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Shock and Vibration
Volume 2015 (2015), Article ID 574846, 12 pages
Research Article

Reliability Analysis of Damaged Beam Spectral Element with Parameter Uncertainties

Department of Computational Mechanics, University of Campinas (UNICAMP), 13083-970 Campinas, SP, Brazil

Received 12 December 2014; Accepted 24 May 2015

Academic Editor: Gang Li

Copyright © 2015 M. R. Machado and J. M. C. Dos Santos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper examines the influence of uncertainty parameters on the wave propagation responses at high frequencies for a damaged beam structure in the structural reliability context. The reliability analyses were performed using the perturbation method, First-Order Reliability Method (FORM), and response surface method (RSM) which were compared with Monte Carlo simulation (MCS) under the spectral element method environment. The simulated results were performed to investigate the effects of material property and geometric uncertainties on the response at high frequency modes, such as the computational efficiency of reliability methods. For the first time, the spectral element method is used in the context of reliability analysis at medium and high frequency bands applied to damage detection. It has shown the effects of parameters uncertainty on the dynamic beam response due on an impulsive load and the robustness of each method. Numerical examples in a bending vibrating beam with random parameters are performed to verify the computational efficiency of the present study.