Low Frequency Band Gaps and Localised Modes for Arrays of Coated Inclusions
We study the scattering of plane elastic waves (pressure and shear) by a finite stack of gratings, infinite and periodic in the x-direction, of circular cylindrical elastic inclusions placed in an infinite elastic medium. The inclusions are connected to the surrounding medium via a thin soft elastic layer. The constitutive equations for the layer are derived using an asymptotic technique . The problem is then solved using the method of multipole expansions. Results show regular arrays of cylinders which act as elastic polarisers (i.e. they reflect one type of wave and transmit the other) and elastic filters, structures that do not transmit elastic waves. We also demonstrate that an elastic inclusion surrounded by a thin soft “coating” layer is responsible for creating localised modes in the low frequency range.
KeywordsLocalise Mode Multipole Expansion Phononic Crystal Elastic Inclusion Shear Problem
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