Stability Analysis of Nonlinear Differential Autonomous Systems with Applications to Flutter

This paper deals with the general theory of stability analysis of nonlinear differential autonomous systems of the type x=A(\)x+f(x, X), with the linear system stable (unstable) for *0>- T116 analysis is performed by a singular perturbation method, the multiple time scaling. The solution is obtained in the form of an asymptotic expansion in the neighborhood of the stability boundary, X= \0 . It is shown that there always exists a limit cycle, either for X \0 (stable limit cycle). The analytical expression for the limit cycle amplitude also is given. Applications to nonlinear flutter of panels and wings are included. Numerical results are in excellent agreement with existing ones.