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--- com:hvdequations [2019/04/25 12:50]
phil created
+++ com:hvdequations [2019/04/25 16:16] (current)
phil [HVD Coefficient Equations]
@@ Line 1: / Line 1: @@
-====== HVD Matrix Coefficient Equations ======
+====== HVD Element Information ======
+===== 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.
-\(alpha)

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