Abstract: A non-random vibration analysis method is proposed in this paper, which calculates the dynamic response bounds of vibrational systems under time-variant uncertain excitations.It provides a prominsing alternative computational tool for uncertain vibration analysis in case of lack of experimental information and the corresponding reliability design in the future.The non-probabilistic convex model process, rather than traditional stochastic process, is used to describe uncertain dynamic excitations because the former needs only the bound information instead of precise probability distribution at any time point and therefore dependence on large sample size is weakened effectively.Based on the convex model process, non-random vibration analysis algorithms are formulated to obtain dynamic response bounds of SDOF system and MDOF system under time-variant uncertain excitations, respectively.Besides, corresponding Monte Carlo method is proposed to verify accuracy of the response bounds calculated and provide a general analytical tool for non-random vibration analysis.Finally, the feasibility of the non-random vibration analysis method is validated by several numerical examples.The proposed non-random vibration analysis method could provide a promising supplement for random vibration theory, and thereby plays an important role in structural uncertain dynamic analysis and reliability design.for engineering problems.