| Popis: |
A formal method that is essentially an extension to viscoelasticity of the Karal‐Keller method for elastodynamics is presented for solving three‐dimensional wave‐propagation problems for a wide class of homogeneous, isotropic, and linear viscoelastic media. As applied to high‐frequency time‐harmonic waves, it consists of asymptotically representing the solutions in a series of inverse powers of the frequency. However, the expansion method is not necessarily limited to time‐harmonic waves. The approximation given by the first term in the expansion is called the geometrical theory of viscoelasticity. Subsequent terms provide corrections to this theory. The method can be employed to solve problems for media that contain boundaries. Applications are given to the reflection of incident waves from smooth obstacles and “asymptotic” reflection laws are derived. As an example, the first two terms are determined in the expansion of the reflected waves that result from a time‐harmonic plane dilatational wave striking a rigid plane. |
