/DAMP

Block Format Keyword This keyword can be used to define the Rayleigh mass and stiffness damping coefficients applied to a set of nodes. The damping can be applied to any nodal DOF either in local or global coordinate system.

Format 1 (short format)


(1)	(3)	(5)	(6)	(7)	(9)
/DAMP/`damp_ID`
`damp_title`
$α$	$β$	`grnd_ID`	`skew_ID`	`T`_start	`T`_stop

Format 2 (full format)


(1)	(3)	(5)	(6)	(7)	(9)
/DAMP/`damp_ID`
`damp_title`
$α$ _x	$β$ _x	`grnd_ID`	`Skew_ID`	`T`_start	`T`_stop
$α$ _y	$β$ _y
$α$ _z	$β$ _z
$α$ _xx	$β$ _xx
$α$ _yy	$β$ _yy
$α$ _zz	$β$ _zz

Definition


Field	Contents	SI Unit Example
`damp_ID`	Damping identifier. (Integer, maximum 10 digits)
`damp_title`	Damping title. (Character, maximum 100 characters)
$α$	Mass damping coefficient used for all DOF. 5 (Real)	$[\frac{1}{s}]$
$β$	Stiffness damping coefficient used for all DOF. 5 (Real)	$[s]$
`grnd_ID`	Node group identifier. (Integer)
`Skew_ID`	Skew identifier. (Integer)
`T`_start	Start time. (Real)	$[s]$
`T`_stop	Stop time. Default = 10³⁰ (Real)	$[s]$
$α$ _x	Mass damping coefficient for translational degree of freedom (DOF) in x direction. 6 (Real)	$[\frac{1}{s}]$
$α$ _y	Mass damping coefficient for translational DOF in y direction. 6 (Real)	$[\frac{1}{s}]$
$α$ _z	Mass damping coefficient for translational DOF in z direction. 6 (Real)	$[\frac{1}{s}]$
$α$ _xx	Mass damping coefficient for rotational DOF in xx direction. 6 (Real)	$[\frac{1}{s}]$
$α$ _yy	Mass damping coefficient for rotational DOF in yy direction. 6 (Real)	$[\frac{1}{s}]$
$α$ _zz	Mass damping coefficient for rotational DOF in zz direction. 6 (Real)	$[\frac{1}{s}]$
$β$ _x	Stiffness damping coefficient for translational DOF in x direction. 6 (Real)	$[s]$
$β$ _y	Stiffness damping coefficient for translational DOF in y direction. 6 (Real)	$[s]$
$β$ _z	Stiffness damping coefficient for translational DOF in z direction. 6 (Real)	$[s]$
$β$ _xx	Stiffness damping coefficient for rotational DOF in xx direction. 6 (Real)	$[s]$
$β$ _yy	Stiffness damping coefficient for rotational DOF in yy direction. 6 (Real)	$[s]$
$β$ _zz	Stiffness damping coefficient for rotational DOF in `zz` direction. 6 (Real)	$[s]$

Comments

Rayleigh damping computation is:
$C = α M + β K$
$C_{i} = α m_{i} + β k_{i}$
$C_{c r i t} = \sqrt{4 m_{i} k_{i}}$
Where,

$C$

Viscosity matrix

$M$

Mass matrix

$K$

Stiffness matrix

$α$ and $β$

Coefficients

$C_{i}$

Nodal viscosity

$m_{i}$

Nodal mass

$k_{i}$

Nodal stiffness

$C_{c r i t}$

Critical damping
The damping is applied to the nodes belonging to a node group (grnd_ID).
The specification of grnd_ID is compulsory.
It is possible to define multiple /DAMP keywords in the same input file.
If there are several /DAMP keywords, each applied to different node groups, then these node groups should not have common nodes.
Two formats of this keyword are available. In the Format 1 (short format), only three lines are prescribed. In this case $α$ _x, $α$ _y, $α$ _z, $α$ _xx, $α$ _yy, $α$ _zz, $β$ _y, $β$ _z, $β$ _xx, $β$ _yy and $β$ _zz are not provided, and the values of $α$ and $β$ are used as damping coefficients for all degrees of freedom (DOFs). In the Format 2 (full format), six lines are provided and all damping coefficients should be prescribed directly.
The coefficients in Format 2 are used to define non-isotropic damping, when the full keyword format is used, in a global reference system or in a local one if skew_ID is specified.
Stiffness damping is a unit of time and for any DOF cannot be greater than the current time step. If stiffness damping becomes greater than the current time step, the time step value is used as the stiffness damping, instead.
The damping parameters can be modified with the Engine option /DAMP. In this case the values of $α$ and $β$ will substitute the corresponding values of $α$ _x, $α$ _y, $α$ _z, $α$ _xx, $α$ _yy, $α$ _zz, $β$ _y, $β$ _z, $β$ _xx, $β$ _yy and $β$ _zz are not provided, and the values of $α$ and $β$ .