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https://doi.org/10.1080/17455030.2018.1430407

has been cited by the following article:

• TITLE: The Scattering of SH Wave in a Nano Hole Embedded the Infinite Inhomogeneous Medium

  AUTHORS: Yongqiang Sun, Tong Shang

  KEYWORDS: Conformal Mapping Method, Power-Law Variation Inhomogeneous Medium, Helmholtz Equation with Variable Coefficient, Dynamic Stress Concentration Factor, Nano-Sized Cylindrical Cavity

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.12 No.12, December 28, 2022

  ABSTRACT: Scattering of the shear waves by a nano-sized cylindrical hole embedded the inhomogeneous is investigated in this study. The Helmholtz equation with a variable coefficient is transformed the standard Helmholtz equation by the complex function method and the conformal mapping method. By wave function expanding method, the analytical expressions of the displacement field and stress field in the inhomogeneous medium are obtained. Considering the surface effect and using the generalized Young-Laplace equation, we obtain the boundary conditions at nano arbitrary-shaped hole, then the field equations satisfying boundary conditions are attributed to solving a set of infinite algebraic equations. Numerical results show that when the radius of the cylindrical cavity shrinks to nanometers, surface energy becomes a dominant factor that affects the dynamic stress concentration factor (DSCF) around the cylindrical cavity. The influence the density variation of the inhomogeneity on the DSCF is discussed at the same time.