Title: Dynamic analysis of uncertain structures using imprecise probability

Authors: Mehdi Modares; Joshua Bergerson

Addresses: Department of Civil, Architectural and Environmental Engineering, Illinois Institute of Technology, 3201 South Dearborn, AM 213, Chicago, IL 60616, USA ' Department of Civil, Architectural and Environmental Engineering, Illinois Institute of Technology, 3201 South Dearborn, AM 213, Chicago, IL 60616, USA

Abstract: A new method for dynamic response spectrum analysis of structures with uncertainty in their mechanical properties utilising the notion of imprecise probability is developed. This finite-element-based method is capable of obtaining probabilistic bounds of the dynamic response of the structure with uncertainty defined by enveloping imprecise probability structures. The developed method obtains probabilistic bounds on (1) natural circular frequencies, (2) mode shapes, (3) modal coordinates and (4) modal participation factors leading to the imprecise probability structures of modal responses. Finally, maximum modal responses are combined to obtain the structure's maximum total response with consideration of uncertainty. Numerical examples demonstrating the developed method are presented.

Keywords: structural dynamics; uncertainty; imprecise probability; dynamic response spectrum analysis; finite element method; FEM; natural circular frequencies; mode shapes; modal coordinates; modal participation factors.

DOI: 10.1504/IJRS.2015.072720

International Journal of Reliability and Safety, 2015 Vol.9 No.2/3, pp.203 - 219

Received: 02 Dec 2014
Accepted: 15 Apr 2015
Published online: 27 Oct 2015 *

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