Sound Wave Propagation through Periodic and Nonreciprocal Structures with Viscous Components Page: 22
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2
- - - - - Approximation
Exact I
Ni 150
o 100-
8mm 2mm
1 50 0
rC-r
SUk
0
0 1 2 3
kX d__ _ _ _ _ _
0 50 100 150
Frequency (kHz)
FIGURE 2.2. Frequency dependence of the attenuation coefficient of the longi-
tudinal sound and normal incidence for water-glycerol superlattice with filling
fraction of water f = 0.8. The exact result is calculated from Eq. (2.33) and
the linear over viscosity approximation is given by Eq. (2.37). Both results
exhibit fast growth near the band edge: the exact value remains finite and the
approximate approaches infinity. Note that even for relatively high viscosity
of glycerol the decay length is of the order of 104 lattice periods. The oppositecase of very strong viscous absorption when the boundary layers overlap within
the lattice period is numerically considered in Ref. [80, 95]. Left inset: the
band structure of the water-glycerol superlattice. The band gaps are shaded
in grey. Right inset: the unit cell with geometrical parameters.22
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Shymkiv, Dmytro. Sound Wave Propagation through Periodic and Nonreciprocal Structures with Viscous Components, dissertation, May 2024; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc2332612/m1/34/: accessed July 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .