1999
DOI: 10.1590/s0100-73861999000400007
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Multiple scales analysis of nonlinear oscillations of a portal frame foundation for several machines

Abstract: 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 fre… Show more

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Cited by 8 publications
(5 citation statements)
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“…Different authors studied dynamical system with nonideal excitation (Nayfeh & Mook, 1979;Balthazar et al, 2003;Dantas & Balthazar, 2007). Brasil (1999) performed an analytical study of the nonlinear vibrations of a portal frame excited by two ideal energy sources, consisting of unbalanced rotating machines. This same problem with two non-ideal sources was studied by Balthazar et al (2004), which focused on the self-synchronization of the energy sources.…”
Section: Introductionmentioning
confidence: 99%
“…Different authors studied dynamical system with nonideal excitation (Nayfeh & Mook, 1979;Balthazar et al, 2003;Dantas & Balthazar, 2007). Brasil (1999) performed an analytical study of the nonlinear vibrations of a portal frame excited by two ideal energy sources, consisting of unbalanced rotating machines. This same problem with two non-ideal sources was studied by Balthazar et al (2004), which focused on the self-synchronization of the energy sources.…”
Section: Introductionmentioning
confidence: 99%
“…The linear stiffness of the columns and the beam can be evaluated by a Raleigh-Ritz procedure from cubic trial functions. Moreover, geometric nonlinearities are introduced by considering the shortening due to columns and beams bending under inextensibility hypothesis as presented by Brasil [4] and shown in Eq. (2).…”
Section: Flexible Portal Frame Modellingmentioning
confidence: 99%
“…The device under consideration here consists of a Duffing electrical circuit coupled magnetically to a flexible portal frame. This system modeling was previously addressed by Brasil [4] and Balthazar et al [5].…”
Section: Introductionmentioning
confidence: 98%
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“…All the review articles and the majorities of the research on vibration energy harvesting using piezoelectric materials have been released in the last decade. The importance of nonlinearities and sinusoidal and random excitations in the process of harvesting were studied by [1][2][3][4][5][6][7][8].…”
Section: Introductionmentioning
confidence: 99%