Dynamic analysis of uncertain structures using imprecise probability

A new method for dynamic response spectrum analysis of structures with uncertainty in their mechanical properties utilising the notion of imprecise probability is developed. This finite‐element‐based method is capable of obtaining probabilistic bounds of the dynamic response of the structure with uncertainty defined by enveloping imprecise probability structures. The developed method obtains probabilistic bounds on (1) natural circular frequencies, (2) mode shapes, (3) modal coordinates and (4) modal participation factors leading to the imprecise probability structures of modal responses. Finally, maximum modal responses are combined to obtain the structure's maximum total response with consideration of uncertainty. Numerical examples demonstrating the developed method are presented.