# José Abell's research blog

## Talk Given at IngeoKring 2016 - Physics-Based Earthquake-Soil-Structure Interaction for Near-Field Induced Seismicity

This is a talk given at the IngeoKring 2016 Autumn symposium, hosted at TU Delft.

## Simulation of a surface wave (Rayleigh)

This simulation, done in the UCD ESSI simulator and visualized in VisIt using VisIt-ESSI plugin, shows the passage of a surface wave (Rayleigh wave). The simulation consists on a surface impact on an elastic domain of 900m by 1800m depth, and a shear wave velocity of 1000km/s. Elliptical-retrograde motion can be seen as an illustration of Rayleigh waves.

VisIt can be obtained here, and the plugin here.

## Visualizing ESSI output with VisIt-ESSI

VisIt-ESSI is a plugin for the VisIt post-processor created my CompGeoMech. It allows for remote (soon parallel also) visualization of outputs produced by ESSI in the HDF5 format (*.h5.feioutput).

VisIt can be obtained here, and the plugin here.

## NTS-02. On Rayleigh damping coefficients for FE analysis

Note to self. How to compute Rayleigh damping coefficients for given damping ratios $\xi_1$ and $\xi_2$ at frequencies $f_1$ and $f_2$.

This is textbook content, I just need to remind myself too often how this is done and end up re-deriving the equations.

Given the second-order system of differential equations representing the FE model

$$M \ddot{u} + C \dot{u} + K u = F(t)$$

The damping matrix $C$ can be written as a Rayleigh damping matrix:

$$C = a_0 M + a_1 K$$

$a_0$ and $a_1$ are Rayleigh damping coefficients found by solving

$$\left[ \begin{array}{cc} \dfrac{1}{2\pi f_1} & 2 \pi f_1 \ \dfrac{1}{2\pi f_2} & 2 \pi f_2 \end{array} \right] \left[ \begin{array}{c} a_0 \ a_1 \end{array} \right] = \left[ \begin{array}{c} \xi_1 \ \xi_2 \end{array} \right]$$

Which I do in the following code:

## SNE # 01. Example of ESSI simulation and visualization with visitESSI

These are the results of a simple elastic-domain simulation. Mesh consists of

• 154523 Nodes (46359 DOFs)
• 1250 27 node bricks (LT formulation)
• 1200 time-steps (dt = 0.01s)

Results were stored in the new format of output for ESSI simulator and visualized in VisIt post-processor where the movie was created.