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Time-varying uncertain parameters such as wind excitations on bridges or road excitations on vehicles are widely exist in engineering. Traditionally, the stochastic process and random vibration methods are adopted for quantification of a time-varying parameter and corresponding mechanical vibration analysis. However, prohibitively huge data are required to obtain the precise values of the characteristic parameters that needed for stochastic process modelling, which is often very costly or relatively difficult to obtain in engineering. Committed to provide an effective mathematical tool for time-varying uncertainty quantification of structural dynamic analysis when inadequate information can be derived for stochastic process modelling, we proposed a non-stochastic process model and corresponding non-random vibration method. Only upper and lower bounds of the time-varying uncertain parameters are required for non-stochastic process modelling. A self-correlation function is defined for interval variables at any two different time points of a non-stochastic process. With correlation information, the dependent non-stochastic process can be transformed into an independent one, which will significantly facilitate the subsequent uncertainty analyses such as dynamic reliability analysis, etc. Correspondingly, by combining the non-stochastic process model with classical mechanical vibration, a non-random vibration method is developed for dynamic response bounds of structures under external excitations. The dynamic responses of both single degree-of-freedom (SDOF) and multiple degree-of-freedom (MDOF) systems are provided, in the form of upper and lower bounds. Several numerical examples are investigated, including damped and undamped systems, under stationary or non-stationary excitation forces, and some interesting and reasonable phenomena are observed.

non-stochastic process; time-varying uncertainty; non-random vibration; dynamic response analysis