Chaotic vibrations of flexible curvilinear beams in temperature and electric fields

• Dynamics of flexible curvilinear beams for different mechanical and thermal boundary conditions is studied.
• Chaos, hyperchaos, hyper-hyperchaos and deep chaos have been detected and discussed using Fourier analysis and Lyapunov exponents.
• Influence of temperature and electric fields on non-linear beam dynamics is reported.

In this paper regular and chaotic vibrations of flexible curvilinear beams with (and without) the action of temperature and electric fields are studied. Results obtained are based on the reduction of PDEs governing non-linear dynamics of straight and curvilinear beams to large sets of non-linear ODEs putting emphasis on reliability and validation of the results. In spite of the applied classical approaches to study bifurcational and chaotic dynamics, we have employed 2D and 3D Morlet wavelets and we have computed first four Lyapunov exponents. Numerous results are reported regarding scenarios of the transition from regular to chaotic vibrations including the occurrence of hyper-hyper chaos and deep chaos. Snap-through phenomena have been detected and analyzed, and the influence of boundary conditions of three types of the considered fields (mechanical, thermal and electrical) as well as of temperature on non-linear dynamics of the beam have been reported.