On interactive fuzzy solutions for mechanical vibration problems - Eduardo Sanchez, Daniel; Wasques, Vinicius F. [UNESP]; Arenas, Jorge P.; Esmi, Estevao; Barros, Laecio Carvalho de (Elsevier B.V., 2021)
Fuzzy initial value problems describing classical mechanical vibrations are the focus of this paper. In particular, this work considers systems described by nth-order linear ordinary differential equations whose initial conditions are uncertain and given by interactive fuzzy numbers. The concept of interactivity arises from the concept of joint possibility distribu-tion ( J). An approach based on the sup -J extension principle, which is a generalization of Zadeh & rsquo;s extension principle, is presented. This theory is applied to two major examples of oscillatory systems: the forced vibration of an uncoupled mass-spring-damper system and the free vibration of a coupled undamped mass-spring system. In both cases, we have that the solution via sup -J extension, where the fuzzy initial conditions are given by linearly correlated fuzzy numbers, is contained in the solution via Zadeh & rsquo;s extension. (c) 2021 Elsevier Inc. All rights reserved.
Keywords: Fuzzy initial value problems; Interactive fuzzy numbers; Sup-J extension principle; Mechanical vibration