Active Parametric Damping of Distributed Parameter Beam Transverse Vibration

An active vibration control for a modified, nonlinear, 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 first mode vibration of an undamped system model yields an asymptotically stable system which loses its total system energy to a level that is 0.26 percent of its initial value in five and one half cycles.