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.