Chaotic Dynamics of Flexible Closed Cylindrical Nano-Shells Under Local Load

In this chapter the mathematical model of a geometrically nonlinear closed cylindrical nano-shell is constructed. The solution convergence depending on the used series number terms in the Bubnov-Galerkin method is investigated. In particular, scenarios of transition into chaos of the nano-shell versus a number of the mentioned series terms N and the size dependent parameter l are analyzed. We have also detected, illustrated and discussed the scenarios of the Feigenbaum, Ruelle-Takens-Newhouse and their combination for differential values of N and l.