Analysis of nonlinear limit cycle flutter of a restrained plate induced by subsonic flow

Abstract

The nonlinear flutter oscillations of a restrained cantilevered plate induced by subsonic flow have been investigated in this paper. A non-smooth piecewise linear spring is considered to simulate the motion constraints. A set of discrete equations is obtained by the Galerkin method. Emphasis is placed on the limit cycle oscillations (LCOs) of the aeroelastic system due to the nonlinearity. A flutter determinant is developed to the analysis of flutter instability. The system loses stability by flutter and undergoes LCOs afterward due to the nonlinearity. The stability of LCOs is addressed on the basis of the equivalent linearized method. The location of the nonlinear motion constraints is intimately bound up with the type of Hopf bifurcations (subcritical or supercritical). Interestingly, for some special cases, the Hopf bifurcations are both subcritical and supercritical. The two-multiple semi-stable limit cycle bifurcation due to the extreme point of the flutter curve is also determined. The analytical results predicted by the analysis scheme are sufficiently validated by numerical calculations.