Stochastic interval analysis of natural frequency and mode shape of structures with uncertainties

• Mixed random and interval uncertainties are introduced into structural dynamics.
• Dynamic characteristics are determined by a hybrid stochastic and interval approach.
• Boundaries of probabilistic features such as mean, variance and PDF are achieved.
• The proposed strategy is capable of solving pure random and pure interval problems.

In this paper, natural frequencies and mode shapes of structures with mixed random and interval parameters are investigated by using a hybrid stochastic and interval approach. Expressions for the mean value and variance of natural frequencies and mode shapes are derived by using perturbation method and random interval moment method. The bounds of these probabilistic characteristics are then determined by interval arithmetic. Two examples are given first to illustrate the feasibility of the presented method and the results are verified by Monte Carlo Simulations. The presented approach is also applicable to solve pure random and pure interval problems. This capability is demonstrated in the third and fourth examples through the comparisons with the peer research outcomes.