Alternating chaos versus synchronized vibrations of interacting plate with beams

- Mathematical models of contact/no-contact interacting beams with a plate are given.
- Novel chaotic and synchronized contact/no-contact phenomena are detected.
- Influence of boundary conditions, clearance and symmetry of beams locations is studied.
- Alternating beams vibration are detected and discussed.
- Benefits of application of 2D Morlet wavelets versus FFT are shown.

We study networks of coupled oscillators governed by ODEs and yielded by physically validated sets of a few PDEs governing dynamics of structural members (plate and beams), chaos and phase synchronization and contact/no-contact non-linear dynamics of structural members coupled via boundary conditions. We have detected, illustrated and discussed a few novel kinds of hybrid states of the studied plate-beam(s) contact/no-contact interactions as well as novel scenarios of transition into chaos exhibited by the interplay of continuous objects. Classical (time histories, phase portraits, Poincaré maps, FFT, Lyapunov exponents) and non-classical (2D Morlet wavelets) approaches are used while monitoring non-linear dynamics of the interacting spatial structural members. Our results include examples from structural mechanics and the studied objects are modelled by validated mechanical hypotheses and assumptions. Novel non-linear phenomena including switching to different vibration regimes and phase chaotic synchronization are illustrated and discussed.