties in a single substructure. Herein, PROMs are extended to the general case of multiple substructures with uncertain parameters or damage. Two damage cases are considered: severe structural deformation (dents), and cracks. For the first damage case, an approximate method based on static mode compensation (SMC) is used to perform fast re-analysis of the vibration response of the damaged structure. The re-analysis is performed through a range of locations and severity levels of the damage. For selected damage locations and levels, the SMC approximation is compared to full finite element analysis to demonstrate the accuracy and computational time savings for the new method. For the second damage case (cracks), the vibration problem becomes nonlinear due to the intermittent contact of the crack faces. Therefore, to estimate the resonant frequencies for a cracked structure, the bi-linear frequency approximation (BFA) is used for cracks of various lengths. Since BFA is based on linear analyses, it is fast and particularly well suited for implementation with PROMs for structural re-analysis. In contrast, most other nonlinear techniques for predicting the dynamic response are computationally intensive and cumbersome. For validating the proposed PROMs, resonant frequencies predicted using BFA and PROMs are shown to agree very well with results obtained using a much more expensive commercial finite element tool.