Vibration Attenuation And Band Gap Characteristics Of Phononic Crystals

Phononic crystals (PCs) are material with elastic or vibration band gaps where the propagation of vibrations is forbidden. This property provides new prospects for technology of vibration attenuation. In this thesis, based on the research status and the basic theory of PCs, the vibration band gap in PCs and its properties are studied. The vibration transmission property of the one-, two-, and three-dimensional PCs with finite structure as well as the beams and plates based on the idea of PCs is researched with the finite element simulation and the vibration experiment. Furthermore, with the basic principles of vibration attenuation, the applications of PCs in field of vibration attenuation are researched. The chief contents and conclusions are showed as follows.(1) The vibration experiments are used in the study of PCs systematically. The band structure calculations for infinite periodic structures, the finite element simulations for finite periodic structure and the vibration experiments are integrated. The band gap property and vibration attenuation ability of the one-, two-, and three-dimensional PCs as well as the periodic beam and plate structures are studied deeply.(2) Based on the one-dimensional double atomic chain model in solid physics, the calculation methods of the band structure and vibration transmission property of the periodic mass-spring structures are derived. Numerical simulations and experiments are combined and used to study the vibration attenuation ability of the periodic mass-spring structures. Conclusions show that there exist band gaps in the periodic mass-spring structures. The frequency ranges of it can be designed, where the propagation of vibration will be attenuated obviously. The damping will not affect the range of the band gap, while excessive damping can restrain the formation of it.(3) Based on the idea of lumped mass method, the one-dimensional PCs are simplified to the infinite periodic mass-spring structures. Thus the lumped-mass method for the calculation of band structure of one-dimensional PCs is proposed, which has a good convergence and can handle the one-dimensional PCs with complex structures.(4) The influences of the material and structural parameters on the band gaps of one-, two-and three-dimensional PCs are discussed systematically. It has been concluded that PCs composed of high density scatter and hosting material of proper density and small elastic parameters are most likely to obtain low-frequency band gaps with an optimized filling fraction,when both the density and elastic parameters of the scatters are larger than that of the hosting. The propagation of vibration can be restrained within the band gap of a finite sample of PCs, which means that it can be used in the vibration attenuation or shelter. These results are theoretically meaningful to the design of band gap property of PCs in the application of vibration attenuation or shelter.(5) For the first time the idea of PCs is introduced in the design of beam and plate structures and the band gap property are used to restrain the vibration in them. The feasibility of these ideas is validated with the theoretical and experimental studies. The plane-wave expansion method for the calculation of band structure of the periodic beam and plate structures are derived. The influences of the material and structural parameters on the flexural band gaps are discussed systematically and validated with the finite element simulation and the vibration experiments. These results provide a new technical way for the vibration/noise attenuation in beam and plate structures.In summary, the basic theory and problem in the application of band gap property of PCs are studied theoretically and experimentally. Comprehensive studies on the vibration properties of the PCs and the periodic beam/plate structures prove that the PCs can be used to restrain the vibration within the band gap. Qualitative influencing factors of the band gap are summarized. The vibration restraining method based on the band gap of periodic beam/plate structure are proposed, which provides a new idea in the vibration/noise attenuation in beam and plate structures. The research results in this thesis are meaningful in both the theory and engineering of the application of the new concepts and principles of the phononic crystals in vibration control.