On interactive fuzzy solutions for mechanical vibration problems

• Autor(a) principal: Eduardo Sanchez, Daniel
• Data de Publicação: 2021
• Outros Autores: Wasques, Vinicius F. [UNESP], Arenas, Jorge P., Esmi, Estevao, Barros, Laecio Carvalho de
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1016/j.apm.2021.03.002; http://hdl.handle.net/11449/210390
• topic: Fuzzy initial value problems; Interactive fuzzy numbers; Sup-J extension principle; Mechanical vibration

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.