Invariant Characteristics of Forced Oscillations of a Beam with Longitudinal Compression

Abstract

Oscillations of an elastic beam with longitudinal compression are considered. The beam consists of two steel strips connected on free ends and fixed on opposite ones. Compression is achieved by a strained string. Excitation of oscillations is performed by exposure of alternating magnetic field on a magnet placed on the loose end. The law of motion with a change in the frequency of the harmonic action is registered. As a result of the full-scale experiment a large set of data is obtained. This set contains ordered periodic oscillations as well as disordered oscillations specific to dynamical systems with chaotic behaviour. To study the invariant numerical characteristics of the attractor of the corresponding dynamical system, a correlation integral and a correlation dimensionality as well as β-statentropy are calculated. A large numerical experiment showed that the calculation of β-statentropy is preferable to the calculation of the correlation index. Based on the developed algorithms the dependence of β- statentropy on the frequency of the external action is constructed. The constructed dependence can serve as an effective tool for measuring the adequacy of the mathematical model of forced oscillations of buckling beam driven oscillations.

Keywords

• buckling beam
• stability
• bifurcations
• duffing’s equation
• ueda attractor
• chaotic oscillations
• entropy
• lyapunov exponents