SeminarsSome Effective Properties of the Periodic Structure: a Homogenization Theory Study
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In this study, we apply the homogenization theory to periodic structures and two main characteristics of that are addressed. First, we investigate band structures of phononic crystals with particular emphasis on the effects of the mass density ratio and of the contrast of elastic constants. It is shown that the density ratio rather than the contrast of elastic constants is the dominant factor that opens up phononic band gaps. Then we aimed to study propagating modes of acoustic wave in periodic solid layers in ideal or viscous fluids. In particular, at long wavelength limit, a three-scale homogenization analysis is developed to derive the effective group velocities in analytical forms for the shear-vertical (SV) as well as for the longitudinal-shear horizontal (P- SH) waves. It is found that propagating modes, i.e., modes with real group velocities may be supported even if the fluid phase is viscous. The physical background of these observations is explained by applying the theory of homogenization to investigate the group velocities of the low-frequency bands at the center of symmetry Γ.
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Ying-Hong Liu
2008-05-16
11:10:00 - 12:00:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
In this study, we apply the homogenization theory to periodic structures and two main characteristics of that are addressed. First, we investigate band structures of phononic crystals with particular emphasis on the effects of the mass density ratio and of the contrast of elastic constants. It is shown that the density ratio rather than the contrast of elastic constants is the dominant factor that opens up phononic band gaps. Then we aimed to study propagating modes of acoustic wave in periodic solid layers in ideal or viscous fluids. In particular, at long wavelength limit, a three-scale homogenization analysis is developed to derive the effective group velocities in analytical forms for the shear-vertical (SV) as well as for the longitudinal-shear horizontal (P- SH) waves. It is found that propagating modes, i.e., modes with real group velocities may be supported even if the fluid phase is viscous. The physical background of these observations is explained by applying the theory of homogenization to investigate the group velocities of the low-frequency bands at the center of symmetry Γ.