Vibration confinement in beams

We develop approaches for vibration confinement to within an arbitrary region in both non-fluid-loaded beams and fluid-loaded beams. The approach for non-fluid-loaded beams makes use of a novel forward/backward substitution algorithm that generates an evanescent response that exhibits exponential growth from one end of the beam to a specified node, and then exponential decay from that node to the other end of the beam. A weighted sum of such solutions supports vibration confinement while requiring only one actuator at each edge of the confined region. We also demonstrate vibration confinement with just a single actuator term when one edge of the confined region extends to the end of the beam. For fluid-loaded beams, we use a weighted sum of solutions having compact support to achieve near-confinement. While the displacement vector is nonzero outside of the confined region (as a consequence of the acoustic loading on the beam), its amplitude is significantly reduced.