Scattering of harmonic P-wave and dynamic stress concentration by a nanosized elliptical hole with surface effect

This paper studies the scattering and dynamic stress concentration around an elliptical hole with a surface effect embedded in an infinite elastic medium under a far-field incident plane harmonic P-wave. We obtain the series solutions for the scattered wave functions by employing the Mathieu functions in the corresponding elliptical coordinate system. We discuss the dynamic stress concentration around the elliptical hole relative to the wave frequency and few surface parameters in some numerical examples. It is observed that a negative surface modulus amplifies dynamic stress concentration, whereas a positive surface modulus attenuates it. The surface mass density exhibits negligible influence at low frequencies but significantly increases the amplitude of dynamic stress at high frequencies.