Page - 791 - in Book of Full Papers - Symposium Hydro Engineering

Figure 3: Ratio between the natural frequencies of Timoshenko and Euler theories, for a cantilever beam with constant cross-section, considering only shear deformation effects. Figure 4: Ratio between the natural frequencies of Timoshenko and Euler theories, for a cantilever beam with constant cross-section, with all effects. In the analysis, it was noted that the behavior for the first frequency differs from that expected: the consideration of the Timoshenko theory effects made the beam behave more rigid in the first natural frequency, resulting in ratios higher than the unity. Such behavior is contrary to the very nature of considering such effects, which is achieving a more realistic behavior, considering additional effects that induces a more flexible model. Although the consideration of only the rotational inertia produced values ratios below the unity for the first frequency, the consideration of shear deformation and all effects, including coupling, caused the Timoshenko beam to produce more rigid results. Thus, it was chosen to disregard the analysis of the first frequency which, although it is the most relevant in the dynamic study of structures, could not be well represented by the algorithm developed, either due to the implementation made or by inaccuracies of the Finite Differences Method, since it could not be identify the source of such difference. 791