Page - 790 - in Book of Full Papers - Symposium Hydro Engineering

4. PARAMETRIC ANALYSIS OF A CANTILVER BEAM WITH VARIABLE CROSS-SECTION As already presented, the dam dynamic problem can be analyzed, in an initial study, as a cantilever beam with variable cross-section, based on the plane strain state hypothesis. In this section, the FDM algorithm is used to evaluate the impact of shear deformation and rotary inertia consideration on the natural frequencies of a clamped-free beam, representing a dam in plane strain state. For all analyzes performed, the following properties of the material were used (Table 1): ρ (kg/m³) 2400 Young's modulus- E (GPa) 20 Poisson coefficient 0.2 Table 1: Properties of material First, a beam with constant section is analyzed, to identify only the influence of the shear deformation effects and rotational inertia on the section. For this, three analyzes are made: two with only one of the effects acting, and a third considering all the effects, including the coupling. The Figures 2, 3 and 4 present the results. The first frequency was not included due to an unexpected behavior, which will be further discussed. Figure 2: Ratio between the natural frequencies of Timoshenko and Euler theories, for a cantilever beam with constant cross-section, considering only rotary inertia effects. 790