Abstract
The great developing of numerical analysis of the dynamic systems emphasizes the existence of a strong dependence of the initial conditions, described in the phase plane by attractors with a complicated geometrical structure. The Lyapunov exponents are used to determine if there is a real strong dependence on the initial conditions: there is at least a positive exponent if the system has a chaotic evolution and all the Lyapunov exponents are negative if the system has not such an evolution. Determining the largest Lyapunov exponent , which is easier to calculate, is sufficient to draw such conclusions. In this paper we shall use the greatest Lyapunov exponent to study two well-known problems who leads to chaotic motions: the problem of the buckled beam and the panel flutter problem. In the problem of the buckled beam we verify the results obtained with the Melnikov theorem with the maximum Lyapunov exponent [1]. The flutter of a buckled plate is also a problem characterized by strong dependence of the initial conditions, existence of attractors with complicated structure existence of periodic unstable motions with very long periods (sometimes infinite periods).
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