Control of bending wave transmission through an uncoupled force and moment neutraliser

Undamped vibration neutralisers are commonly used to suppress a problematic excitation frequency in a narrow frequency range, much like a notch filter. There is a great interest to increase the bandwidth of these devices. For applications concerning the control of wave propagation in beam structures, one such method has been to combine a traditional force neutraliser, that exerts a force on a structure in proportion to the displacement at the attachment point, with a moment neutraliser, that exerts a moment on a structure proportional to the rotation. The aim is to reduce the power transmitted through the neutraliser. Qualitative benefits in increased bandwidth have previously been observed for an uncoupled force-moment neutraliser. Benefits have been mainly attributed to a second notch in the transmission response being produced. The goal of this paper is to investigate the qualitative and quantitative behaviour of undamped force-moment neutralisers relative to force only neutralisers and determine the parameters that maximise the bandwidth. The natural frequency of the moment resonator can be different to that of the force resonator. Increases in bandwidth are observed by introducing such a change. Expressions are developed for the frequencies at which the neutralisers suppresses vibration completely. The two physical mechanisms that govern vibration suppression are determined. The first is a phase condition that requires a pi/2 phase difference between the shear force and velocity, as well the bending moment and angular velocity. The second mechanism results from a magnitude condition: the displacement and slope are minimised. Two levels of attenuation are considered: first the 3 dB bandwidth, within which less than half the power is transmitted, and is relevant for applications requiring general vibration suppression; secondly, for applications that require near total isolation, the 17 dB bandwidth, where 1/ 50th of power is transmitted. Analytical expressions for the bandwidths at 3 dB and 17 dB are presented. The parameters for the maximum bandwidths at 3 dB and 17dB are found, as well as the frequencies specifying vibration suppression. Numerical results are presented for all power transmission ratios. The proportional increase in bandwidth using an optimally tuned moment neutraliser in addition to a force neutraliser increases for higher attenuation levels, but decreases for lower levels. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This study investigates the qualitative and quantitative behavior of undamped force-moment neutralisers relative to force only neutralisers, aiming to determine the parameters for maximizing bandwidth. Two physical mechanisms governing vibration suppression are identified: a phase condition and a magnitude condition. Results show that the proportional increase in bandwidth using an optimally tuned moment neutraliser in addition to a force neutraliser varies for different levels of attenuation.