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The tower of the wind turbine (see Figure 6) has a height of 30 m and a circular hollow cross-section that has an inner diameter of 0.4 m and an outer diameter of 1 m. The rotor and hub mass is 0.3 × 103 kg and the tower is made of steel that has a Young’s modulus of 200 GPa and density 7800 kg/m3. When the tower’s weight is ignored, determine: a) the natural frequency of transverse vibration of the system; b) the time response due to initial transverse displacement x0 = 0.1 m; c) the maximum values of velocity and accelerations. When the tower’s weight is taken into account using equivalent weight 23.57% of its actual weight, repeat the above sub-questions a), b), and c).
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