A Review of Uncertainty Quantification Techniques for Frequency Responses of Mechanical Systems

Evaluations of frequency response functions (FRFs) of various linear and non-linear mechanical systems are of utmost importance. Considerations of uncertainties attract attention in the current research community, and a reasonable assessment of the variabilities of FRFs under uncertainties is a challenging task. Indeed, several critical issues emerge and prevent successful uncertainty quantifications. In linear FRFs, spurious peaks often deteriorate the quality of response estimations, which are induced by the multimodality and discontinuity. For non-linear FRFs, the multi-solution phenomenon and complex curve structures caused by turning points or bifurcations pose a great challenge to researchers, as no existing uncertainty analysis methods can effectively handle them. The current work provides an overview of the available techniques dedicated to solving these problems by elaborating on their principles, conducting a comparative analysis of their pros and cons, demonstrating benchmarks, and illustrating their applications to various linear and non-linear systems. Outlooks for future research directions are outlined by highlighting the remaining shortcomings of current methods. Hopefully, this overview will navigate readers through different approaches, guide them in choosing the correct techniques to deal with various uncertain mechanical problems, and promote promising future developments.