Dynamic bucking criteria for spherical shells of a rectangular form under sinusoidal lateral load are proposed and developed taking into consideration geometric and physical non-linearity. A mathematical model of thin shallow shells is constructed on the basis of the Kirchoff-Love hypothesis and the von Kármán geometric non-linearity, whereas the physical non-linearity follows the Ilyushin theory of plastic deformations. Reliability of the results is proved by comparing them with the results obtained by means of higher-order approximations of the Faedo-Galerkin method. Three scenarios (Feigenbaum, Ruelle-Takens-Newhouse and Pomeau-Manneville) are detected while transiting from regular to quasi-periodic/chaotic vibrations.
ASJC Scopus subject areas
- Civil and Structural Engineering
- Modelling and Simulation
- Materials Science(all)
- Mechanical Engineering
- Computer Science Applications