Stochastic Analysis of Nonlinear Euler-Bernoulli Beams with Dynamic Absorbers under Uncertain Parameters

This paper presents a stochastic model to investigate a nonlinear Euler–Bernoulli beam with dynamic absorbers subjected to moving loads. The uncertainties in beam deflection are estimated for the three cases: uncertain applied load (Case I), uncertain beam natural frequency (Case II), and uncertain absorber stiffness (Case III). The existing Stochastic Finite Difference Method based on Homogeneous Chaos (SFDHC) is applied and compared with the Quasi-Monte Carlo Simulation (QMCS) method, which is used for validation and demonstrates higher computational efficiency. A probabilistic evaluation of the deflection PDFs and key statistical parameters of maximum deflection is performed with the proposed approach. The results show that both cases (I and II) have large deflection variations with the standard deviation up to 95% of the coefficient of variation (COV) of the input stochastic parameter. The deflection ranges for Case I are 44.60% and 155.64% of the mean value at a COV equal to 15%, respectively. For Case II, they are 72.07% and 165.24% of the mean, respectively; in Case III, they shift to a much narrower range, from 94.31% to 108.80% of the mean. The uncertainties, particularly in the former two cases, have to be taken into consideration to enable safe and trustworthy dynamic system design, and different safety factors are recommended for safe design under different uncertainty cases based on the results obtained. The SFDHC method used in the present study is shown to be accurate and efficient and can be used in other structures having different configurations in which the deterministic finite-difference solution exists.