Free Vibration Analysis of Arches with Interval-Uncertain Parameters

The dynamic characteristics of a structure serve as a crucial foundation for structural assessment, fault diagnosis, and ensuring structural safety. Therefore, it is imperative to investigate the impacts of uncertain parameters on the dynamic performance of structures. The dynamic characteristics of arches with uncertain parameters are analyzed in this paper. The uncertain parameters are regarded as non-probabilistic uncertainties and represented as interval variables. A model of an arch considering interval-uncertain parameters is built, and kinematic equations are established. The natural frequencies are obtained using the differential quadrature (DQ) method, and the relationships between natural frequency, radius, and central angle are also analyzed. On this basis, the Chebyshev polynomial surrogate (CPS) model is employed to solve the uncertain dynamic problem, and the natural frequencies are seen to be the objective functions of the CPS model. The accuracy verification of the model is achieved by comparison with the Monte Carlo simulation (MCS). Simulations are carried out considering different uncertainties, and the results show that the bounds of natural frequencies are influenced not only by the types of uncertain parameters, but also by their combinations.