Frequency analysis of uncertain structures using imprecise probability

Two new methods for finite element based frequency analysis of a structure with uncertainty are developed. An imprecise probability formulation based on enveloping p‐boxes is used to quantify the uncertainty present in the mechanical characteristics of the structure. For each element, independent variations are considered. Using the two developed methods, P‐box Frequency Analysis (PFA) and Interval Monte‐Carlo Frequency Analysis (IMFA), sharp bounds on natural circular frequencies at different probability levels are obtained. These methods establish a framework for handling incomplete information in structural dynamics. Numerical example problems are presented that illustrate the capabilities of the new methods along with discussions on their computational efficiency.