PARAM, W3

Bulk Data Entry Converts structural damping to equivalent viscous damping for transient analysis.

Parameter	Values	Description
`W3`	<Real> Default = 0.0 Used in transient analyses to convert structural damping to equivalent viscous damping.	The damping matrix $[B]$ for transient analysis is assembled from: (1) $[B] = [B^{1}] + \frac{Γ}{Ω_{3}} [K] + \frac{1}{Ω_{4}} \sum Γ_{E} [K_{E}]$ Where, $[B^{1}]$ Contribution from damping elements (CDAMP#, CVSIC) and B2GG. $Γ$ Overall structural damping coefficient (PARAM, G). $Ω_{3}$ Frequency of interest in radians per unit time (PARAM, `W3`) for the conversion of overall structural damping into equivalent viscous damping. $[K]$ Global stiffness matrix. $Γ_{E}$ Element structural damping coefficient (`GE` on the MAT# entry). $Ω_{4}$ Frequency of interest in radians per unit time (PARAM, W4) for the conversion of element structural damping into equivalent viscous damping. $[K_{E}]$ Element stiffness matrix.

Parameter

Values

Description

W3

<Real>

Default = 0.0

Used in transient analyses to convert structural damping to equivalent viscous damping.

The damping matrix

[B]

for transient analysis is assembled from:

(1)

[B] = [B^{1}] + \frac{Γ}{Ω_{3}} [K] + \frac{1}{Ω_{4}} \sum Γ_{E} [K_{E}]

Where,

$[B^{1}]$: Contribution from damping elements (CDAMP#, CVSIC) and B2GG.
$Γ$: Overall structural damping coefficient (PARAM, G).
$Ω_{3}$: Frequency of interest in radians per unit time (PARAM, W3) for the conversion of overall structural damping into equivalent viscous damping.
$[K]$: Global stiffness matrix.
$Γ_{E}$: Element structural damping coefficient (GE on the MAT# entry).
$Ω_{4}$: Frequency of interest in radians per unit time (PARAM, W4) for the conversion of element structural damping into equivalent viscous damping.
$[K_{E}]$: Element stiffness matrix.

Comments

This parameter can be specified in the Bulk Data section and/or Subcase section. If it is defined in the Subcase section, then it is subcase-specific and this value is only used for this subcase. This is done by defining PARAM, W3, <Real> for each subcase in the Subcase Information section.
PARAM, W3 is supported with direct transient, modal transient and nonlinear transient analysis types.
The order of priority is TSTEP or RSPINR/RSPINT entry, Subcase specific PARAM, followed by Bulk Data PARAM.