Open AccessMultiple scales analysis of nonlinear oscillations of a portal frame foundation for several machines
Author(s) -
Reyolando Manoel Lopes Rebello da Fonseca Brasil
Publication year - 1999
Publication title -
revista brasileira de ciências mecânicas
Language(s) - English
Resource type - Journals
ISSN - 0100-7386
DOI - 10.1590/s0100-73861999000400007
Subject(s) - nonlinear system , vibration , frame (networking) , portal frame , perturbation (astronomy) , multiple scale analysis , mathematics , mathematical analysis , mode (computer interface) , natural frequency , normal mode , set (abstract data type) , physics , control theory (sociology) , classical mechanics , computer science , engineering , acoustics , mechanical engineering , artificial intelligence , control (management) , quantum mechanics , programming language , operating system
An analytical study of the nonlinear vibrations of a multiple machines portal frame foundation is presented. Two unbalanced rotating machines are considered, none of them resonant with the lower natural frequencies of the supporting structure. Their combined frequencies is set in such a way as to excite, due to nonlinear behavior of the frame, either the first anti-symmetrical mode (sway) or the first symmetrical mode. The physical and geometrical characteristics of the frame are chosen to tune the natural frequencies of these two modes into a 1:2 internal resonance. The problem is reduced to a two degrees of freedom model and its nonlinear equations of motions are derived via a Lagrangian approach. Asymptotic perturbation solutions of these equations are obtained via the Multiple Scales Method