Invariant Characteristics of Forced Oscillations of Beams with Longitudinal Compression

Abstract

Oscillations of an elastic beam with longitudinal compressions are investigated. The beam consists of two steel strips connected at the free ends. The compression is caused by tensioned thread. The oscillations are excited by the action of an alternating magnetic field on a magnet mounted at the end of the beam. The law of motion under changes of the frequency of harmonic action is registered. As a result of a full-scale experiment, a large set of data has been obtained. This set contains ordered periodic oscillations as well as disordered oscillations specific to dynamic systems with chaotic behavior. To study the invariant numerical characteristics of the attractor of the corresponding dynamic system, the correlation integral and correlation dimensionality as well as β-statentropy are calculated. A large numerical experiment showed that the calculation of β-statentropy is preferable compared with calculation of the correlation index. Based on the developed algorithms, the dependence of β-statentropy on the frequency of external action is constructed. The constructed dependence can serve as an effective tool to measure the adequacy of the mathematical model of forced oscillations of a beam with loss of stability.