Dynamic Analysis Of Elastic Waves In A Elliptic Cavity In An Inhomogeneous Medium With Two-Dimensional Density Variation

This paper presents an analytical solution of SH waves scattering by an elliptic cavity which is modelled in an inhomogeneous unbounded space. The density of wave propagation medium changes in two dimensions. Based on complex function method, the form of two-dimensional density variation is studied. By extending the analytical solution of the dynamic stress concentration problem of elliptic holes in inhomogeneous media with one-dimensional density variation, a new form of density variation is found, and two conformal mapping methods are used to transform the variable coefficient Helmholtz equation into the standard Helmholtz equation to solve the new elliptic hole scattering problem. Through numerical examples, distribution of dynamic stress at the elliptic cavity's boundary is discussed. Wave number, inhomogeneous parameter and cavity's shape parameter have significant influence on dynamic stress concentration.