Chaotic synchronization of vibrations of a coupled mechanical system consisting of a plate and beams

Nowadays a progress in investigation of chaotic dynamics in various branches of science like mechanics, physics, biology, chemistry, medicine, economy, etc. is achieved. In the field of mechanical continuous systems like beams/plates/shells there exists already a vast number of paper devoted to investigation of their bifurcational and chaotic behaviour. For instance, axially accelerating beams have been analysed in [1-4] using analytical approaches, whereas squared plates parametrically excited have been studied in [5-7] with respect to local and global bifurcations, the existence of heteroclinic and Shilnikov-type homoclinic orbits, Smale horseshoes and chaotic dynamics. Recently, in three companion papers chaotic dynamics of flexible plate and cylinder like panels of infinite length, rectangular spherical and cylindrical shells, closed cylindrical shells, axially symmetric plates, as well as spherical and conical shells have been studied (see [8-10]). A role of counter examples to deterministic behaviour of continuous systems plays the synchronization of non-linear dynamical processes. The governing PDEs have been reduced to ODEs via the Finite Difference Method, the BubnovGalerkin Method and the Ritz Method. A few novel scenarios of transitions from regular to chaotic dynamics, as well as phase transitions chaos-hyper chaos and chaos-hyper chaoshyper-hyper chaos have been reported, illustrated and discussed. Beginning from seminal works of Blekhman [11, 12], J. Awrejcewicz, A.V. Krysko, T.V. Yakovleva, D.S. Zelenchuk, V.A. Krysko