On the stability and chaos of a plate with motion constraints subjected to subsonic flow

• The non-linear fluid-induced motions of a plate with motion constraints in subsonic flow is investigated theoretically and numerically.
• The plate would lose its stability either by divergence or flutter, and the flutter and divergence boundaries are also determined in a parameter space.
• Three typical bifurcations and their physical implications are presented.
• The boundaries of different motion types in the flutter regions are shown in a parameter space with numerical analysis.

The non-linear dynamical behavior of a cantilevered plate with motion constraints in subsonic flow is investigated in this paper. The governing partial differential equation is transformed to a series of ordinary differential equations by using the Galerkin method. The fixed points and their stabilities of the system are presented in a parameter space based on qualitative analysis and numerical studies. The complex non-linear behavior in the region of dynamical instability is investigated by using numerical simulations. The region of dynamical instability is divided into four sub-regions according to different types of plate motion. Results show that symmetric and asymmetric limit cycle motions would occur after dynamical instability; the route from periodic motions to chaos is via doubling-period bifurcation; symmetric and asymmetric period-3 and period-6 motions appear along with chaotic motions; chaotic divergence and divergent motions occur with the increases of dynamic pressure.