Uncertain Friction Induced Vibration Study: Coupling of Fuzzy Logic, Fuzzy Sets, and Interval Theories

Abstract

This paper presents a complete method to carry out a fuzzy study of a frictioninduced vibration system and to analyze the effects of uncertainty on the output data of a stability problem. The proposed approach decomposes the fuzzy problem into interval problems and calculates interval output solutions by optimization. Next, each calculation of the stability problem output data, which is useful during the optimization process, is reanalyzed by integrating fuzzy logic controllers for the static step and homotopy development and projection techniques for the modal step. Finally, the obtained results are compared with Zadeh’s extension principle reference.