NONLINEAR DYNAMICS OF UNIDIRECTIONAL, FIBER-REINFORCED TORI

The symbolic manipulator Mathematica is used to model the nonlinear dy namic behavior of closed, elastic toroidal shells. Transverse shears a re neglected and the nonlinearities are of the Von Karman type. Two fi ber-reinforcing schemes are considered: reinforcement with fibers alon g the major direction of the torus, and reinforcement with fibers alon g the minor direction of the torus. These schemes result in orthotropi c material characteristics. Differential geometry is used to derive th e nonlinear kinematic relationships, and a combination of the Rayleigh -Ritz technique and the method of harmonic balance is used to approxim ate the nonlinear natural frequencies of the tori. Numerical examples show that the linear natural frequency increases as the fiber volume f raction increases for any radii ratio. On the other hand, the nonlinea r analysis of some reinforcing schemes shows a competition between the geometric and material parameters of the tori. This competition has a significant effect on the qualitative behavior of the torus and demar ks the borders separating shell-like behavior and ring like behavior.