Research on the structural vibration attenuation characteristics of locally resonant metamaterial

Abstract

Low-frequency structural vibration is a common issue in engineering applications. In recent decades, the local resonant type metamaterial concept was proposed as a potential solution to the vibration control problems. In particular, the membrane-type metamaterial (MemM) is widely studied for its extraordinary sound isolation performance. As a lightweight metamaterial, the related research works mainly focus on MemM’s acoustic property yet its structural vibration absorption capability is not fully investigated. Research works that focus on the 1) development of an analytical model for bandgap property prediction; 2) the investigation of bandgap formation mechanism; 3) the confirmation of key design parameters and the corresponding effect on bandgap property and 4) the development analytical models of the semi-active control system are still limited in the MemM research area. Therefore, to further investigate the MemM, the main research contents and novelty of this study are: 1. Based on the local resonant phenomenon, this study proposes a novel design of elastic metamaterial (EM) for the purpose of investigating the bandgap formation mechanism. Modal analysis is conducted to help to understand the relationship between the local resonant phenomenon and bandgap formation. Also, the tuning of bandgap properties through geometrical structure adjustment is investigated. The structural vibration attenuation capability and bandgap tunability of the EM is verified through numerical simulation and experiment. 2. This study proposes a modified Plane Wave Expansion (PWE) model for predicting the bandgap property of MemM applied on a thin plate. A further modification is made to allow the bandgap calculation for bilayer MemM. It can predict the MemM’s vibration suppression performance when applied to a thin plate. The tensile stress of the membrane is contained in the model as an independent variable. To the best of author’s knowledge, it is the first analytical model derived specifically for the application of MemM. The accuracy of the model is verified through numerical simulation and experiments. 3. This study also proposes an analytical model that can predict the bandgap property and bandgap tunability of MemM equipped with polyvinylidene difluoride (PVDF) membrane. It integrates the piezoelectric material constitutive equations into MemM model for bandgap prediction. Based on this model, the semi-active control system’s analytical models for the PVDF MemM are derived. It demonstrates the feasibility of PVDF MemM in the future application and the realisation of conducting semi-active control to MemM. 4. This study combines the analytical model of the membrane-type resonator (MemR) with the thin plate – resonator coupling model. The integrated model allows the prediction and investigation of a thin plate structure’s vibration response when MemRs are attached. Different from the modified PWE model, this analytical model allows the adjustment of resonator settings individually. Therefore, the optimisation of resonator allocation and distribution can be achieved through this model. In conclusion, this research has systematically studied MemM’s structural vibration attenuation performance and the feasibility of conducting bandgap tuning. Analytical models are developed to conduct bandgap prediction and to reveal the effect of design parameters. The conducted numerical simulation and experimental works demonstrate the effectiveness of MemM in structural vibration control. It contributes to the body of knowledge in the analytical foundation of the MemM, and will be helpful for the design, optimisation and application of MemM.

Date of Award	8 Nov 2020
Original language	English
Awarding Institution	Univerisity of Nottingham
Supervisor	Dunant Halim (Supervisor) & Xiaosu Yi (Supervisor)