Multiple scales analysis of nonlinear oscillations of a portal frame foundation for several machines

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.

On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

O fundamento epistemológico da metafísica da Vontade de Arthur Schopenhauer

Analisamos neste artigo a teoria do conhecimento de Arthur Schopenhauer com base em sua dissertação Sobre a quádrupla raiz do princípio de razão suficiente (1813), seu ensaio Sobre a visão e as cores (1816), os dois primeiros livros de O mundo como vontade e representação (1819), bem como o apêndice a esta obra intitulado Crítica da filosofia kantiana. Aqui temos em mente a relação de Schopenhauer com as filosofias anteriores (em especial a de Kant) e a fundamentação de sua intuição do mundo como Vontade baseada em uma epistemologia de raízes kantianas.