Uniform modal damping of rings by an extended node control theorem

The node control theorem for uniform beams is extended to uniform rings. In contrast with uniform beams, uniform rings possess no boundary conditions and are degenerate in the sense that, for each natural frequency, there are two orthogoanl mode shapes: a sine mode and a cosine mode. It is shown here that 2M + 2 control forces evenly spaced around the ring can uniformly dampen the lowest 2M + 1 modes and preserve the associated natural frequencies and mode shapes. (AIAA)