An airplane standing on a runway is shown in Fig. 5.37. The airplane has a mass \(m=20,000 \mathrm{~kg}\) and a mass moment of inertia \(J_{0}=50 \times 10^{6} \mathrm{~kg}-\mathrm{m}^{2}\). If the values of stiffness and damping constant are \(k_{1}=10 \mathrm{kN} / \mathrm{m}\) and \(c_{1}=2 \mathrm{kN}-\mathrm{s} / \mathrm{m}\) for the main landing gear and \(k_{2}=5 \mathrm{kN} / \mathrm{m}\) and \(c_{2}=5 \mathrm{kN}-\mathrm{s} / \mathrm{m}\) for the nose landing gear, (a) derive the equations of motion of the airplane, and (b) find the undamped natural frequencies of the system. Assume \(l_{1}=20 \mathrm{~m}\) and \(l_{2}=30 \mathrm{~m}\).

Transcribed Image Text:

Main landing gear 41 FIGURE 5.37 Airplane standing on runway. m. Jo C.G. -12- T Nose landing gear