Nonlinear dynamics and contact interactions of the structures composed of beam-beam and beam-closed cylindrical shell members

Nonlinear beam-beam and beam-cylindrical shell contact interactions, where a beam is subjected to harmonic uniform load, are studied. First, the nonlinear dynamics governed by four nonlinear PDEs including a switch function controlling the contact pressure between the mentioned structural members are presented. Relations between dimensional and dimensionless quantities are derived, and the original problem of infinite dimension has been reduced to that of oscillator chains via the FDM (Finite Difference Method). Time histories, FFT (Fast Fourier Transform), phase portraits, Poincaré maps, and Morlet wavelets are applied to discover novel nonlinear chaotic and synchronization phenomena of the interacting structural members. Numerous bifurcations, full-phase synchronization of the beam-shell vibrations, the evolution of energy of the vibrating members, damped vibrations of the analyzed conservative system of the beam and the shell surface deformations for various time instants, as well as the buckling of the shell induced by impacts are illustrated and discussed, among others. In addition, we have detected that in all studied cases, in spite of analyzing a large set of nonlinear ODEs approximating the behavior of interacting structural members, the scenario of transition from regular to chaotic dynamics follows the Ruelle-Takens-Newhouse scenario.