Derive the stiffness and mass matrices of a uniform beam element in transverse vibration rotating at an
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Derive the stiffness and mass matrices of a uniform beam element in transverse vibration rotating at an angular velocity of \(\Omega \mathrm{rad} / \mathrm{s}\) about a vertical axis as shown in Fig. 12.40(a). Using these matrices, find the natural frequencies of transverse vibration of the rotor blade of a helicopter (see Fig. 12.40(b)) rotating at a speed of \(300 \mathrm{rpm}\). Assume a uniform rectangular cross section \(0.02 \mathrm{~m} \times 0.3 \mathrm{~m}\) and a length \(1.2 \mathrm{~m}\) for the blade. The material of the blade is aluminum.
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