Based on complex variable theory, this study investigates the scattering of SH-waves by a circular inclusion in exponentially inhomogeneous media with nanoscale-dependent density and modulus. First, to solve the scattering problem governed by the variable-coefficient Helmholtz equation for a circular inclusion, a conformal mapping method is introduced, transforming the original problem into a standard Helmholtz equation with a circular inclusion. Assuming the medium density varies exponentially along the horizontal direction while the elastic modulus remains constant, explicit analytical expressions are derived for the incident wavefield, scattered wavefield, refracted wavefield within the inclusion, and stress distributions under macroscopic conditions. Second, a generalized boundary condition incorporating nanoscale effects is established using surface elasticity theory. By constructing infinite series equations and leveraging the orthogonality of trigonometric basis functions, numerical solutions for the stress field are rigorously obtained through a truncated series approach. Analysis of the dynamic stress field distribution around the inclusion reveals: 1) Surface elasticity effects significantly alter the stress distribution pattern at the inclusion boundary; 2) The incident wavenumber and inhomogeneity parameter jointly govern the multiscale diffraction characteristics of stress waves.
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