Example No. 1 Flutter Instability

The equilibrium configuration is found by setting all temporal derivatives to zero. We have 

The linearized system of equations with respect to small vibrations around the equilibrium state is found as 

we notice that the inertia matrix is symmetric and positive definite (i.e., (mi + m2)fi 0 and det(M) = fm2 mi + m2 sin 0o) 0). The divergence insta-bihty is ruled out since det(K) =k k2 0. To check for the possibility of flutter instability, first we need to derive the characteristic equation. According to (3.29) we have 

On the other hand, the origin is unstable whenever fl2 = b P — b2 0 (i.e., 0)J 0). Thus, the critical value of the load for the flutter instability boundary is 

In the following paragraphs, some illustrative numerical results are given. Table 4.2 lists the numerical value of the system parameters used in these simulations. Fig. 4.8 shows the evolution of the eigenvalues aP) as the magnitude of the 

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