STABILIZATION OF NONLINEAR PANEL VIBRATIONS BY BOUNDARY DAMPING

By introducing boundary damping, the exponential stabilization of a no n-linear elastic panel is considered. With the left edge clamped, a co mbination of a bending moment and two point forces is applied to the r ight edge. For no flow, we find that the free panel vibration under a static compressive loading can be stabilized by a tensile force and bo undary damping. The applied tensile force, if needed, is to produce a net thrust below a critical level for buckling, and the boundary dampi ng is introduced by a frictional force and a braking torque, which may be regarded as a passive control and depends linearly on the transver se and angular velocities of the controlled edge. For time-dependent f low and compressive loading, it is shown that the fluttering panel can be stabilized, either when a flow parameter fluctuates and decays rap idly or when the flow parameter and the rate of change in compression are both small. In all cases, sufficient conditions for stability are given explicitly. Numerical examples are provided for the purpose of i llustration.