Investigation Of One-dimensional Metamaterial Beams With Tunable Bandgaps

Periodic structures such as phononic crystals(PCs)or metamaterials have bandgaps in which elastic wave propagations are forbidden.Thus,one of the applications of PCs/metamaterials is to suppress unwanted structural vibrations.To allow the bandgap to be adaptive for various environmental scenarios,bandgap tuning of phononic crystals/metamaterials has attracted a lot of attention in recent years.In this paper,we focus on elastic wave bandgap tuning of one-dimensional phononic crystal beams.Based on shape memory alloys and designs of coupled dual-beam resonators,we studied and realized tunable bandgaps of one-dimensional phononic crystal beams.Specifically,we use fiber sensing techniques to perform the corresponding expriments.The main research contents in this thesis are as follows:(a)We derived the formula of the Bragg bandgap width of a PC beam whose bandgaps are constructed by a periodic array of concentrated masses.To realized the concentrated masses,we arrange steel balls on a shape memory alloy(SMA)beam.The Young's modulus of the shape memory alloy can be changed by controlling its temperature and thus the bandgaps can be actively tuned.In addition,we generated a local mismatch of Young's modulus in the PC beam to induce the defect mode that can localize strain responses when the beam is excited at these frequencies.With the properties of defect modes,energy can be harvested at the location of the material mismatch.(b)We designed a tunable metamaterial using two-way SMA beams as local resonators.The SMA beams have two state,being curved and flat.When its shape is curved by thermal excitation,its resonance frequency will change and the induced local resonance bandgaps change accordingly.Our design using SMAs provides new strategy for tunable metamaterials with broad bandgaps.In our study,we also discovered that the vertical vibration component directly affects the bandgap width of the local resonance.(c)We designed a new elastic metamaterial beam based on coupled dual-beam resonators.Each resonator consists of a pair of parallel rectangular rotatable beams coupled by one end mass.The coupling of the double beams can cancel the in-phase bending vibration of each beam resonators.By simply rotating the coupled double beam,we verified,both theoreticall,numerically,and experimentally that the bandgaps of the metamaterial can be tuned continuously over a wide frequency range.As the coupled dual-beam vibrators rotate from 0° to 90°,the start frequency of the bandgap can achieve a large control ratio of 42%.Although passive tuning is considered in our work,active components can be incorporated in the proposed design to enable adaptive tuning.(d)We used the characteristics of two-way SMAs and combined each SMA with a steel ball to form a "switching" metamaterial structure.When being heated,each vibrator bends to form a local oscillator,realizing the local resonance bandgap.When being naturally cooled,the periodic arrangement of the steel balls achieve Bragg scattering bandgap from concentrated mass.By controlling the temperature of the SMAs,it is possible to switch the bandgaps between the Bragg scattering ones and the local resonance ones.If we only thermally activate some of the resonators,the Bragg lattice constant of the structure and the corresponding Bragg scattering bandgaps can be tuned.