| The recent developments in aerospace exploration have stimulated extensive research into the mechanics of large flexible space structures, such as dish antennas, space telescopes and solar collectors. Highly flexible structures are designed to undergo large displacements and rotations without plastic deformation. But when a structure undergoes large displacements, various secondary effects (e.g., rotary inertias, cross section warping) may become significant, and its statics and dynamics may involve several nonlinear effects, such as shortening effect, nonlinear curvatures, mid-plane stretching and modal couplings among vibration modes. Hence, nonlinear structural theories that can model large displacements and rotations are needed. Moreover, it is important to understand the nonlinear static and dynamic behaviors of highly flexible structures in order to design such structures.; In this thesis we derive and use a geometrically exact beam theory to analyze large static deformations of beams, and perform numerical and experimental studies on the nonlinear dynamics of highly flexible beams. The multiple shooting method and the method of multiple scales were used to solve the nonlinear governing equations of a highly flexible cantilevered beam. A 3D motion analysis system is used to perform dynamic testing and to verify numerical results. Comparison of numerical and experimental results shows that the derived nonlinear beam theory can model very large displacements and rotations of beams. |
