This research is focusing on the bending-torsion coupled free vibration modeling as well as the analysis of intact and defective pre-stressed beams subjected to combined axial force and end moment. In the recent years, many studies have been conducted in an attempt to investigate the free vibration of pre-stressed beams using numerical and analytical techniques. However, despite their numerous applications, there is limited research done on pre-stressed beams subjected to both axial force and end moment in addition to the coupled behavior caused by the latter one. In the present study, current trends in the literature are critically examined, new models are proposed, and numerical and semi-analytical formulations are developed to find the natural frequencies and mode shapes of different pre-stressed slender beam configurations. The proposed methods are compared in terms of accuracy and convergence. Furthermore, the effects of axial force, end moment and delamination defect on the vibrational behavior of each model are also investigated.
Four different general types of thin beams, including isotropic, layered, composite and delaminated beams, are modeled using traditional Finite Element Method (FEM) and frequency-dependent Dynamic Finite Element (DFE) technique. The DFE formulation is distinct from the conventional FEM by the fact that the former exploits frequency-dependent basis and shape functions of approximation space, whereas the polynomial ones are used in the latter method. With regard to layered beams, a novel layer-wise method is introduced for both DFE and FEM. Delaminated beam is also modeled using both ‘free mode’ and ‘constrained mode’ models showing that the continuity (both kinematic and force) conditions at delamination tips, in particular, play a large role in formulation of ‘free mode’ model. In this case, the defect is assumed to be a single-symmetric through the thickness delamination. However, the presented models and formulations could be readily extended to more general cases. Where available, the results were validated against existing limited experimental, analytical, and numerical data in literature. In addition, the investigated cases are modeled in the commercial finite element suite ANSYS® for further validation. Finally, general concluding remarks are made on the performance of the presented models and solution techniques,
where the advantages and disadvantages of the proposed formulations as well as possible future research works are highlighted.