# /DAMP

Engine Keyword Used to modify the Rayleigh mass and stiffness damping coefficients defined using the Starter /DAMP option.

## Format 1 (Short Format)

/DAMP/`damp_ID`

$\alpha $ $\beta $

## Format 2 (Full Format)

/DAMP/`damp_ID`

$\begin{array}{l}{\alpha}_{x}\text{}{\beta}_{x}\\ {\alpha}_{y}\text{}{\beta}_{y}\\ {\alpha}_{z}\text{}\beta z\\ {\alpha}_{xx}\text{}{\beta}_{xx}\\ {\alpha}_{yy}\text{}{\beta}_{yy}\\ {\alpha}_{zz}\text{}{\beta}_{zz}\end{array}$

## Definition

Field | Contents | SI Unit Example |
---|---|---|

damp_ID |
Identifier of damping option in Radioss Starter (/DAMP). | |

$\alpha $ | Mass damping coefficient used for all DOF. | $\left[\frac{\text{1}}{\text{s}}\right]$ |

$\beta $ | Stiffness damping coefficient used for all DOF. | $\left[\text{s}\right]$ |

${\alpha}_{x}$ | Mass damping coefficient for translational degree of freedom (DOF) in x direction. | $\left[\frac{\text{1}}{\text{s}}\right]$ |

${\alpha}_{y}$ | Mass damping coefficient for translational DOF in y direction. | $\left[\frac{\text{1}}{\text{s}}\right]$ |

${\alpha}_{z}$ | Mass damping coefficient for translational DOF in z direction. | $\left[\frac{\text{1}}{\text{s}}\right]$ |

${\alpha}_{xx}$ | Mass damping coefficient for rotational DOF in xx direction. | $\left[\frac{\text{1}}{\text{s}}\right]$ |

${\alpha}_{yy}$ | Mass damping coefficient for rotational DOF in yy direction. | $\left[\frac{\text{1}}{\text{s}}\right]$ |

${\alpha}_{zz}$ | Mass damping coefficient for rotational DOF in zz direction. | $\left[\frac{\text{1}}{\text{s}}\right]$ |

${\beta}_{x}$ | Stiffness damping coefficient for translational DOF in x direction. | $\left[\text{s}\right]$ |

${\beta}_{y}$ | Stiffness damping coefficient for translational DOF in y direction. | $\left[\text{s}\right]$ |

${\beta}_{z}$ | Stiffness damping coefficient for translational DOF in z direction. | $\left[\text{s}\right]$ |

${\beta}_{xx}$ | Stiffness damping coefficient for rotational DOF in xx direction. | $\left[\text{s}\right]$ |

${\beta}_{yy}$ | Stiffness damping coefficient for rotational DOF in yy direction. | $\left[\text{s}\right]$ |

${\beta}_{zz}$ | Stiffness damping coefficient for rotational DOF in zz direction. | $\left[\text{s}\right]$ |

## Comments

- Rayleigh $\alpha $
damping
computation:$$C=\alpha M+\beta K$$$${C}_{i}=\alpha {m}_{i}+\beta {k}_{i}$$$${\text{C}}_{\text{crit}}=\sqrt{4{\text{m}}_{\text{i}}{\text{k}}_{\text{i}}}$$$$\frac{{\text{C}}_{\text{i}}}{{\text{C}}_{\text{crit}}}=\frac{\alpha}{2{\omega}_{\text{i}}}+\frac{{\beta \omega}_{\text{i}}}{2}$$Where,
- $C$
- Damping matrix
- $M$
- Mass matrix
- $K$
- Stiffness matrix
- $\alpha $ and $\beta $
- Coefficients
- ${C}_{i}$
- Nodal damping matrix
- ${m}_{i}$
- Nodal mass matrix
- ${k}_{i}$
- Nodal stiffness matrix
- ${C}_{crit}$
- Critical damping

- This option can be used only if damping card (/DAMP) is defined in the Runname_0000.rad file.
- Arbitrary coefficients alpha and beta may be declared in the Runname_0000.rad file and modified when repeating the option in the Radioss Engine file Runname_run#.rad.