Active Parametric Damping of Distributed Parameter Beam Transverse Vibration

[+] Author and Article Information
M. S. Habib

Department of Mechanical Engineering, Ain Shams University, Abassia, Cairo, Egypt

C. J. Radcliffe

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824

J. Dyn. Sys., Meas., Control 113(2), 295-299 (Jun 01, 1991) (5 pages) doi:10.1115/1.2896378 History: Received September 01, 1988; Revised March 01, 1990; Online March 17, 2008


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.

Copyright © 1991 by The American Society of Mechanical Engineers
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