Parametric Reduced-Order Models of Structural Dynamics for Design, Damage Detection and Structural Optimization.

Abstract

The main goal of this work is to develop new modeling and fast reanalysis techniques for predicting the dynamic response of complex structures with parameter variability 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. Two new types of models are developed. The first type, referred to as multiple component parametric reduced-order models (MC-PROMs), are designed for multiple substructures modeled with shell-type elements with parameter variabilities. Three types of parametric variabilities are considered: (a) geometric variability, (b) structural deformations, and (c) cracks. For validating the MC-PROMs, dynamic responses predicted MC-PROMs are shown to agree very well with results obtained using full-order models. The second type of models are developed to address two important accuracy and performance challenges of MC-PROMs, namely: (a) the transformation matrix is not always mathematically stable, (b) the Taylor series parameterization techniques do not capture thickness variations of the structure modeled with solid-type elements due to the highly nonlinear dependence on thickness changes. Thus, herein, a new transformation matrix and novel parameterization techniques are proposed. Usual reduced-order models have difficulty handling the interface degrees of freedom. Thus, a novel way of reducing the interface degrees of freedom is proposed also. The novel models are referred to as the next-generation parametric reduced-order models (NXPROMs). The vibration responses predicted by NX-PROMs are in excellent agreement with the responses predicted by full-order models. Both types of PROMs are used in three applications: (a) to establish a robust signal processing approach for damaged vehicles (crack) with structural variability, (b) to develop a damage detection algorithm to identify the size of a crack in complex structures, and (c) to provide a methodology for choosing joining locations for attaching structural reinforcements onto complex structures. Numerical results for each application are presented focusing on a high mobility multipurpose wheeled vehicle with structural variabilities.