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.