Due to complexity of real engineering problems, aleatory and epistemic uncertainties may exist simultaneously. Realistically modeling these uncertainties in determination of natural frequency and mode shape is crucial for studying characteristics of dynamic systems. In this paper, natural frequency and mode shape of structures with mixed aleatory and epistemic uncertainties are investigated by using a hybrid probabilistic and fuzzy approach. Aleatory uncertainties and epistemic uncertainties are modeled as random variables and fuzzy sets respectively. By applying α-level strategy, a fuzzy set is transferred into a series of interval sets at corresponding levels, and consequently a mixed random and fuzzy problem is converted into a mixed random and interval problem, which is solved by using random interval moment method and perturbation method. A numerical example is given to illustrate applications of the presented method and results are verified by direct Monte Carlo simulation method.
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