Theoretical And Experimental Investigation Of Band Gap Tuning In Periodic And Quasi-periodic Beam Structures

In recent years,research on artificial structures such as phononic crystals(PC)and elastic metamaterials has received much attention.Analogy to the concept of photonic crystals,phononic crystals have band gaps prohibiting acoustic/elastic wave propagation in specific frequency ranges.Due to the band gaps,phononic crystals can be applid in vibration reduction,filtering or signal transmission.Wide clastic band gaps are desirable for phononic crystals.Related experimental techniques suitable for investigating phononic crystals are also required.In this paper,a systematic and in-depth study is made on the Bragg-scatterring and local resonance-based phononic crystals.Based on the spectral element method(SEM)and a fiber Bragg grating(FBG)displacement sensing system,theoretical and experimental studies on the phononic crystals are carried out.The main contents of the research include(1)Inerter dynamic vibration absorber is applied on elastic metamaterials,and its potential in widening the band gaps is studied.Based on an array of periodic inerters,longitudinal waves in mass-spring system and bending waves in Euler-Bernoulli beams are respectively considered.For the discrete systems,the additional introduction of conventional vibration absorbers creates two band gaps,one of which is a narrower gap at low frequencies and the other one is wider at high frequencies For distributed beams,in addition to the two local resonant bandgaps,the Bragg band gap can also be significantly broadened by the inerter-based dylalic absorbers When considering the dissipative damping mechanism,the separated local resonant band gaps in discrete systems can be combined into a larger one allowing significant attenuation for longitudinal waves over a wider frequency range.When considering the contribution of the Bragg bandgap,a wider band gap can be achieved for the distributed periodic beam structure(2)The band-gap and transmission properties of phononic crystal beams immersed in water are investigated experimentally and theoretically.Spectral element method is developed for theoretical analysis in which the added mass by fluid is taken into consideration.Influences of the added mass by fluid on band-gap and transmission properties of the PC beams are studied.Obvious lowering of the band gaps due to fluid-solid coupling is clearly demonstrated.To directly detect the displacement transmission of a fully or partially submerged PC beam,an FBG displacement sensing system is set up.Agreement between the experimental results and theorctical/numerical calculations also indicates the FBG sensing system can be used in the research of the fluid-structure interaction problem.This phenomenon might be useful in research such as active tuning of the band-gap and transmission properties of the PCs through fluid-solid coupling.(3)The bending wave localization phenomenon in the band gaps of a binary phononic crystal beam with point defects is studied.By introducing an additional point defect cell in the phononic crystal beam,the localization of the bending waves in the phononic crystal beam inside the band gaps is realized.Additionally,the localization of the bending wave is related to the position of the point defect.By properly arranging the position of the defect,Bragg scattering and the effect of the defect modes can be combined to achieve maximum bending wave localization.In order to explain and observe the localization of the bending wave,the displacement transmission and dynamic displacement/strain vibration shape of the phononic crystal beam are analyzed by the spectrum element method.Through the highly sensitive fiber Bragg grating displacement sensing system,the displacement transmission and the defect states of the phononic crystal beam are experimentally obtained(4)Unidirectional transmission of bending waves based on phononic crystal beam is studied.The phononic crystal beam is realized by setting up distribute concentrated masses on a straight beam periodically.The band-gap resonance defect states are found in odd-order band gaps of the PC beam.It is pointed out that the resonant states inside the band gaps are caused by the separation of the pass bands and are inherently caused by the imperfect structural periodicity of the finite phononic crystal beam.With gradient concentrated mass,noticeable asymmetric propagation of the bending waves can be seen in the displacement transmission.The directional relationship between mass gradient and defect state arc also studied with spectral element method.In order to realize gradient concentrated masses,steel balls with a gradual diameter distribution are employed.The band gaps of the phononic crystal beam are again measured by the FBG sensing system and the directionality of displacement transmission is verified.The transient Hanning-window lodulated tone bursts are respectively excited at the two ends of the phononic crystal beam to further verify the asymmetric bending wave propagation in time domain.The agreement between the spectral element method and the experimental results clearly shows that the gradient concentrated masses set up on the straight beam can achieve asymmetric unidirectional bending wave propagation.