A Self-demodulated Fiber Bragg Grating For Investigating Bending/torsional Band-gap Properties Of Phononic Crystal Beams

Phononic crystals are a kind of periodic materials possessing elastic wave band gaps.Elastic waves are forbidden or supressed in the band-gap frequency ranges.The unique properties of band gaps makes phononic crystals promising in the applications of noise and vibration control.Since beams are the most commonly used structures in engineering,vibration reduction of beam structures have long been an important research topic.Focusing on the bending/torsional band-gap properties of phononic crystal beams,this thesis provides new sensing techniques and corresponding theoretical validations.The steady-state transmission properties and transient responses of bending and torsional vibration of phononic crystal beams are studied by theoretical,simulation and experimental methods.The main contents are listed as follows:(1)We introduce the Method of Reverberation-Ray Matrix(MRRM).The band structures of the infinite phononic crystals,transmission properties of the finite phononic crystals,and the early short-time transient responses can be solved by the MRRM.The MRRM provides a new and effective method for calculating the band-gap properties and transient responses of bending and torsional waves in phononic crystal beams.(2)A self-demodulated fiber Bragg grating(SFBG)displacement sensing method is provided whose linearity is examined by the coupled mode theory and transfer matrix method.The dynamic sensing capability is verified by static stretching and dynamic sensing experiments.The SFBG displacement sensing system to experimentally investigate the dynamic behaviors of phononic crystal is established,which presents a set of high precision,simple,and practical experimental means for phononic crystal experimental research.(3)The SFBG displacement sensing system is used to investigate the transmission properties and transient responses of phononic crystal(PC)beams.The steady-state experimental results show that the band gaps can effectively attenuate the vibration,and the localization of the bending waves occurs in the defect states of the imperfect phononic crystals.In transient experiments,the long-time transient response directly reflects the effect of band gaps on suppressing the bending wave propagation.Spectral analysis shows that,compared to the long-time transient responses,the early short-time transient responses can greatly reduce the influence of the damping ratios and the environmental noises on the high-frequency contents in the frequency domain The results of experimental,theoretical(MRRM),and finite element method are in excellent agreement,which simultaneously verifies the MRRM theory and the high precision sensing ability of the SFBG displacement sensing system.(4)A method for extracting the torsional waves/vibrations of the phononic crystals,based on the differential responses of a pair of the SFBGs,is proposed.Based on the proposed extraction method,the steady torsional band-gap properties of a phononic crystal beam(with a rectangular cross-section)and the transient responses of the PC beam subjected to eccentric excitations are experimentally studied.Compared with the results obtained by the MRRM theory and the finite element method,the proposed extraction method is verified both in steady-state transmissions and in transient responses.It is found that the band gaps greatly attenuate the torsional vibrations.We also found that,when the torsional wave propagates in the phononic crystals,a certain arrangement of the materials or geometric periodicity allows the existence of the localized states at the free surface of the phononic crystals.The existence of localized states reduces the effectivity of the vibration suppression in the bandgap range,which might be taken into consideration in the design process of the PCs for the purpose of the structural vibration reduction.