We consider the propagation of acoustic waves in a medium with a periodic array of small inclusions of arbitrary shape. The inclusion size a is much smaller than the array period. We show that global gaps do not exist if a is small enough. The notion of local gaps which depends on the choice of the wave vector is introduced and studied. We determine analytically the location of local gaps for the Dirichlet and transmission problems.
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Godin et al. (2024) studied this question.
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