DYNAMICS OF ELASTIC BEAMS UNDER IMPACT LOADING, ACCOUNTING FOR WHITE NOISE

Abstract

Chaotic dynamics of elastic isotropic Euler - Bernoulli beams under the effect of infinite in time impact loading is considered, accounting for white noise. Based on the results of the investigation, a mathematical model is constructed, a computational algorithm and a software complex are developed. A conservative system is analyzed. The partial differential equation is reduced to Cauchy problem. Three types of boundary conditions are considered. It is found that when only white noise of various intensity acts on a beam, the oscillations are chaotic. If the impact loading amplitude is equal to or less than the white noise intensity, the oscillations are chaotic; if the amplitude of the infinite in time impact loading is larger than or equal to the white noise intensity, then the transversal loading is dominant, and classical transfer of oscillations into a chaotic state following Ruelle - Tuckens scenario is possible.

Keywords: elastic Euler − Bernoulli beams, white noise, impact loading, Ruelle − Tuckens scenario.