Research On The Mechanism And The Vibration Attenuation Characteristic Of Locally Resonant Band Gap In Phononic Crystals

Phononic crystals are the periodic elastic materials or structures with elastic wave band gaps, which is proposed twelve years ago. The locally resonant band gap mechanism of phononic crystals has a much shorter history of only five years. The new mechanism can exhibit low frequency band gaps with structures of small size. Therefore, it has many important potential applications in the decreasing of low-frequency vibration and noise. In this thesis, the scientific problems according to the mechanism of locally resonant band gap are studied with theoretical and experimental methods deeply and systemically, and meaningful attempts are done in the application of locally resonant band gaps on vibration attenuation. Our research works include:The lumped-mass method in the calculation of band structure of one-dimensional phononic crystals is extended into two and three dimensions. It has been concluded that, by comparing with other algorithms, the applicability of the lumped-mass method is wider, and the convergence of it is better. Thus a powerful facility is provided for the research of band gap mechanism of the phononic crystals.The existence of the locally resonant band gap in the two-dimensional binary phononic crystals has been proposed and proved theoretically and experimentally. Thus the original view that the locally resonant band gap exists only in ternary systems is changed. The key factor that influences the formation of a locally resonant band gap corresponding to a resonant mode in the phononic crystals is found and proved, which can be stated as: the interaction between the vibration of the localized oscillator in the resonant mode and the long-wavelength elastic wave in the hosting media must exist.The vibration mode corresponding to the upper edge of the locally resonant band gaps is proposed. Simple analog models of the two- and three-dimensional ternary phononic crystals with locally resonant band gap are improved. Such models can be used to describe the vibration modes on the edges of the lowest band gap and estimate the frequencies of it correctly. With the analog models, we can get the analytical expressions of the factors that influence the frequencies on the edges of the locally resonant band gap.With the analytical study on the locally resonant band gap of one-dimensional phononic crystal, the equivalent stiffness ratio and mass ratio are discovered as the deciding factors of the attenuation in the band gap. It is also shown that the equvalent stiffness ratio is the key factor. As the two- and three- dimensional phononic crystals with locally resonant band gaps are all equivalent to corresponding one-dimensional models, this conclusion is also valid for them.The locally resonant band gap mechanism of phononic crystals is introduced in the design of beam and plate structures, where the band gap property is used to restrain the flexural vibration in them. Further theoretical and experimental studies proved the feasibility of it and illustrated the vibration attenuation properities of the locally resonant flexural wave band gap.In summary, drawn by the application to the decreasing of low-frequency vibration and noise with small structures, the locally resonant band gap mechanism and its capability in vibration attenuation are studied therotically and experimentally in this thesis. The algorithm problems restricting the study on the locally resonant band gap of phononic crystal are solved. Several important therotical and technical questions about the formation, the frequency and the attenuation of locally resonant band gap that restricting the application of it in low-frequency vibration/noise attenuation are answered. These research results are meaningful for the application of the new concept and principles of the phononic crystals in the control of vibration and noise.