The Determination of Convex Sets of Uncertainty in Structural Dynamics

ABSTRACT. Many analysis and design problems in engineering and science involve uncertainty to varying degrees. This paper is concerned with the structural vibration problem involving uncertain material or geometric parameters, specified as bounds on these parameters. This produces interval parameter values which may be interpreted as interval stiffness and mass matrices. However this approach produces very conservative bounds on the features of the dynamic response such as the eigenvalues or the frequency response. This paper explores the shape of the sets of eigenvalues of the system, allowing for the dependencies between the outputs, and considers various options to approximate this set. Of particular interest is the use of ellipsoids to specify and propagate the uncertainty. Simple two and three degree of freedom discrete systems are used to explore these concepts.