Active Parametric Damping of Distributed Parameter Beam Transverse Vibration

An active vibration control for a modified, non-linear, dynamic, simply supported, Bernoulli-Euler beam is introduced using one of the distributed, time-dependent parameters of the system. The control is carried out by observing the axial velocity of the end point of the beam and applying a modified bang-bang variation of beam tensile stress to control beam transverse stiffness. Numerical simulation of the closed-loop system of partial differential equations demonstrates the effectiveness of the control. Two cases representing initial value problems are given as examples. This active control applied to a undamped system model yields an asymptotically stable system which loses its total system energy to a level that is 0.26% of its initial value in five and one half cycles.