Title: Frequency analysis of uncertain structures using imprecise probability

Authors: Mehdi Modares; Joshua Bergerson

Addresses: Department of Civil, Architectural and Environmental Engineering, Illinois Institute of Technology, Chicago, IL, 60616, USA ' Department of Civil, Architectural and Environmental Engineering, Illinois Institute of Technology, Chicago, IL, 60616, USA

Abstract: Two new methods for finite element based frequency analysis of a structure with uncertainty are developed. An imprecise probability formulation based on enveloping p-boxes is used to quantify the uncertainty present in the mechanical characteristics of the structure. For each element, independent variations are considered. Using the two developed methods, P-box Frequency Analysis (PFA) and Interval Monte-Carlo Frequency Analysis (IMFA), sharp bounds on natural circular frequencies at different probability levels are obtained. These methods establish a framework for handling incomplete information in structural dynamics. Numerical example problems are presented that illustrate the capabilities of the new methods along with discussions on their computational efficiency.

Keywords: structural dynamics; uncertainty; imprecise probability; p-box; interval Monte-Carlo; frequency analysis; uncertain structures; finite element analysis; FEA.

DOI: 10.1504/IJRS.2015.073126

International Journal of Reliability and Safety, 2015 Vol.9 No.4, pp.235 - 254

Available online: 19 Nov 2015 *

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