Active Modification of Wave Reflection and Transmission in Flexible Structures

A theory for active control of elastic wave propagation in structures is developed. Attention is focused on active modification of the scattering behavior of discrete locations in a structural network. The wave mode input/output relation at a structural junction containing control actuators can be altered in two ways. First, the closed loop reflection and transmission coefficients can be specified, and the necessary feedback to achieve these coefficients determined. Second, an optimal wave controller can be formulated which maximizes the average power dissipation at a junction. If the open loop structure is stable, then the optimal control guarantees stability, since energy is actively dissipated at the junction. Sample controllers are derived and simulated for a free-free beam to demonstrate the techniques and indicate the achievable performance.