this is for holding javascript data
Pol Grasland-Mongrain edited The_absorption_of_the_laser__.tex
over 8 years ago
Commit id: 06235774293cfb7307114d5675325110fc6ee06d
deletions | additions
diff --git a/The_absorption_of_the_laser__.tex b/The_absorption_of_the_laser__.tex
index 4442281..d8fe334 100644
--- a/The_absorption_of_the_laser__.tex
+++ b/The_absorption_of_the_laser__.tex
...
To verify this physical model, a numerical calculation was performed. The thermal dilatation was modeled as two opposite forces directed along Y direction with a depth of 50 $\mu$m and decreasing linearly from 2.5 to 0 mm (respectively -2.5 to 0 mm), to simulate an approximate Gaussian shape \cite{Davies_1993}. Propagation as a shear wave along Z axis was calculated using Green operators $G_{yz}$ as calculated by Aki Richards \cite{aki1980quantitative}:
\begin{equation}
G_{yz} (r,\theta,z)= \frac{\cos \beta \sin \theta}{4\pi \rho c_p^2 r} \delta_P + \frac{-\sin \theta \cos \theta}{4\pi \rho c_s^2 r} \delta_S + \frac{3\cos \theta \sin
\beta}{4\pi \theta}{4\pi \rho r^3} \int_{r/c_p}^{r/c_s}{\tau \delta_{NF}}
\label{eq:Gyz}
\end{equation}
where $\theta$ is the angle between the applied force and the considered point (r,$\theta$,z), $c_p$ and $c_s$ the compression and shear wave speed respectively, $\delta_S$ and $\delta_P$ Dirac distribution indicating the position of the compression and shear waves along space and time, $\tau$ the time and $\delta_{NF}$ representing near-field effects. The three terms correspond respectively to the far-field compression wave, the far-field shear wave and the near-field component.