Enforcing Nodes to Suppress Vibration Along a Harmonically Forced Damped Euler-Bernoulli Beam

Abstract

In this paper, properly tuned damped absorbers are used to suppress excess vibration anywhere along an arbitrarily supported, damped Euler-Bernoulli beam during forced harmonic excitations. This vibration suppression is achieved by enforcing distinct nodes, or points of zero vibration, at desired locations along the beam. Instead of directly solving for the absorber parameter, which is highly computationally intensive, an efficient method is developed whereby the restoring forces exerted by the damped absorbers are first determined using Gaussian elimination. These restoring forces are then used to tune the parameters of the damped oscillators. Numerical experiments show that by inducing nodes at the appropriate locations, a region of nearly zero vibration amplitudes can be enforced, effectively quenching vibration in that segment of the beam.