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Flexural wave bandgap properties of phononic crystal beams with interval parameters

Applied Mathematics and Mechanics(English Edition) 2023年第2期44卷 173-188页

作者： Feiyang HE Zhiyu SHI Denghui QIAN Y.K.LU Yujia XIANG Xuelei FENG State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China School of Naval Architecture&Ocean Engineering Jiangsu University of Science and TechnologyZhenjiang 212100Jiangsu ProvinceChina Department of Ophthalmology University of PittsburghPittsburgh 15213PAU.S.A.

Uncertainties are unavoidable in practical engineering,and phononic crystals are no exception.In this paper,the uncertainties are treated as the interval parameters,and an interval phononic crystal beam model is established.A perturbation-based interval finite element method(P-IFEM)and an affine-based interval finite element method(A-IFEM)are proposed to study the dynamic response of this interval phononic crystal beam,based on which an interval vibration transmission analysis can be easily implemented and the safe bandgap can be defined.Finally,two numerical examples are investigated to demonstrate the effectiveness and accuracy of the P-IFEM and A-IFEM.Results show that the safe bandgap range may even decrease by 10%compared with the deterministic bandgap without considering the uncertainties.

关键词： phononic crystal beam interval parameter safe bandgap perturbation-based interval finite element method(P-IFEM) affine-based interval finite element method(A-IFEM) interval vibration transmission analysis

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AN EXPERIMENTAL INVESTIGATION OF SLOW GROUP VELOCITIES IN A phononic crystal beam WITH A POINT DEFECT

AN EXPERIMENTAL INVESTIGATION OF SLOW GROUP VELOCITIES IN A ...

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2016年全国压电和声波理论及器件应用研讨会

作者： Kuo-chih CHUANG Zhi-qiang ZHANG Hua-xin WANG Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province School of Aeronautics and Astronautics Institute of Applied Mechanics Zhejiang University

Background, Motivation and Objective phononic crystals(PCs) have gained much attention for their potential applications in vibration suppression, sound insulation, filters, and so on. Apart from the phenomena of band gaps, existence of the crystal defects makes confinement of elastic waves in a localized mode possible. When the periodicity of the lattice is broken by the defects, localized resonance peaks can occur inside the band gaps. Various wave-manipulation devices can be designed through the introductions of the defect modes(e.g., frequency filters, couplers, focusing devices, etc). Here we experimentally investigate influences of the point defect modes on the propagations of flexural waves in a PC Timoshenko beam. Statement of Contribution/Methods In this work, the dispersion curves and the group velocities around the defect modes are theoretically obtained by the transfer matrix method with a supercell technique. In order to demonstrate the existence of the localized defect modes inside the band gaps, we set up a high-sensitivity fiber Bragg grating(FBG) sensing system and measure the displacement transmittance of the PC beam. Hanning windowed tone burst excitations are generated through a multilayered piezoelectric actuator and the transient elastic waves are then measured by the FBG sensing system. Results We show that the proposed FBG sensing system is able to obtain point-wise input and output displacements at the two ends of the PC beam for the obtainment of the displacement transmittance. In addition, we experimentally demonstrate that flexural waves propagate with slow group velocities around the defect modes. Discussion and Conclusions In conclusion, we have investigated the transmission properties of a PC Timoshenko beam with a point defect. The defect mode is existed inside the band gaps, validated theoretically by the transfer matrix theory with a supercell technique and experimentally by the proposed FBG displacement sensing system. The slow group velocity via the defect coupling is experiment

关键词： phononic crystal beam Group velocity Defect mode Fiber Bragg grating（FBGs）

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