Interval dynamic responses analysis of the damaged arch with uncertainties subjected to a moving load

This paper focuses on the interval dynamic response of a damaged arch with uncertain parameters under a moving load. The differential quadrature method (DQM) is employed to derive the equation of motion of the arch. The moving load, modeled as the Dirac delta function, is approximated by a Fourier trigonometric series to tackle the issue of discretizing the singular function in the differential equation. The bending moment at each discrete point is obtained via the equilibrium equation. The damage in the arch is modeled as the cross-section reduction model. The Newmark-β method is then used to obtain the dynamic response. Moreover, uncertain damage-related parameters of the arch are treated as interval variables, and the Chebyshev polynomial surrogate model is utilized to obtain the interval dynamic response, followed by a comparison with the deterministic one. The results obtained from our study address the question of how to accurately analyze the interval dynamic response of damaged arches with uncertain parameters under a moving load, which can offer valuable references for the design and assessment of arch structures.