Stabilization of non-linear panel vibrations by boundary damping

✍ Scribed by P.-L. Chow; L. Maestrello

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 860 KB
• Volume: 182
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1995.0215

✦ Synopsis

By introducing boundary damping, the exponential stabilization of a non-linear elastic panel is considered. With the left edge clamped, a combination of a bending moment and two point forces is applied to the right edge. For no flow, we find that the free panel vibration under a static compressive loading can be stabilized by a tensile force and boundary damping. The applied tensile force, if needed, is to produce a net thrust below a critical level for buckling, and the boundary damping is introduced by a frictional force and a braking torque, which may be regarded as a passive control and depends linearly on the transverse and angular velocities of the controlled edge. For time-dependent flow and compressive loading, it is shown that the fluttering panel can be stabilized, either when a flow parameter fluctuates and decays rapidly 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 illustration.