Stochastic Nonparametric Models of Uncertain Hysteretic Oscillators

• Published in: AIAA journal 2006-10, Vol.44 (10), p.2319-2330
• Main Authors: Masri, S. F, Ghanem, R, Arrate, F, Caffrey, J. P
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Nonlinear systems; Oscillators; Physics; Solid mechanics; Stochastic models; Structural and continuum mechanics; Studies; Uncertainty; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 0001-1452; 1533-385X
• DOI: 10.2514/1.19859

A study is presented of the significant issues encountered in the modeling and characterization of uncertainties in the parameters of hysteretic nonlinear systems that are subjected to deterministic excitations. A single-degree-of-freedom system, with bilinear hysteretic characteristics, is employed to investigate the propagation of uncertainties in the dominant parameters that control the idealized restoring force associated with such a system. Random variations are introduced in the nominal value of each of the dominant parameters. Monte Carlo simulation approaches are used to generate a large, statistically significant, ensemble of time history records that are subsequently used to determine the distribution of the corresponding transient response and establish the probabilistic bounds on the response time history. The restoring force method is used to determine the power-series coefficients that define an approximating surface that characterizes the system behavior. The statistics of the identified coefficients are determined and shown to provide a powerful tool for quantifying the level and features of the uncertainty in the nonlinear system. Furthermore, it is shown that the general methodology presented allows the estimation through analytical procedures of the uncertain system's response bounds when it is excited by a different dynamic load than the one used to identify it. [PUBLICATION ABSTRACT]