Study On The Elastic Wave Dispersion Relation Of Periodic Structure And Vibration Localization

Periodic structures are extensively used in many engineering fields; there are a lot of particular mechanic characteristics in these structures. Such as when elastic waves propagate in them, pass band and stop band will appear. The modes of vibration can extend all over the whole structure in pass band, but it will disappear in stop band. The limiting frequencies of starting and stopping band gaps are derived by analyzing the dispersion relation.Phonon crystal is a type of functional materials, which has the elastic band gap. As the conception of phonon crystal is introduced that has outstanding function of damping and denoising, extensive attentions are paid on.Establishing proper models to describe the physical phenomena validly is the key step for solving problems. In this paper, based on the theory of continuum mechanics, lattice dynamics (single spring-oscillator), and multiple spring-oscillator model, the properties of elastic wave in 1D periodic structure are investigated, the dispersion relation and band gap structure of elastic waves in are analyzed and compared, continuum models and discrete particle models are similar when vibration frequency is low and wavelength is long. However, as vibration frequency is high and wavelength is short, there is large difference between the two models, which are continuum models are invalid in this case.As an example, the shear and torsion wave characteristics of tungsten/natural rubber phonon crystal in certain components are analysis, the first and second starting,stopping frequencies are derived, the displacement of internal particle under three typical exciting force are studied, from which, the difference of steady-state amplitude is founded.With the effect that the number of unit cells to the vibration being analyzed and the properties of forbidden band and passing band being verified, the band gap in periodic structures, which is a special mechanic performance, is profound and overall comprehended.Propagation of elastic waves through disordered periodic structures will be limited in local region; the localization phenomenon of elastic wave will appear. By employing the expression of elastic wave transfer matrix, the localization factor of this system is calculated; the influence of material component ratio on...