CHAOTIC VIBRATION OF BUCKLED BEAMS AND PLATES

Abstract

The great developing of numerical analysis of the dynamic systems emphasizes the existence of astrong dependence of the initial conditions, described in the phase plane by attractors with acomplicated geometrical structure. The Lyapunov exponents are used to determine if there is a realstrong dependence on the initial conditions: there is at least a positive exponent if the system has achaotic evolution and all the Lyapunov exponents are negative if the system has not such anevolution. Determining the largest Lyapunov exponent , which is easier to calculate, is sufficient todraw such conclusions. In this paper we shall use the greatest Lyapunov exponent to study twowell-known problems who leads to chaotic motions: the problem of the buckled beam and the panelflutter problem. In the problem of the buckled beam we verify the results obtained with theMelnikov theorem with the maximum Lyapunov exponent [1]. The flutter of a buckled plate is alsoa problem characterized by strong dependence of the initial conditions, existence of attractors withcomplicated structure existence of periodic unstable motions with very long periods (sometimesinfinite periods).