PARAM, W4

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

Parameter	Values	Description
`W4`	<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: $[B] = [B^{1}] + \frac{Γ}{Ω_{3}} [K] + \frac{1}{Ω_{4}} \sum Γ_{E} [K_{E}]$ 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

W4

<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:

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

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.
PARAM, W4 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.