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.