The Effect of Nonlinearities on Flexible Structures.
Annual rept. 30 Apr 86-30 Apr 87,
VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG
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Experimental-theoretical studies have been conducted on the influence of nonlinearities on flexible structures in the presence of either an external or a parametric excitation. A single-degree-of-freedom system with quadratic and cubic nonlinearities under the influence of a harmonic parametric excitation was studied using the method of multiple scales and digital-and analog-computer simulations. A global bifurcation diagram was obtained showing the different possible attractors point, limit cycle, chaotic attractors. For small excitation amplitudes, the perturbation results are in excellent agreement with the digital-and analog-computer simulations. For moderate to large excitation amplitudes, the accuracy of the perturbation solution is questionable and only digital -and analog- computer simulations were used. The results are in full agreement. Keywords Nonlinear oscillations, Flexible structures, Resonances, Attractors, Bifurcations.