Open AccessDynamic Response of Non-linear Beam Structures in Deterministic and Chaos Perspective
Author(s) -
Anwar Dolu,
Amrinsyah Nasution
Publication year - 2019
Publication title -
kontribusi fisika indonesia
Language(s) - English
Resource type - Journals
ISSN - 0854-6878
DOI - 10.5614/itb.ijp.2019.30.2.3
Subject(s) - phase plane , nonlinear system , mathematical analysis , chaotic , duffing equation , plane (geometry) , mathematics , beam (structure) , differential equation , displacement (psychology) , poincaré map , bifurcation , physics , classical mechanics , geometry , optics , computer science , psychology , quantum mechanics , artificial intelligence , psychotherapist
The behavior of large deformation beam structures can be modeled based on non-linear geometry due to geometricnonlinearity mid-plane stretching in the presence of axial forces, which is a form a nonlinear beam differential equationof Duffing equation type. Identification of dynamic systems from nonlinear beam differential equations fordeterministic and chaotic responses based on time history, phase plane and Poincare mapping. Chaotic response basedon time history is very sensitive to initial conditions, where small changes to initial terms leads to significant change inthe system, which in this case are displacement x (t) and velocity x’(t) as time increases (t). Based on the phase plane, itshows irregular and non-stationary trajectories, this can also be seen in Poincare mapping which shows strange attractorand produces a fractal pattern. The solution to this Duffing type equation uses the Runge-Kutta numerical method withMAPLE software application.