ACS SASSI Documentation

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====== HVD Element ======

===== HVD Coefficient Equations =====

\\
$$ C_{ne(\omega)} = K_n*\frac{(\frac{\omega}{\omega_n})^2}{1+(\frac{\omega}{\omega_n})^2}
\qquad C_{nv(\omega)} = K_n*\frac{\frac{\omega}{\omega_n}}{1+(\frac{\omega}{\omega_n})^2} $$
\\
$$ \omega_n = K_n/B_n \qquad n = \text{v or h} $$

===== HVD Matrix Pattern =====
\\ 
$$ \begin{bmatrix} 
&C_h &0 &0 &0 &0 &0 &-C_h &0 &0 &0 &0 &0 \\
& &C_h &0 &0 &0 &0 &0 &-C_h &0 &0 &0 &0 \\
& & &C_v &0 &0 &0 &0 &0 &-C_v &0 &0 &0 \\
& & & &0 &0 &0 &0 &0 &0 &0 &0 &0 \\
& & & & &0 &0 &0 &0 &0 &0 &0 &0 \\
& & & & & &0 &0 &0 &0 &0 &0 &0 \\
& & & & & & &C_h &0 &0 &0 &0 &0 \\
& & & & & & & &C_h &0 &0 &0 &0 \\
& & & & & & & & &C_v &0 &0 &0 \\
& & & & & & & & & &0 &0 &0 \\
& & & & & & & & & & &0 &0 \\
& & & & & & & & & & & &0 \\
\end{bmatrix} $$
The elastic (real) and viscous (imaginary) parts of the HVD element share the same pattern matrix.

ACS SASSI Documentation

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