Equivalent Medium Model Of Acoustic Bandgap Material And Relationship Between Band Structures Of Various Modes

ABSTRACT:Acoustic bandgap material (ABG material), which has unique properties and wide potential applications, is one of the active research areas in physics, acoustics, mechanics and the other related disciplines. Many researchers have done a lot of work about the properties of the band gaps. In this thesis, we examine the relationship between the dispersion curves of various bulk and surface waves by establishing an equivalent nonlocal medium model of the ABG materials. The thesis discusses the wave propagation along the main symmetry directions (i.e.Γ-X andΓ-M directions of the Brillouin zone) in both square and triangular lattices. The equivalent nonlocal elastic moduli (i.e. the products of the classical local elastic moduli and influence functions) are determined by matching of the dispersion relations. The dispersion curves of various wave modes are calculated by assuming the unified form of the influence functions. The results are compared with those of the plane wave expansion method to verify the validity of the present equivalent nonlocal elastic model.The results for the bulk waves in two lattice structures show:Along theΓ-X direction, the difference between the three influence functions is slight in the first Brillouin zone (BZ), so they can take the same form. Therefore, the approximate relationship of the dispersion curves of three bulk waves can be obtained. In the second BZ, the difference between three influence functions is observable. The approximate relationship between the dispersion curves holds for the SH wave and SV wave, but not for the P wave and SV or SH wave. Along theΓ-M direction, the difference between three influence functions is pronounced, and thus the influence functions cannot take the same form. No approximate relationship between the dispersion curves of various wave modes exists.The results for the surface waves in the square lattice structure show:Along theΓ-X direction, the dispersion curves of the surface wave, which is obtained by taking the same form of the influence functions, is very close to the results of the plane wave expansion method in the first BZ. This implies the approximate relationship between the dispersion curves of the bulk waves and surface waves. The approximation in the second BZ is not as good as in the first BZ.In conclusion, the equivalent nonlocal elastic model is a new continuum model which is hopeful to undrestand the behaviors of the waves in ABG materials. However, the determination of the equivalent nonlocal elastic moduli (or influence functions) is difficult when the waves propagate along an arbitrary direction. Further research is necessary.