Quenching vibration along a harmonically excited linear structure using lumped masses

Abstract

Undamped oscillators consisting of spring-mass systems are commonly deployed as vibration absorbers to quench excess vibration in structural systems. While masses can be easily made to specification, it is often costly and more difficult to manufacture springs with the desired stiffness values precisely. In this paper, lumped masses only are used to suppress vibration by imposing points of zero displacement or nodes anywhere along an arbitrarily supported elastic structure during harmonic excitations. An efficient approach is developed that can be used to tune the required lumped-mass parameters and their attachment locations so that nodes are induced at the desired locations. Instead of solving for lumped masses directly, one solves for the restoring forces exerted by the lumped masses, which can be easily obtained using Gauss elimination. These restoring forces are then used to tune the required mass parameters. Design plots are proposed that show all the feasible attachment locations, and numerical experiments are performed to validate the proposed scheme of quenching vibration using lumped masses only.