Dynamic analysis of vehicle-bridge interaction system with uncertain parameters

Abstract

Dynamic behaviour of vehicle-bridge interaction systems with uncertain properties is comprehensively studied. Prediction of the dynamic responses of a bridge excited by moving vehicles is crucial to the bridge design as the deterioration and reduction in long-term serviceability of a bridge are mainly caused by its vibration. It is vital to provide insight into the influences of unavoidable uncertainties of system parameters on the dynamic behaviour of vehicle-bridge coupling systems which are commonplace in structural engineering. This thesis aims to develop a rational non-deterministic framework for dynamic analysis of vehicle-bridge interaction systems including the uncertainties in all the system parameters. Probabilistic analyses are firstly implemented to calculate the statistical moments of bridge responses considering all the system parameters as random variables. Random variable functional moment method, combined with modal analysis, is extended to develop the expressions for calculating the mean value and variance of bridge dynamic response. Non-probabilistic approaches are also proposed to account for the uncertainties in the vehicle-bridge interaction systems when sufficient statistical data are unavailable. Interval operations, Taylor expansions and perturbation theory are integrated to analyse the vehicle-bridge interaction dynamic problems with predefined small intervals of system parameters. Mathematical formulations are formed for the midpoint value, interval width, lower and upper bounds of interval bridge dynamic response. A novel particle swarm optimization algorithm is developed to capture the extreme values of bridge responses regardless of the interval width of system parameters. Finally, the hybrid probabilistic and non-probabilistic analysis are introduced into the vehicle-bridge interaction dynamic system when a mixture of random and interval uncertainties in the system is present. The random interval perturbation method and random interval moment method are incorporated in the implementations to obtain the intervals of the first two statistical moments of bridge response. Investigations into the effects of the individual system parameter on the bridge response are carried out extensively. The effectiveness and accuracy of the presented approaches are demonstrated through comparisons with reference methods. The reported work will assist engineers to perform the cost effective design and assessment of non-deterministic dynamic response of vehicle-bridge interaction systems with uncertain properties.