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Reliability assessment of a softening duffing oscillator under evolutionary stochastic excitation

The softening Duffing oscillator, namely a nonlinear oscillator possessing a linear-plus-cubic stiffness element such that the spring has a softening characteristic, has received considerable attention within the context of deterministic dynamics. Note that besides the importance of the softening Duffing model in nonlinear ship dynamics, applications can be found in diverse scientific fields such as plant biomechanics. Further, although several research papers have focused on the response and stability analysis of a deterministically excited softening Duffing oscillator, limited results exist regarding the response analysis of the oscillator when it is subjected to stochastic excitation. Specifically, most of the results are based on rather heuristic approaches which inherently assume stationarity and that the probability the response leaves the stable region is extremely small; thus, neglecting important aspects of the analysis such as the possible unbounded response behavior when the restoring force acquires negative values. In this paper, an efficient approximate analytical technique for determining the survival probability of a softening Duffing oscillator subject to evolutionary stochastic excitation is developed. Specifically, relying on stochastic averaging (e.g. Spanos and Kougioumtzoglou 2014), and introducing special forms for the response amplitude and transition probability density functions (PDFs) the unbounded character of the system response is rigorously taken into account. In comparison with the numerical path integral based scheme developed in Kougioumtzoglou and Spanos (2014) the herein developed approach appears significantly more efficient computationally. Comparisons with pertinent Monte Carlo simulations demonstrate the reliability of the approach.

Author(s):

Ioannis Kougioumtzoglou    
Department of Civil Engineering and Engineering Mechanics, Columbia University
United States

Yuanjin Zhang    
Institute for Risk & Uncertainty, University of Liverpool
United Kingdom

Michael Beer    
Institute for Risk & Uncertainty, University of Liverpool
United Kingdom