Abstract Summary
An approximate analytical technique is developed for bounding the response and first-passage probability of lightly damped nonlinear oscillators endowed with fractional derivative elements and subjected to imprecise Gaussian loads. The direct identification of such bounds leads to a so-called double-loop approach. In this setting, reliability is repeatedly evaluated at different points of the epistemic parameter space during the solution of an optimization problem, which can lead to significant computational efforts. In this regard, using elements of the theory of fractional calculus, first, the nonlinear equation governing the dynamics of the oscillator is linearized by resorting to statistical linearization and averaging methodologies [1]. Next, the values of the epistemic uncertain parameters that produce bounds on the failure probability of the linearized system are derived by utilizing an operator norm-based framework [2]. The proposed technique can be construed as an extension of a recently developed approach for the reliability assessment of multi-DOF nonlinear systems subject to imprecise stochastic loads [3]. A hysteretic nonlinear oscillator with fractional derivative elements subject to imprecise stochastic loading is considered for demonstrating the efficiency of the technique. References [1] Roberts, J.B. and Spanos, P.D., 2003. Random vibration and statistical linearization. Courier Corporation. [2] Faes, M.G., Valdebenito, M.A., Moens, D. and Beer, M., 2021. Operator norm theory as an efficient tool to propagate hybrid uncertainties and calculate imprecise probabilities. Mechanical Systems and Signal Processing, 152, p.107482. [3] Ni, P., Jerez, D.J., Fragkoulis, V.C., Faes, M.G., Valdebenito, M.A. and Beer, M., 2022. Operator Norm-Based Statistical Linearization to Bound the First Excursion Probability of Nonlinear Structures Subjected to Imprecise Stochastic Loading. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 8(1), 04021086.
