An Efficient Method for Tuning Oscillator Parameters in Order to Impose Nodes on a Linear Structure Excited by Multiple Harmonics

Undamped oscillators are often used to attenuate and control excess vibration in elastic structures. In this paper, vibration absorbers are used to impose nodes, i.e., points of zero vibration, along an arbitrarily supported linear structure externally forced by multiple steady-state harmonic excitations. An efficient approach is proposed to tune the absorber parameters based on the active force method. Using the active force approach, the oscillators are first replaced with the unknown restoring forces they exert. These restoring forces are found by enforcing the required node locations, and they correspond to the solution of a set of linear algebraic equations, which can be obtained using Gauss elimination. These restoring forces are subsequently used to tune the sprung masses. Because of the computational efficiency of the proposed method, design plots can be easily generated, from which specific sets of oscillator parameters can be selected. Even if the input consists of multiple frequencies, it is possible to induce multiple nodes anywhere on the structure by attaching properly tuned spring–mass oscillators. An efficient procedure to tune the oscillator parameters necessary to impose nodes at the desired locations is outlined in detail, and numerical case studies are presented to verify the utility of the proposed scheme to impose multiple nodes along an arbitrarily supported elastic structure subjected to external excitations consisting of multiple harmonics.