Behavior of Nonlinear Flutter-Type Oscillations of Flexible Plates in Supersonic Gas Flow

Abstract

The behavior of nonlinear oscillations of isotropic rectangular plate fluttering in a supersonic gas flow is examined. The study was conducted taking into account both types of nonlinearity: wind (quadratic and cubic) and geometric (cubic). It is established that because of aerodynamic nonlinearity (especially its nonsymmetric quadratic part), the relationship A(ν) (where A is the amplitude of nonlinear oscillations and ν is the parameter characterizing the value of the flowing stream) is a two-value function at certain intervals of the speed ν. This fact is illustrated in the figures, which are plotted in the text, in the form of two branches. The lower branches of these figures, in all probability, are unstable. The unstable branches are separated via the gravitational field of two adjacent sustainable solutions. Thus, the perturbation magnitude, which is required in order to transfer the system from one stable branch to another, can easily be found. The existence of certain intervals of ν is shown, where limit cycle oscillations (LCOs) cannot be excited in both precritical speeds and in the postcritical stage.