On the dynamics of spatially curved and twisted rods—A finite element formulation

For spatially curved and twisted rods a set of governing equations consisting of equilibrium equations and strain-displacement and constitutive relations are derived in terms of three translational and three rotational degrees of freedom. By solving the strain-displacement relations for constant and zero states of strain the rigid body and constant strain modes of the rod are obtained. These displacement modes are then used as basis functions for development of a finite element model. To verify the formulation and the elemental matrices, three examples are analyzed for free vibrations and, in each case, the computed results are compared with those obtained experimentally. Good agreement is found for several modes of vibrations.