Chaotic dynamics of two coaxially-nested cylindrical shells reinforced by two beams

Non-linear dynamics and contact interactions of beam-shell structures composed of two closed cylindrical shells which are coaxially nested and reinforced by two beams located symmetrically on the shell external perimeter is studied. In the present work, clearances between the mentioned structural members are taken into account, two beams are subjected to harmonic loads, and the dissipation factors are neglected. 3D PDEs governing non-linear dynamics of beams and shells within the geometric theory of Novozhilov are employed, whereas the contact pressure is defined through Kantor's model. PDEs are reduced to ODEs by means of the FEM (finite element method), and the solution convergence is validated through different numbers of finite elements located along the structural members thickness and by employment of the Runge principle with respect to spatial coordinates. The Cauchy problem is solved by the explicit integration (Euler method), which allows one to carry out the computation without the need to define solutions in a few initial points. Analysis of vibrations, including contact interactions, is realized with the use of methods of non-linear dynamics and the qualitative theory of differential equations, time histories/signals, phase portraits, Poincarè sections, Fourier spectra, wavelet-based analysis as well as the Lyapunov exponents.