this is for holding javascript data
Pol Grasland-Mongrain edited Simu disp maps.tex
over 8 years ago
Commit id: fdc6247232610e3959a5ab5fc02d2ba1c70914dc
deletions | additions
diff --git a/Simu disp maps.tex b/Simu disp maps.tex
index def3048..7c8b789 100644
--- a/Simu disp maps.tex
+++ b/Simu disp maps.tex
...
This physical phenomenon was then modeled numerically. The vaporization was modeled as a point force directed along Z direction with a depth of 50 $\mu$m and increasing linearly from -2.5 to 0 mm and decreasing symmetrically from 0 to 2.5 mm, to simulate an approximate Gaussian shape. Propagation as a shear wave was calculated using Green operator as calculated by Aki Richards \cite{aki1980quantitative}:
\begin{equation}
u_z =
\frac{1}{4\pi \frac{\cos^2 \beta}{4\pi \rho c_p^2 r}
\cos^2 \beta . \delta_P +
\frac{1}{4\pi \frac{\sin^2 \beta}{4\pi \rho c_s^2 r}
\sin^2 \beta . \delta_S +
\frac{1}{4\pi \frac{3\cos^2 \beta-1}{4\pi \rho r^3}
(3\cos(\beta)^2-1) \tau
. Rect.
\label{eq:akirichards}
\end{equation}
It used a medium density $\rho$ of 1000 kg.m$^{-3}$, a compression wave speed of 1500 m.s$^{-1}$ and a shear wave speed of 5.75 m.s$^{-1}$. Results are shown on Figure \ref{Figure3} which represents displacement maps along Y and Z axis 0.8, 1.6, 2.4, 3.2 and 4.0 ms after force application. The displacement maps present many similarities with the experimental results of the Figure \ref{Figure2}.