A bivariate subinterval method for dynamic analysis of mechanical systems with interval uncertain parameters

Dynamic analysis involving interval uncertainties can provide accurate reference to performance evaluation and reliability optimization. However, methodologies for dy-namic problems under high dimensional interval uncertainties in mechanical systems need further exploration and development. To this end, this paper proposes a bi-variate subinterval method (BSM) to handle interval dynamic problems, in which multiple uncertain parameters with small uncertainty levels in mechanical systems are involved. The BSM is developed by combining the subinterval technique and the bivariate decomposition of response functions expanded by the second-order Taylor series. Additionally, the subinterval-division-based bivariate subinterval method (SBSM) is developed to obtain a tight bound for the dynamic analysis of mechanical systems considering interval parameters with large uncertainty levels. To verify the efficiency and accuracy of the developed methods, numerical examples and engineering applications with consideration of interval uncertainties are employed and discussed. Results show that compared with the existing bivariate Chebyshev method, the BSM presents a better tradeoff between the accuracy of results and computational cost, which is more suitable to interval dynamic problems for the analysis of mechanical systems with uncertainties of high dimensions and small uncertainty levels. Furthermore, the SBSM can obtain a tight bound of dynamic responses for the interval dynamic problems with uncertain parameters of low dimensions and large uncertainty levels in mechanical systems. & COPY; 2023 Elsevier B.V. All rights reserved.