Wave based vibration control of membranes

Suppression of vibrations occurring in membranes due to initial conditions is considered. The membrane is modeled by a combination of modal decomposition in the lateral axis and transfer functions in the longitudinal. The transfer functions are irrational and are shown to represent the wave motion in the system. A dedicated closed loop control algorithm is designed to eliminate the wave reflections in the control axis. The resulting controllers are irrational as well, and approximations are used to implement them. Numerical simulations show that controlling only few modes is sufficient to achieve a considerable vibration attenuation.