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RELIABILITY ANALYSIS OF NONLINEAR VIBRATORY SYSTEMS UNDER NON-GAUSSIAN LOADS

[+] Author and Article Information
Vasileios Geroulas

Mechanical Engineering Department, Oakland University, 2200 N. Squirrel Road, Rochester MI 48309
vgeroula@oakland.edu

Zissimos P. Mourelatos

Mechanical Engineering Department, Oakland University, 2200 N. Squirrel Road, Rochester MI 48309
mourelat@oakland.edu

Vasiliki Tsianika

Mechanical Engineering Department, Oakland University, 2200 N. Squirrel Road, Rochester MI 48309
vtsianika@oakland.edu

Igor Baseski

Mechanical Engineering Department, Oakland University, 2200 N. Squirrel Road, Rochester MI 48309
ibaseski@oakland.edu

1Corresponding author.

ASME doi:10.1115/1.4038212 History: Received May 25, 2017; Revised September 21, 2017

Abstract

A general methodology is presented for time-dependent reliability and random vibrations of nonlinear vibratory systems with random parameters excited by non-Gaussian loads. The approach is based on Polynomial Chaos Expansion (PCE), Karhunen-Loeve (KL) expansion and Quasi Monte Carlo (QMC). The latter is used to estimate multi-dimensional integrals efficiently. The input random processes are first characterized using their first four moments (mean, standard deviation, skewness and kurtosis coefficients) and a correlation structure in order to generate sample realizations (trajectories). Characterization means the development of a stochastic metamodel. The input random variables and processes are expressed in terms of independent standard normal variables in N dimensions. The N-dimensional input space is space filled with M points. The system differential equations of motion are time integrated for each of the M points and QMC estimates the four moments and correlation structure of the output efficiently. The proposed PCE-KL-QMC approach is then used to characterize the output process. Finally, classical MC simulation estimates the time-dependent probability of failure using the developed stochastic metamodel of the output process. The proposed methodology is demonstrated with a Duffing oscillator example under non-Gaussian load.

Copyright (c) 2017 by ASME
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