By Ning Hu
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Additional info for Composites and Their Applications
These BIEs have a weak singularity x | at the source point x and a “square-root” singularity at the edge of the inclusion. To regularize the singular BIEs, the following integral relations for the elastostatic kernels are utilized when x S : S f() f() f( x ) dS 2f( x ) 0 dS , Sx 2 a | x | a 12 22 | x | 2 2 1 f( ) f( ) a S (x j j )2 3 a 2 12 22 | x | S 2 2 2 2 1 2 2 dS f() f( x ) (x j j )2 2 f( x) 0 dS , 3 Sx 2 a 2 12 22 | x | (11) f( ) f( x) (x1 1 )(x 2 2 ) (x1 )(x 2 2 ) dS 0 dS .
Effects of the inclusion mass distribution on the normalized attenuation coefficient (a) and the normalized effective wave velocity (b) as the functions of dimensionless wave number for randomly oriented inclusions and TV-wave incidence. 5. Numerical analysis of local dynamic parameters of a composite Description of macroscopic dynamic response of a composite to elastic wave propagation by Eqs. (23) and (28) allows us the extension of analysis on the near-field quantities connected with each inclusion.
At low frequencies, the normalized effective wave velocity cL in the composite is smaller than that in the homogeneous matrix material (see Figure 3(b)). Then the normal inclusion mass distribution is characterized by the bigger (smaller) value of cL in comparison with the aligned (uniform) situation. An opposite tendency is observed in the range of higher frequencies. In addition, the normalized effective wave velocity cL in the composite can be bigger than that in the homogeneous matrix material, for instance for the considered inclusions of aligned mass and 1 .