CHAOTIC VIBRATIONS OF A NONLINEAR VISCOELASTIC BEAM

The differential equation of motion of a nonlinear viscoelastic beam i s established and is based on a novel and sophisticated stress-strain law for polymers. Applying this equation we examine a periodically for ced oscillation of such a simply supported beam and search for possibl e chaotic responses. To this purpose we establish the Holmes-Melnikov boundary for the system. All further investigations are developed by m eans of a computer simulation. In this connection the authors examine critically the Poincare mapping and the Lyapunov exponent techniques a nd distinguish in this way between chaotic and regular motion. A set o f control parameters of the equation is found, for which either a chao tic or a regular motion can be generated, depending on the initial con ditions and the corresponding basins of attraction. Thus, in this part icular case two attractors of completely different nature-regular and chaotic, respectively-coexist in the phase space. The basins of attrac tion of the two attractors for a fixed instant of time are plotted, an d appear to possess a very complex fractal geometry.