Efficient probabilistic vibration analysis of complex structures using substructuring and reliability techniques.
Lee, Soo-Yeol
2006
Abstract
A complex structure always has some parameter uncertainties due to manufacturing tolerances, material property variations, and other factors. The variability that is inherent in the manufacturing and assembly processes may have significant effects on the structural dynamics. Thus, it is important to be able to determine the sensitivity of the vibration response to various types of uncertainties. In this work, component-based reduced order modeling is used as a framework for studying and improving probabilistic vibration analysis methods for complex structures. Two classes of structures are considered: one class is characterized by vibration response that is highly sensitive to small, random parameter changes (e.g., a mistuned bladed disk in a turbine engine rotor); and the other is a general complex structure (e.g., the frame and body of an automotive vehicle). They are different not only in their structural sensitivity to uncertainties, but also in the definition of the performance function. For both classes of structures, various reliability and/or probabilistic analysis methods are employed, all of which have been extensively used in structural reliability and durability, and the performance and limitations of these methods are investigated. For general structures, the performance of three types of probabilistic approaches are studied, extended, and improved with respect to structural vibration analysis: (1) response surface method, (2) most probable point (MPP)-based method, and (3) a sampling method based on a simplified model. For the response surface method, modal velocities are described with locally linear interpolation functions, based on the first-order approximations of the modal impedance and modal force over a random variable space. Thus, this approach can achieve increased efficiency over a classical response surface method that utilizes a radial based function. Next, it is found that representative MPP-based methods---first-order reliability method (FORM), second-order reliability method (SORM), and iterative advanced mean value (AMV+) method---are not well suited for probabilistic structural vibration analysis. Thus, an improved approach, which can handle multiple limit-states, is developed. This is called a sequential MPP search method. Finally, a sampling-based approach with a simplified model, which relies on perturbation of a diagonalized reduced order model (ROM), is presented. A mode-based Monte Carlo simulation process is developed, which involves searching for and constructing perturbation models about center points before performing Monte Carlo simulation.Subjects
Analysis Complex Structures Efficient Most Probable Point Search Probabilistic Vibration Reliability Substructuring Techniques Using
Types
Thesis
Metadata
Show full item recordCollections
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.