Nonlocal micropolar elastic Rayleigh waves

Abstract

The problem of Rayleigh waves propagating in nonlocal micropolar isotropic elastic half-spaces modeled by Eringen’s (integral) nonlocal micropolar elasticity theory has been investigated (Ultrasonics 73 (2017) 162–168). However, since the authors employed the non-equivalent differential nonlocal model and the Eringen method which does not satisfy the original equations of motion, the obtained solution is incorrect. In this paper, we reconsider this problem. The problem is reformulated based on the equivalent differential nonlocal micropolar elasticity model and its solution is found by a novel method introduced recently (Proc. R. Soc. A 480 (2293) 20230814, 2024) which satisfies the original equations of motion. The solution of the Rayleigh wave problem has been obtained including explicit expressions of displacements, microrotation, nonlocal stresses and couple stresses along with explicit dispersion equation. The paper also provides a well-posedness criterion of Eringen’s nonlocal micropolar elasticity theory for harmonic plane wave problems. From the well-posedness criterion, it implies that it is impossible for a Rayleigh wave to propagate in nonlocal micropolar elastic half-spaces characterized by the kernel $K_0$ (the modified cylindrical Bessel function of the second kind of order zero).