Abstract
This paper proposes a frequency-domain formulation of the bridging multiscale method specifically developed to study the interaction of elastic waves with heterogeneities and defects. The adopted approach utilizes a coarse-scale discretization that captures the global wave behavior, while a localized fine-scale mesh resolves the portion of the domain around the discontinuity. The occurrence of spurious waves at the interface is avoided by imposing proper dynamic compatibility conditions between the two domains. The formulation of such conditions is based on the two scale bridging. The frequency domain implementation of the bridging presented herein simplifies the dynamic compatibility operators between the discretizations which constitutes the major source of computational costs when implemented as part of commonly used time marching schemes. The potentials of the proposed technique are presented in the analysis of propagating elastic waves in several kinds of one- and two-dimensional structures with localized imperfections.
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