*MODAL DAMPING

Keyword type: step

This card is used within a step in which the *MODAL DYNAMIC or *STEADY STATE DYNAMICS procedure has been selected. There are two optional, mutually exclusive parameters: RAYLEIGH and MODAL=DIRECT (default).

If MODAL=DIRECT is selected the user can specify the viscous damping factor
**\zeta** for each mode separately. This is the default. Direct damping is not
allowed in combination with nonzero single point constraints.

If RAYLEIGH is selected Rayleigh damping is applied in a
global way, i.e. the damping matrix
**\left [ C \right ]** is taken to be a linear combination of the
stiffness matrix
**\left [ K \right ]** and the mass matrix
**\left [ M \right ]**:

\left [ C \right ] = \alpha \left [ M \right ]+ \beta \left [ K \right ]. | (810) |

The coefficients apply to all modes. The corresponding viscous damping factor
**\zeta_j** for mode j amounts to:

\zeta_j=\frac{\alpha}{2 \omega_j}+ \frac{\beta \omega_j}{2}. | (811) |

Consequently, **\alpha** damps the low frequencies, **\beta** damps the high
frequencies.

The *MODAL DAMPING keyword can be used in any step to redefine damping values defined in a previous step.

First line:

- *MODAL DAMPING,RAYLEIGH
- Enter any needed parameters and their values.

Second line if MODAL=DIRECT is selected (or, since this is default, if no additional parameter is entered):

- lowest mode of the range
- highest mode of the range (default is lowest mode of the range)
- viscous damping factor
**\zeta**for modes between (and including) the lowest and highest mode of the range

Second line if RAYLEIGH is selected:

- not used (kept for compatibility reasons with ABAQUS)
- not used (kept for compatibility reasons with ABAQUS)
- Coefficient of the mass matrix
**\alpha**. - Coefficient of the stiffness matrix
**\beta**.

Example: *MODAL DAMPING,RAYLEIGH ,,0.,2.e-4

indicates that the damping matrix is obtained by multiplying the stiffness matrix with
**2 \cdot 10^{-4}**

Example files: beamdy3, beamdy4, beamdy5, beamdy6.