Customize vibration mode

we introduce acoustic metamaterial into vibration mode customization. Vibration mode customization may facilitate the localization of vibration response/energy to certain regions of the structure without employing major changes of structural or material properties mechanically.

We consider a uniform beam with free-free boundary condition for illustration. In this illustration the metamaterial beam is divided into two regions. Here we hypothesize that, with proper selection of the inductance values, under a given frequency of interest, one region can vibrate within its bandgap (minimum displacement) while the entire metamaterial beam (including the other region) exhibits resonant motion. In such a scenario, in the other region, the forward and reflected waves have the same amplitude and phase and, as they overlap with each other, yield vibration amplification, which is analogous to the resonant cavity effect.

This figure presents the relation of mechanical energy density stored in Region 2 versus the inductive load. Modes with vibration localization at the right hand side are created. Resonant motion in Region 2 accumulates and amplifies the mechanical energy transmitted through Region 1.

The piezoelectric metamaterial has great advantage of being adaptive. ‘1’ refers to the region working in effective resonant cavity condition with amplified displacement, and ‘0’ refers to the region working in bandgap with vibration attenuation. Since the metamaterial beam is segmented into two regions, four cases for the resonance assignment are assessed, indicated as 0-1, 0-0, 1-0, and 1-1 respectively.

Despite the efforts and the tempting, potential outcome, the subject of vibration mode customization has so far seen limited success. Most of the methods are based on inverse analysis of eigenvalue problem at the system level. In passive methods, significant change of geometry/material properties would be needed. In active methods, a large number of actuators and sensors become necessary. In both passive and active methods the performance has been limited because of the small design space due to physical constraints. This proposed concept takes advantage of the unusual dynamic behaviors yielded by piezoelectric metamaterial, and looks at the mode customization problem from a new, wave propagation perspective. As illustrated in the manuscript, the mode customization can be achieved with very good performance. In addition to vibration suppression, the customized mode shapes can also assist the design of electro-mechanical system in terms of distribution of actuators and sensors to potentially enhance the actuation, sensing and energy harvesting performances.

Publications:

* J. Xu, S. Li and J. Tang, “Customized Shaping of Vibration Modes by Acoustic Metamaterial Synthesis,” Smart Materials and Structures, 235(1), 2018.