 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2005/iii/paper-82/2/solution

Take a stable isotropic elastic material with mass density

ρ > 0

λ, μ

, where

μ > 0

and

3 λ + 2 μ > 0

c_{ij pq} = λ δ_{ij} δ_{pq} + μ (δ_{i p} δ_{j q} + δ_{i q} δ_{j p}), α^{2} = \frac{λ + 2 μ}{ρ}, β^{2} = \frac{μ}{ρ} .

The P wave is longitudinal and the S wave transverse. The wavefront-transport alternative and all three steps of the Love wave alternative are given below.

 New to topics? Read the docs here!