Vibration control of a linear flexible beam structure excited by multiple harmonics

Abstract

This paper deals with designing a control force to create nodal point(s) having zero displacement and/or zero slope at selected locations in a vibrating beam structure excited by multiple harmonic forces. It is shown that the steady state vibrations at desired points can be eliminated using applied control forces. The control forces design method is implemented using dynamic Green’s functions that transform the equations of motion from differential to algebraic equations, in which, the resulting solution is analytic and exact. The control problem is greatly simplified by utilizing the superposition principle that leads to calculating the control forces to create node(s) for each excitation frequency independently. The calculated control forces can be realized using passive elements such as masses and springs connected to the beam having reaction forces equal to the calculated control forces. The effectiveness of the proposed method is demonstrated on various cases using Numerical examples. Through examples, it was shown that creating node(s) with zero deflection as well as zero slope not only results in isolated stationary points but also suppress the vibrations along a wide region of the beam.