An airplane wing, Fig. 6.30(a), is modeled as a three-degree-of-freedom lumped-mass system, as shown in Fig. 6.30(b). Derive the flexibility matrix and the equations of motion of the wing by assuming that all \(A_{i}=A,(E I)_{i}=E I, l_{i}=l\) and that the root is fixed.

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A3, (EI)3 A2, (EI)2 (a) A, (EI) (b) FIGURE 6.30 Modeling of an airplane wing. x1 x2 S