Experimental results are presented on chaotic oscillations of a post-buckled reinforced beam subjected to lateral excitations. The beam is partially reinforced and is clamped at both ends. One end of the beam is arranged to move to an axial displacement by an elastic spring. The beam is deformed to a post-buckled configuration by the axial constraint. Under the post-buckled condition of the beam, chaotic responses are generated in specified regions of exciting frequency. The chaotic responses are examined by the Fourier spectrum, the Poincare projection and the maximum Lyapunov exponent. It is found among other things that the chaos of the reinforced beam is mainly generated with the lower modes of vibration. The instability regions of chaos as well as the effect of inertia in the axial direction are also examined. The main results of the detailed experiments can be summarized as follows: the violent chaotic vibrations are generated close to the responses of principal resonance with indicating the maximum Lyapunov exponent as 2. Number of the resonance vibration modes generated in the chaos is identified as 3. As the excitation amplitude increases, the chaotic vibrations accompanied with the subharmonic resonance of one-half-order are generated with the first mode of vibration. Under large excitation amplitude, the chaos originated from the subharmonic resonance of one-third-order is emerged. By the change of the axial inertia to the beam, the chaos boundary is shifted to the lower range of frequency with a same width of instability region. Poincare maps of the reinforced beam show the typical fractal features involving the stretching and folding mechanisms.
Experiment on chaotic oscillations of a post-buckled reinforced beam constrained by an axial spring
Untersuchung zum chaotischen Schwingungsverhalten nachträglich verformter verstärkter Balkenträger mit Bewegungseinschränkung und axialer Federung
1998
7 Seiten, 14 Bilder, 14 Quellen
Article (Journal)
English
Balken , Dünnwand , Rippenverstärkung , Automobilindustrie , Rahmen (Fahrzeug) , Schwingungsverhalten , Steifigkeit , Ausbeulung , Resonanzfrequenz , instabile Schwingung , Instabilität , Anregungszustand , Scheitelwert , Stahlblech , Feinblech , Biegefestigkeit , Linearbewegung , Frequenzgang , dynamisches Verhalten , Frequenzspektrum , Trägheit , Chaostheorie
Experiments on chaotic vibrations of a post-buckled beam with an axial elastic constraint
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