The equations and boundary conditions governing the non-linear non-planar (flexural-flexural-torsional) vibrations of isotropic inextensional beams with small geometric imperfections have been derived using Hamilton 's principle. The results of an experiment are incorporated to investigate the validity of the proposed model. In this thesis, the base flexibility has been accounted for by modifying the proposed imperfect beam model. Then, by adjusting the base flexibility and geometric imperfection parameters simultaneously, a better agreement between the experimental results and theoretical predictions of the proposed model has been achieved. The effect of small geometric imperfection on dynamic response of resonantly base excited cantilevered beams with a one-to-one internal resonance has been also investigated by conducting a sensitivity analysis of perfect beam limit cycles to small geometric imperfections and dynamic bifurcation analysis of the branches of dynamic solutions pertaining to the perfect and imperfect beams. The sensitivity analysis reveals that depending on the frequency detuning parameter associated with each limit cycle, the sensitivity to small geometric imperfections may be to a great extent. Comparison of branches of dynamic solutions and chaotic bands associated with the perfect and imperfect beams in a specific range of excitation frequency detuning indicates that similar dynamic branches of perfect and imperfect beams have a frequency shift with respect to each other; furthermore, dynamic bifurcation points of the similar branches do not coincide completely. Key Words: Geometric imperfection, Bifurcation, Limit cycle, Chaos
