Dynamic response analysis of structure with hybrid random and interval uncertainties

With the increasing complexity of uncertain parameters, the single uncertainty modeling is challenged for structures involving multiple types of uncertainties. However, in the contrast to research on static problems with hybrid uncertainties, dynamic mixed uncertainty problems have not been well addressed. A novel dynamic analysis of structure with hybrid uncertainties is developed for the expressions for the lower and upper bounds of the mean value and standard deviation of the dynamic response. Within this approach, interval variables are adopted to quantify the non-probabilistic uncertainty associated with objective limited information. Some other parameters are considered as random variables. Based on series expansion of random and interval quantities with respect to uncertain parameters, the proposed method evaluates the lower and upper bounds of the first- and second-order moments of the structure response through solving deterministic equations. This method is also capable to solve pure interval problems. Finally, numerical examples are analyzed to illustrate the feasibility and effectiveness of the proposed method. The influence on the structure response caused by the individual system parameters is also investigated.