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Chaotic motion under parametric excitation. (English) Zbl 0688.58026

The chaotic behaviour of a parametrically excited system is studied in some detail. An example of such a system is seen in the transverse vibration of a buckled column under axial excitation. The existence of homoclinic orbits for the parametrically excited systems is predicted by Melnikov’s method. Lyapunov exponents, Poincaré maps, power spectra and other characteristics of chaotic motions are analyzed numerically to confirm the results. An experiment on a buckled column is also carried out to qualitatively verify the theoretical results.
Reviewer: K.Brod

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37G99 Local and nonlocal bifurcation theory for dynamical systems
70K40 Forced motions for nonlinear problems in mechanics
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