Mitigating Vibration Along an Arbitrarily Supported Elastic Structure Using Multiple Two-Degree-of-Freedom Oscillators

Simple spring-mass systems are often deployed as vibration absorbers to quench excess vibration in structural systems. In this paper, multiple two-degree-of-freedom oscillators that translate and rotate are used to mitigate vibration by imposing points of zero displacement, or nodes, along any arbitrarily supported elastic structure during harmonic excitations. Nodes can often be enforced along an elastic structure by attaching suitably chosen two-degree-of-freedom oscillators. In application, however, the actual selection of the oscillator parameters also depends on the tolerable translational and rotational vibration amplitudes of the attached oscillators, because if these vibration amplitudes are large, then theoretically feasible solutions would not be practical to implement. In this paper, an efficient approach is developed that can be used to tune the oscillator parameters that are required to induce nodes, while satisfying the tolerable vibration amplitudes of the oscillators. Instead of solving for the oscillator parameters directly, the restoring forces exerted by the springs are computed instead. The proposed approach is simple to apply, efficient to solve, and more importantly, allows one to easily impose the tolerable translational and rotational vibration amplitudes of the two-degree-of-freedom oscillators. A design guide for choosing the required oscillator parameters is outlined, and numerical experiments are performed to validate the proposed scheme of imposing nodes along a structure at multiple locations during harmonic excitations.